1. ii; 1.11.. L..:... .1..- 1. . .11. .. I. . .5 I . .. 11.1Hdnu.u.n1.nni.su Ii... .11. .11.) an}; finial, . .111 .. . . .t 17"..‘3mlntrn..t‘.‘.ll,.\l.brh.v.CIv \1 I: . 1., J.‘ ..W).Ns-HU1..C\\. o; THVHI 111...). r . «5‘...» 1.1.1“... . ..3\.11.. “0.6.3 .. . 1,1. cw . .v .. .\ ~ .. . . 2.1.15.0.“ ._ O A In, Vol.0- 1 tvn'lhvuyrfituvmffllffir .1; .H)..(1...v1"lfvli I.O!P. I . . . . rl f; 1.. I :1. 3.0. 11 £5 2E 5 1 r 1 43. 3 . 4 . . 4C. .1 1 ! I I I I i f '1 o. , l . .g. 31‘ .fi . a; J: .L‘ .0.- i P . 021% v 1 ply- - .lh I: -r l .41...1 .1171. . .LQVI...1.}.'1 1 . (I 1 . 1 1!. I P»)! 1. Ar .11.! a... think» u. .. . .1... Utrgnwflflrol 2;!” (I’Jt . ..\\rv . ,.Or¢!’r£)¢‘ It..." I...‘.' O 11" fie I (I. - Egg "Dfl’f. ".‘V' n 1‘ .0!- .r . .1. 1'1th01330.’ .I’o 5‘ . '0: .f’h. . .slurl 3.3;.v.) catgknhl In I33! 1 1. .1. .1 - 2v. » 1%: II o. I - 1 5.1.41N11L ungrllté. 1111 1 r. 111.11.111.13 911311.151)“; . \.u..' 1 . .J ...D111Va’l!ar.ll .t‘. o flux. G: :11.-. .. .. 1.. 3.1%.11 1.. run 1.»)..11. _ . . . . . . . .1".1|[..I‘~1\FQ( 1 ”tin“: 11.“.‘l‘nsn'... Y... ....I1 ...11.111 11..&fit>....:...4 1, 1. 5.1..- -1... {Elli}? ruti‘é’v . .. nhgflnf a»... [$390.13. “\Jl 0' A“ ‘7 . ml . 1 . . 7w! . £1.11“... 1110.1 1 0. j I; but!” v‘\c‘.-|¢‘ 2 {1191111. .15.??? . . .I; . 15.1.1.5 111; {.1 .11 :1 .9511. . 1.. . '3 z 1. 1.... h. . . b} .0 C. “filéfiq v 11111.. 241. . .1ufglr’ur‘l . 15.211. 1.11... g... .21 . ll . . . 81' l .. 1 1 V11. 11......211 , .. 2.1.1.5113! . . . .1... . 11.1 . . . 35.1.1552. . - D'V. "nwllislyi‘.’ 0.1}! 1.... . .wf.1.1.51.$5:xo11 r4 .1, flaw. 61......1. 111.31. .. . u . 1.3.1.1». .1. . .. . 1.? up, 1.. v. 01"." .0059 1'): . pl 1" (d! 21. 11. .1 . 1.1.53 0’ V‘ b. ’6 n .1 . 11!}... 3‘. I2. . ., . .1. It? v'?$g 9.}! I. 1.. ,- -135 s. L. . . . s.....:.d:..u .n: §11.-.9«1¥). .. 1.15.... .. . . . 12.1.1.1. H1131. . 1p ._ .11....11h7... xv . , . whispfinwwrh. 11-1%...5...1n r319...» 1:3.UWn1hoowm. d . . 1.9 7 11.111.12.10. 1 . 1...»... .n ’I 13...} . | . .. o .. .1 1'1... . .J (in... $9.)!!! . . 1 uvsgv1131. I; {EEK-n . .. . .. 41111012’4. (0:! .1%§ 1“ 4. .. v . eD-ngibfll‘ 3.11.}:- H. u . 1 _ l ‘l'i 99..- lggil' ‘ I; . 1'15". . "I 10.9.)? tin-91.! "I .9 . . . .I. .0: l3!!!)3tr 1 iii: ..| . VIA 0| .. IV 3’ l r; ’l-I. . '5’... 1.111.». - 1 r .I‘. .3 LI! 110).. 41.11"” . b .11 .OVAI . Ip'p), {\Aavabz‘i’ I. (3.1... 1 D1 1. II '1. .V‘. Ii... 15!} vu) 5'91} ‘| .11 5.1.1-. s \I. 5.5.1.). {sizin‘llidu‘hvfi b... .15.?L. . 1. $1....)I»!..l.u....\’ :1- g .11 . .Fl . . I II: )‘a‘lvklvblzohll 1.01. 1.\I.1P... I:;.l‘tob..r:."nur! t... l I i \ - C‘fit-VI r' . ‘ c 4 s1. 1 u .hyllx . 1’)? 1. . . :11 J. {.11 .1 t... .l . 1.1 .. . .1, , 4h“..: I . IA-Iipl .15p116 [.21).]? . .1 r0 . 1‘“ Aflqizviool. .0 . . .. L {(1.1}. 111111. :11? .. .1. I 5"- .\. r .. .2- . 7 D 1 . . v v I . ‘ 4.1,‘Qt‘t‘ A 1-. Ix I . .13.? ..1. 111111". 1.51.. .IWJHU... 1 ....1..11.1.11 .x.t.v.i.:-..l.4..h.mn.1..u.nk.w _ , _ . .. .1111 :c 1 O. ...n .' . f. .. 91111 H11 (.1 1.. 11......» 11 kvr! ..u6.U.....11.\1L. 11.11} 111.1 1 1.11. . u 1.1.01. . .11 1101431,. 2‘: lOV 1.10:1! .L 1.... .L. 55 v... 1.11. . 3151.. L11 . 1-. 1.1 . .r . . . 1 . .1 v ‘ I-.. l I 1 1%.:1 [1141])... ‘10..“ . 1.5““ .11... 1! 1n: 11111.4(!“ 1.1 1... 9.49% 193v... L. 1| I.“ . ‘ t1. 1 i 1“. £svksf ¢ takes, fewer delays, snags; ——>Productivity quality better use of machine-time improves and materials Capture the ——-> market with ——’ Stay in —’ Provide more better quality business jobs and lower price Unfortunately, much of American management believes that if more steps are taken to improve quality, productivity will suffer. 1.2.2 W The new philosophy requires American industry to change its perspective from short term gains to long range goals. Cunently, American 8 management works with daily production reports, quarterly dividends, quarterly budgets, monthly goals and production targets. This short term emphasis is reinforced by the fact that American corporate managers typically change jobs every two to three years [4]. According to Deming, the primary purpose of a company is to stay in business and provide jobs, not to make money. Profits, he claims, will come as a by-product of an organization with this philosophy. Deming advises management to create constancy of purpose through innovation and continual research, education and improvement of product design [2,5]. This is a difficult proposition to accept if success is measured by dividends and short term profits. According to Deming [2], "Dividends and paper profits, the yardstick by which managers of money and heads of companies are judged, make no contribution to material living for people anywhere, nor do they improve the competitive position of a company or of American industry. " In the short term, improving quality may increase costs. This includes employee training and education in statistical methods and the use of manpower, materials, production time and machinery to identify, correct and improve quality. In addition, the corporation may have to hire a quality professional to lead the quality improvement program. However, these short term or fixed costs are justified due to the increase in profits that result in the long run, according to the Deming chain reaction. Each time the organization invests a fixed amount of money and time into eliminating a long term quality problem, the cost savings are realized for every year that quality problem does not exist. Specifically, the intangible cost of lost sales to superior quality competitors is avoided by providing continuous quality improvement. ' Many managers want to know the elapsed time before their company will be able to regain its market position after implementing a quality improvement program. It took Japan only four years to invade world markets after starting its quality revolution [2]. Deming estimates that it will take America 30 years to accomplish what the Japanese have done to improve quality because "a big ship, traveling at full speed, requires distance and time to turn" [1 1]. Within an organization, it will take several years for the workers to understand their roles within the framework of Deming's management method [2]. Just getting management and the workers to understand quality and dispel the current erroneous methods of quality control will take a year. In the early stages of implementation of Deming's statistical and management methods, the gains are not measurable. It is impossible to quantify in dollars the positive change in quality awareness, teamwork, recognition of quality problem areas, analysis, and better understanding of processes and improved reputation that results from practicing the methods. 1.2.3 Won In order to achieve higher quality at a lower cost, the quality program must practice defect prevention instead of the traditional post-production inspection type quality control program which merely removes defective products from the production line after they occur. Deming asserts that only when quality is constantly improved does productivity constantly increase and costs decrease [2,5]. It is more expensive to correct defects on finished products than it is to take action to prevent the defects and improve quality 10 in the first place. Philip Crosby's "do it right the first time" standard is important in preventing defects [8]. Crosby has concluded that the secret of prevention is to analyze each stage of the process and identify opportunities for error which can be controlled. Statistical Process Control (SPC) is the most popular and universal technique for the control of a process. SPC detects quality problems early in the production of the product using control charts to monitor the variation of product quality characteristics. The control chart signals when unnatural behavior in the process exists. Other statistical tools are used to analyze the system and aid in the correction or elimination of these unnatural problems until a stable production system results. Quality improvement is achieved by continually reducing the variation of each process and moving the process average toward a desired level. Deming states that with continual improvement, the distribution or variation of the chief quality characteristics of parts, materials and services become so narrow that the specifications are lost beyond the horizon [2]. 1.2.4 Deming's 14 Points for Management Deming's 14 points for management provide a basis for the transformation of American management to increase quality, productivity and competitive position. All 14 points are meant to be implemented simultaneously since only their synergistic effect will transform the organization. The following is a condensation of Deming's 14 points for management [4]: 11 MW Create constancy of purpose for the improvement of product and service. p—r Break down barriers between staff areas. Eliminate slogans, exhortations, and targets for the workforce. 11. Eliminate numerical quotas. 12 Remove barriers to pride of workmanship. 13. Institute a vigorous program of education and retraining. 14. Take action to accomplish the transformation. 2. Adopt the new philosophy. 3. Cease dependence on mass inspection. 4. End the practice of awarding business on price tag alone. 5. Improve constantly and forever the system of production and service. 6. Institute training and retraining. 7. Institute leadership. 8. Drive out fear. 9. 10. 1.3 mm Statistical methods aid in the presentation and interpretation of data for a better understanding of the process. Actions taken to prevent defects and improve processes are more effective and economical when statistical tools are utilized. The Deming method requires process improvement decisions and actions to be based on accurate and timely data. In most cases, SPC data is obtained by random sampling, since inspecting every single item in a manufacturing process is either too expensive, physically impossible, or very time consuming. A sample of products taken at random provides information about the larger population of manufactured products based on inference; the larger the sample size, the better the picture of the parent population. Depending on the costs of inspecting products after the process, testing equipment and labor for 12 testing, large samples can be expensive. There are seven basic statistical tools used in SPC: Pareto diagram Flow chart Cause and effect diagram Scatter diagram Run chart Frequency distribution Control chart .‘IP‘MPP‘NE‘ These seven statistical tools are the basic methods used to organize and graphically present data and are intended for use by all employees involved in process improvement. SPC follows a basic problem solving procedure which utilizes these seven tools for continuous process improvement. The systematic approach for process improvement is as follows: p 1. Identify the vital few quality problems. (Pareto Analysis) 2. Defrne the problematic process. (Flow Diagram) 3. Determine the problem causes. (Cause and Effect Diagram, Scatter Diagram) ‘—’ 4. Establish the sampling plan and collect data. 5. Analyze the data. (Frequency Histogram, Run Chart, Control Chart) ~<-'Hmr:":10 6.1— Pressure 6.0— 5.9-— 5.8— ] l I I I 200 240 280 320 360 Temperature Figure 5. Scatter diagram 19 13.5 W Once all of the important quality characteristics have been identified and data has been collected, several tools are used to analyze the quality data. The simplest, the frequency distribution, is a graphical tabulation of the data that relates size to frequency of occurrence. By comparing a frequency distribution composed of sample data measurements of a product to preset specification limits, a reliable prediction of product quality for the entire lot can be made without the need for 100% inspection. To construct a frequency distribution, the frequency of occurrence of each data value is first tabulated. A graph is then constructed in which the horizontal scale represents the data values and the vertical scale represents their frequency. The data is shown on the X-axis as points or ranges depending on whether the data is discrete or continuous. The most common application of this idea is the vertical bar chart shown in Figure 6 for continuous data, also called the frequency histogram [17]. 40— V 30 — Frequency 20 10— \Vu\ 4 8 12 16 20 Quality characteristic measurement Figure 6. Frequency histogram A frequency distribution is characterized by its shape. Most distributions 20 are "normal" in the sense that a line connecting the peaks of the bars in Figure 6 has the familiar bell shaped curve. The tendency for the data in a distribution to cluster near a central value and trail off at the upper and lower limits is called "central tendency". The most commonly used measure of central tendency in quality control is the arithmetic mean or average. The population average, represented by u, is unknown but the average derived from small samples lots drawn from the population denoted by X can be used as an estimate of u. The arithmetic mean or average of a set of N measurements X1,X2,X3,...,XN is [17]: N x=1 2 xi N i=1 A frequency distribution is also characterized by the dispersion of the individual data about the average. The most common measure of dispersion is the standard deviation. The standard deviation of the population is represented by the symbol a. As with the mean, an estimate of o is made from small sample lots and designated as s. The standard deviation of a set of N measurements X1,X2,X3,...,XN is [17]: N S = _1_ 2 (xi - X)?” N - 1 i=1 which can be interpreted as the average squared deviation from the mean. If the distribution is perfectly symmetrical about the mean and has a "bell shape", then some properties associated with it are [9,13,18]: 68.26% of the data fall within :t 1 o of the mean. 95.44% of the data fall within 1: 2 o of the mean. 99.73% of the data fall within 3; 3 c of the mean. 21 This information can be used to predict approximately how many individual data are likely to fall outside any given limit. For quality control purposes, if a product quality characteristic is normally distributed, an estimate of that percentage of the lot which conforms to specification can be made. Not all symmetrical distributions are normal however. They may be skewed in one direction or multi-modal (influenced by additional independent variables). Serious mistakes can be made when it is falsely assumed that the distribution of a quality characteristic is normal [18]. Incorrect process improvement decisions or actions may result from an analysis performed with abnormal data. The frequency distribution is a critical tool used in determining the capability of a process or machine. A process capability analysis involves finding the natural tolerances of a process or machine under normal operating conditions and comparing them to desired product upper and lower specification limits (USL and LSL respectively). The natural tolerance is customarily defined as 6 0 [6,13]. By comparing the natural tolerance to the specification range, an estimate as to whether the manufacturing process is capable of manufacturing the product to specification can be made. A process whose natural tolerance does not lie completely within engineering specification limits produces some nonconforming products. Only when the natural tolerance lies within the specification limits, can it be said that the process is capable. Specifically, the process capability index defined by [13]: Cp = W = ESL—LSL- Process Width 6 o is a measure of the degree to which a process is capable of performing the required function. The minimal acceptable CI) is usually taken to be 1.33, 22- assuming that the distribution for the variable being measured is at the target value [6]. The process capability analysis is not valid unless it has been determined with a control chart that the data is in control. 1.3.6 Burglar: A run chart is another tool used in SPC to analyze quality characteristic data. This chart is a simple graphical tool that displays trends in data over time. Product quality characteristic data is tracked on a run chart to reveal process behavior and valuable time sequence data pattern information which the frequency histogram lacks. The horizontal axis of the chart represents time in hours, days, weeks or months and the vertical axis represents the data characteristic under consideration as shown in Figure 7. The data characteristic can be either individual readings, average readings, the number defective, or the percent defective [4]. In many cases, data that is already available from inspection records or other time related records may be used to construct this chart. 5- Quality 4 — Characteristic 3.— 2.. 'MTWTFMTWTFMTWTF Weekl Week2 Week3 Figure 7. Run chart 23 "Run analysis" refers to an evaluation of charts based on the central line drawn horizontally through the computed average value of the data. The following conditions indicate that the process has shifted [9,18]: 1. For 11 successive points on the chart, at least 10 are on the same side of the central line. 2. For 14 successive points on the chart, at least 12 are on the same side of the central line. 3. For 17 successive points on the chart, at least 14 are on the same side of the central line. 4. For 20 successive points on the chart, at least 16 are on the same side of the central line. Shifts, gradual changes, and cyclical changes in reference to the central line also provide process information. Finally, by changing a variable suspect of causing variation and holding the other variables constant, the effect of a change in this variable on the process is evident from the run chart. Therefore, a run analysis provides useful information about the causes of a problem and the effect on the process from improvement activities [9,19]. 1.3.7 Control Chart The most important data analysis that can be performed in any SPC program is made with the control chart. This chart provides a graphic illustration of the variability of process data which is compared to derived control limits. These limits are utilized to detect negative trends in the process and to distinguish between common and special sources of variability. Valuable information as to when and where to exert pressure for quality improvement is presented on the control chart. In addition, Deming states that for analytical purposes, distributions and calculations of mean, mode, standard deviation, etc. serve no useful purpose for process 24 improvement unless the data were produced in a state of statistical control [4]. The easiest way to determine this is with a control chart. 1.3.7.1 W Variations in a manufacturing process caused by machines, materials, operators and production processes is inevitable. The control chart is a device which tests the stability of the variation pattern and was developed by Dr. Walter A. Shewhart in the 19205 [9,19]. It consists of data points plotted on a graph along with an established UCL (upper control limit) and LCL (lower control limit) as shown in Figure 8. Variation within the upper and lower control limits is attributed to common causes while variation beyond these limits is due to special causes. The American Society for Quality Control (ASQC) has defined the two different sources of variation as follows [9]: Chance (common) causes are factors, generally numerous and of relatively small importance individually, which contribute to variation, but which are not feasible to detect or identify, and Assignable (special) causes are factors which contribute to variation and which are feasible to detect and identify. Typically, 85% of all manufacturing problems are due to common causes that can only be corrected by management itself [9,16]. The remaining 15% are due to special causes that can be corrected by the manufacturing operator. When a process is operating within the control limits, the process is said to be in a state of statistical control [9,13] in which it is stable and predictable. Further improvement of the process can only take place through fundamental changes instituted by management. The control chart distinguishes between a stable system of chance causes and a special cause. By pointing out assignable causes of variation, the control chart offers important 25 opportunities to improve product uniformity effectively and efficiently. UCL Measurement, Centerline number defective, CtC. LCL Time Figure 8. Control chart schematic The control chart achieves its purpose when assignable causes are eliminated or reduced and only chance variation remains [13,18]. Any evidence of assignable variation proves that the process should be modified or changed. However, even when the process data has reached statistical control, quality improvement is still possible by shifting the process average closer to the target value but this requires a fundamental change. Once the change is implemented, a control chart with recalculated control limits is again needed to monitor the variation. Only process data found to lie within the control limits and follow a stable pattern on a control chart can be used to estimate process performance. A distribution which appears to conform to specification provides conclusions that are not only useless but misleading if the data is not from a stable system [2]. For this reason, a process capability analysis should only be made from data that has been found to be in statistical control with a control chart. Depending on what quality characteristic is under consideration, a control chart for either "variables" data or "attributes" data is used. Data that 26 classifies items into one of two classes, namely conforming or nonconforming, is termed attributes data. This includes criteria such as go/no go, good/no good and accept/reject. The p chart, np chart, 0 chart and 11 chart are all tools used to control attributes data. Data that is characterized by a measurement or an individual reading is termed variables data. This type of data is the preferred measure of product quality. Therefore, the control chart for variables is more commonly used because it provides more detailed information about the process. Variables control charts include the X chart to control the process average and the R chart to control the process variability or dispersion. The data for control charting must be obtained from a rational subgroup. The definition from the "Glossary and Tables for Statistical Quality Control" for a rational subgroup is [9] : "A subgroup, chosen for technical reasons, within which variations may be considered to be due only to nonassignable chance causes; between which there may be variations due to assignable causes whose presence is considered possible and important to detect." The items within the subgroup must be as homogeneous as possible. For example, items produced on the same machine by the same operator on a given day is most often the sensible choice, but not always [19]. 13.72 W The most frequently used control charts in statistical quality control are the X and R charts. The X chart is used to control the average value of the data and the R chart is used to control the variability of the data. Certain quality measurements should be charted only when the opportunity to save costs and improve quality outweighs the costs of taking the measurements [13]. They XI 1.4 1.2 1.0 0.8 0.6 25 20 15 10 27 I I I I T I I 1 2 3 4 5 6 7 Subgroup Number Figure 9a. X chart — UCL “I ................................. I I I I I I I 1 2 3 4 5 6 7 Subgroup Number Figure 9b. R chart 28 are more economical to use since smaller sample sizes of 4 or 5 are required [13,18]. Each chart is a graph with a horizontal axis representing the subgroup number and a vertical axis representing the subgroup average or range. Figures 9a and 9b illustrate an X and R control chart respectively. In constructing both the X and R control charts, usually 20 to 25 rational subgroups are taken and used to establish preliminary control limits for the process [9]. Generally the process average, 1.1, and the range, R, are unknown and are therefore estimated from sample data. The estimated process average or grand average, X, is calculated by averaging the subgroup averages. This process average is plotted as the center line on the graph of the X chart as is shown in Figure 9a. The UCL and LCL for this chart are computed as follows [9]: UCLX = X + k c IflJX = Y " k 0 where k is the number of standard deviations allowed from the process average. Normally k=3. The standard deviation used in the calculation of the X chart control limits is computed from the averages of the subgroups and not from the individual measurements. The distribution of the averages of the measurements is quite different from the distribution of the individual measurements. When the population standard deviation is available, the relationship between the two is [l 3 ,18,20]: «ii— 0 x = Population standard deviation of subgroup averages. c’ = Population standard deviation of individual measurements. 11 = Subgroup size. 29 A shortcut method is commonly used for the calculation of the population standard deviation because it is time consuming if done manually and many times the population standard deviation is unknown. An estimate of the standard deviation of subgroup averages (8) is made by assuming that the process distribution is normally distributed. This assumption is possible through the central limit theorem which states that when the sample size is large, the distribution of X is approximately normal with mean u and standard deviation chT, regardless of the shape of the universe distribution [17]. In a normal distribution, the range, which is the difference between the maximum and minimum values of a subgroup, and the standard deviation of a sample are related as follows [9]: 6 = _R_ (12 where d2 is obtained for various subgroup sizes 11 from a list of standard values. The estimate of the standard deviation is obtained by computing the average range, R, from all the subgroups and using this average range in the above formula. Since the “Ix = o’lfn' and 6 = R/d2, the 3 ox can be calculated by 3 0x = 3R/d2Jr'rf The control limits can be calculated as follows [1 8,20] : UCLX =X + 3 ox LCLx = 7 - 3 02 To further shorten the calculation of the X chart control limits from R, the equation 3 ex = 3R/d2fr'1' is simplified. The factor 3/d2,/E is actually a constant multiplier of R for each n. A table of computed values of 3/d2,/1T for each value of n from 2 to 20 is available and this factor is designated A2. 30 Therefore, the calculation of i 3 0 control limits using A2 for X is as follows [9,13,18,20]: UCLX=X + AZR [Clair-Y-Azk This is the most common method of _-I_- 3 0 control limits calculation for the X control chart, but should only be used when the sample size is 10 or less. The R chart is used for testing homogeneity of dispersion by using the range as a measure of dispersion instead of the standard deviation because it is easier to compute. To construct the range chart, the same principle is followed as in the X chart, using the average of the ranges, R, as the center line and :t 3 o as the control limits. The control limits for the R chart are [20]: UCLR = R + 3 5R LCLR = R - 3 0R Again, instead of computing OR, a shorter method is often used. This involves the use of a constant factor for each n which is designated D 4 for the UCL and D3 for the LCL [20], D4 = 1 + 3 OR l-R D3 = l - 3 OR l-R from which UCLR = R134 LCLR = RD3 The factors D3 and D 4 are tabulated for various subgroup sizes and available from a table. Unless the sample size is 7 or larger, the value shown for D 3 is zero, resulting in an LCL of zero. For sample sizes less than 7, the 31 distribution of sample ranges is positively skewed and the skewness decreases as the sample size increases [20]. The X and R charts are used together. Each subgroup is plotted as a pair of patterns, one for the average and one for the range. The R chart is read first to identify direct causes. In addition, it is necessary to first evaluate whether the variation of the data is in statistical control. If the variability of the process is not in approximate control there is little basis for the estimate of o and therefore little basis for the X chart. The X chart is read in conjunction with the R chart to identify other patterns or causes [21]. 1.3.7.3 p gait Control charts for attributes are used with routine inspection procedures of manufactured products involving inspection by attributes such as rejection or acception of the product and when numerical measurements of a quality characteristic is an unecononrical option. The most frequently used attributes chart is the p chart, which is a control chart for the fraction rejected. The p chart usually makes use of data that is either already available from inspection records or data that has been collected for other purposes. For this reason, lower costs are associated with maintaining this chart compared to the control charts for variables. However, the p chart is less sensitive than the control chart for variables and provides little or no warning of developing trends. This chart is only used as a guide for when and where to implement improvements. It has been found that after successful implementation of the p chart, with detection and correction of out of control situations, the process average fraction rejected decreases and quality improves [18]. The p chart monitors the fraction rejected for nonconfonnance to 32 specification. The reject data can be collected by sampling or by 100% inspection. If sample data is used, the sample size must be large enough to reflect the parent population. Suggested sample sizes are 50 to 100. Subgroup sizes should be 20 or more [21]. The fraction defective, is defined as the ratio of the number of defective items to the total number in the sample [9,13]: p = Number 9f defectives Total number inspected The binomial distribution which assumes a constant probability of finding a defect in random sampling is the basis for the p chart. The population average for the fraction defective is estimated by the statistic p‘ and is computed as follows [13,18]: MB :8 'Ma ..E’ fl II p...- where: np = Number of defectives in the sample. n = Sample size. m = Number of subgroups. If p remains constant, the fraction defective for each sample will fluctuate according to the binomial distribution and the standard deviation of fraction defective op, is as follows [9,13]: op = pq/n where: q =1 =15 33 The p chart is graphed with subgroup numbers on the horizontal axis and fraction defective or nonconforming for each subgroup on the vertical axis as in Figure 10. The Shewhart control chart model is used to establish the center line of average fraction defective, p, and control limits i 3 o away from this central line. Using the above formulas, the control limits for the p chart are calculated as follows [9,13]: 0.7 0.6 Fraction 0. 5 Defective 0.4 0.3 I I I T | T I 1 2 3 4 5 6 7 Subgroup Number Figure 10. p chart An altemative to the p chart is the 11p chart. It is almost identical to the p chart except that the number of defectives are plotted instead of the fraction defective. When the data is already available in the form of number of rejects per subgroup, the 11p chart is preferred. In addition, some believe the np chart is easier to understand [18]. The average number of defectives, up, is the center line on the chart. The standard deviation for the binomial distribution is [9,13]: an = npq 34 Finally, the control limits for the up chart are [9,13]: UCLnp = np + 3 °np LCan= 11f) - 3°np 1.3.7.4 aghart The c chart is used when a count is made of the number of nonconfomrities or defects per item. This includes inspection for one type of blemish or defect or inspection for any type of occurrence of nonconformity found on an item. Although it has restricted use, there is a definite need for the c chart in an SPC program. Similar to the other control charts it is used to detect the presence of assignable causes which signal when to take action [9]. The c chart monitors the total number of observed nonconfonnities of constant size subgroups based on the Poisson distribution. The Poisson distribution provides an approximation of the binomial distribution when there is a large n and and a small is and the product 1115 is of moderate magnitude [17]. It is a useful model for rare events. The count of the number of occurrences of the event of a nonconformity on an item that has an infinite number of opportunities to occur and a very small constant probability of occurrence fits the Poisson model [18]. The c chart graphically plots '6, the average value of the expected number of defects as shown in Figure 11. This average is calculated as follows [9]: m 2 C; a: I=1 m where: c = Number of nonconfomrities in the subgroup. m = Number of subgroups. 35 Following the Shewhart model of limit values placed i 3 o away from the average, the parameters for the c chart are as follows [9,20]: UCLC = E + 3fc= LCLC = E - 3f?— When using the c chart, improvement of the process requires action to reduce not only the variability but c because as c decreases the number of defects decreases. Usually, if a point falls below the LCL, no action is taken since this is a desirable situation in which high quality prevails. In addition, points below the LCL are worthy of investigation since they provide information as to how to achieve higher quality. 50 40 Number of defects 20 10 I I I I I I I 1 2 3 4 5 6 7 Subgroup Number Figure 11. c chart 1.3.7.5 agar: The 11 chart is very similar to the c chart but is used when the number of manufacturing items combined to form a rational subgroup is not constant. This chart monitors nonconfonnities per unit for attributes inspection. The 11 chart is used in the same instances and for the same reasons as the c chart. 36 The characteristic in consideration, u, is defined as u = c/n, where c is the total number of nonconfonnities in the sample and n is the variable sample size. Again u follows the Poisson distribution. The average nonconfonnities per unit, 11, is [13,18]: m Eu, fi=iil_ m 2 “i .___1 where: u = Number of nonconfomritites per unit. 11 = Sample size. m = Number of subgroups. The parameters are again calculated according to the Shewhart model [13]: UCLu=fi+3F n LCLu=iI-3 a II 1.3.7.6 Comllimits The main economic purpose of the control chart is to decide when to adjust a process and when to leave it alone. Since there is a cost associated with overadjustrnent and underadjustrnent of a process, it is economically desirable to minimize adjustments. Therefore, the selection of control limits must involve the calculated cost based on the size of risk and the total cost of making judgment errors based on statistical results [13]. There are two types of errors: Type 1 and Type 2. The Shewhart control chart uses 2*: 3 o unnecessary control limits as a means of identifying the lack of control. 37 Since 99.73% of the data fall within the + 3 o limits, there is still a 0.27% chance that a point will fall outside these limits. This chance occurrence may lead to the incorrect conclusion that the process is out of control when it is actually in control. This is known as Type 1 error and the cost incurred will be the cost of overadjustrnent. Chance may also lead to the incorrect conclusion that the process is in control when it is actually out of control. This is known as a Type H error and the cost associated with it will be the cost of underadjustrnent and poor quality output [13,18]. In some cases, it is desirable to'set less stringent control limits if the costs associated with hunting for assignable causes when they are absent are unjustified and more stringent limits according to the cost of not hunting for them when they are present. Specifically, a _-I_-_ 2 0 limit provides narrower limits when there is pressure for better quality and a :1; 4 0 limit is used for less rigorous quality requirements [13]. 1.3.7.7 lestsforiastahilint The data for a control chart is usually recorded and plotted directly at the workstation by the person performing the operation. The chart is then used on a continuous basis at regular intervals to check the process for unnatural pattenrs to determine whether the cause system is changing. This involves more than the detection of a point outside the control limits. Each half of the control band, the area between the centerline and one of the control limits, is divided into three equal zones. These zones are termed Zone A, Zone B and Zone C as in Figure 12. The pattem is said to be unnatural if any of the following combinations are formed in the various zones for one half of the control chart. These tests apply to half of the control chart at a time [21]. 38 Test 1. A single point falls beyond Zone A. Test 2. Two out of three successive points fall in Zone A or beyond. Test 3. Four out of five successive points fall in Zone B or beyond. Test 4. Eight successive points fall in Zone C or beyond. If a point of instability is detected, the assignable cause is identified and removed if possible. In addition, it is necessary to screen for defects from the output after the last sample was taken. However, many times there is pressure from management to satisfy a customer's urgent demand in which it is necessary to continue operating the out of control process but screen out those defects. Even if the process runs within the control limits and shows no points of instability, process improvement can still take place by moving the process average closer to the specification target and further reducing variation. UCL A Measurement, B number (2 cm defective, etc. C B A LCL Subgroup Number Figure 12. Control chart zones 2. Intros. i o o 1- {19"m1 04.11 unIPHoar; 2.1 Cgmpany Introdagign Valley Container, Inc. located in Bridgeport, CT produces various styles of corrugated shipping containers, die cut specialty boxes, and inserts. About 75% of the products manufactured are regular slotted containers (RSC), 15% are die cut specialty boxes, 5% are pads and inserts and the remaining 5% are miscellaneous products. Of the containers possessing a manufacturer's joint, 80% are glued, 18% are taped and the remaining 2% are stitched. The company specializes in small to medium sized containers and small to medium order quantities. The production facility at Valley Container is 45,000 square feet and employs approximately 40 individuals. Figure 13 illustrates the process flow diagram for the production system and Figure 14 describes each critical operation. 22 Wm The established quality objective of Valley Container is to produce professional corrugated boxes and inserts according to industry standards with on time delivery. Their service quality objective is timeliness, flexibility and a willingness to accommodate the needs and requests of the customer. In the past, quality was not a characteristic that differentiated this company’s product or caused this company to secure orders over its competition. Sufficient quality was rather a requirement for the company to be considered as a supplier and quote a price on a potential order. 39 [ Receiving l H I Slitling Scoring 3 Raw Material Storage Printing/Slotting Eccentric Folding/Gluing Slotting 8 9 Band Rotary Thompson Miehle S awin g Diecutting Diecutting Diecutting 4 5 6 7 Taping 1 1 Unitizing Palletiu'ng l3 I Delivery 15 Figure 13. Valley Container process flow diagram 41 Hit 2"10'12" l 10 11 12 13 14 15 Raw materials received from the supplier are unloaded and inspected. Orders are scheduled by due date and shipping direction for the following day. Corrugated board taken from stock is cut to the specified blank width and horizontal score lines are scored as specified Corrugated board is cut to specified dimensions. Conugated board is scored, slotted and printed to specification by a curved die mounted on a revolving cylinder. Corrugated board is scored, slotted and printed to specification by a flat die. Scrap is manually stripped from the finished die cut blank. Corrugated board is scored, slotted and printed to specification by a flat die. Scrap is manually stripped fiom the finished die cut blank. Scored corrugated board from the slitter is fed into the Flexo machine, which scores the vertical scores, prints, slots and cuts the board to the specified blank length. Glue is applied to the glue flap and the box is folded up. The finished flat boxes are automatically strapped into bundles. Extra or large slots are cut into corrugated box blanks as specified. Corrugated board from the slitter is fed into the press which scores the vertical scores, prints, slots and cuts the board to specified dimensions. ‘ TWO ends of a finished corrugated box blank are brought together and fastened with tape. TWO ends of a finished corrugated box blank are brought together and fastened with stitches. Bundles of finished products are strapped and stacked onto pallets for shipment. Trucks are loaded with bundles of finished products according to a specified shipping schedule. Finished products are delivered to the customer via Valley Container's trucks. Figure 14. Description of critical operations 42 2.3 Wm Due to the small size of this company, there was very little existing documentation of the original quality program. In order to understand the original quality policies and procedures of the production system, it was necessary to investigate and define the original quality program. Only after an understanding of the strengths and weaknesses of the original quality program was achieved could an effective implementation of SPC take place. There were four major policies that supported the quality objectives of the company. These were definite courses of action that had been adopted over the years in response to the need for feasible strategies to promote quality. All the individuals involved were expected to comply with these to achieve the quality goal. The following are the policies and procedures that comprised the original quality program. Pgligy 1 - Ensure the quality of raw materials by inspection. The procedure for ensuring the quality of the raw materials from the supplier was a simple and quick inspection that took place at the point of unloading the raw materials from the supplier's truck. Each bundle of corrugated sheets was inspected by the production manager as a whole without breaking it open. The inspection included checking the accuracy of the board dimensions, the quantity received, the Mullen burst strength type and flute type of the sheets received. In addition, each bundle was spot- checked for warped board, false scores and cracked scores. When an overrun in excess of 25% was received on anything except stock sheets or a repeat item for a customer, the excess was rejected and sent 43 back to the supplier. An underrun of more than 25 % on any item but stock sheets generated a complaint to the supplier and a request for the supplemental material. In addition, any sheets visibly damaged by the supplier due to shipping and fork lift handling were rejected. Instead of breaking open the bundle and sending this small quantity back on the supplier's truck, the production manager reduced the total received quantity by this damaged amount. The raw material inspection procedure did not follow a standard sampling plan and the quality checks were not recorded or documented at any time. Policy 2 - Ensure the quality of the products manufactured by performing quality checks throughout the production and shipping system. The bulk of the original quality program was the responsibility of the machine operators. The strategy was to check the quality of the output at every critical operation during the production and shipping operations. Each machine operator was responsible for checking the quality of the goods that he alone produced. When any one of these checks revealed inferior quality, the individual was expected to take corrective action. The machine operators had the authority to shut down their machines to eliminate a problem. Only when a defect was too difficult to correct or had caused a large quantity of defective products would the production manager, owner or respective salesperson be notified for assistance. It was assumed that since the operators were checking for quality as the product was being manufactured, there was no need to inspect the finished product. There was 44 no final inspection of the products to ensure quality. The following is a list of critical quality characteristics checked at various stages in the production system. Each characteristic has a specified tolerance that is defined by either the corrugated box industry or by Valley Container. Every critical operation in the production system includes an inspection of specific quality characteristics taken from this list. The specific checks required were never documented anywhere for the operators to reference but simply verbally related and memorized. The method of inspection was different at each critical operation depending on the measuring equipment available. All of the checks were informally made by infrequent inspections of the product without documentation. As a result, there was no guarantee that these checks were ever made. g . . 1 Q 1' g . . g 1i . 5 'fi . l. Featheredge - Corrugated board liner must not exceed corrugated medium by more than 1/ ". 2. Flute Must use the specified flute type. 3. Mullen burst test Must use the specified burst test type. 4. Corrugated board color No spots, blotches or dark patches. Must use the specified corrugated board color. 5. ID number Must use the specified ID number. 6. Corrugation direction Corrugation of corrugated board must run in specified direction. 7. Dimension All dimensions must be within i 1/16" of specified dimension. 8. Cut edges 9. Flute crush 10. Printing 11. Score depth 12. Stripping 13. Joint misalignment (fishtail) l4. Gap 15. Slot depth 16. Slot edges 17. Slot centering 18. Glue adhesion 19. Tape adhesion 20. Tape length 45 Corrugated board edges must not be ragged or curved. Corrugated board flutes must not be crushed. Printing must have accurate register, color and location. Printing must be readable, dark and not smeared or transparent. Score on corrugated box blank must not be too light or too deep and cracked. Die cut must be at least 90% stripped. Corrugated box must be square when folded up. Joint misalignment must not be more than 1/8" on a Singlewall box and 3/16" on a doublewall box. Gap at box blank flap scorelines must not be greater than 1/8". Box blank slots must extend to the horizontal score line, - 3/16" to + 1/8" variation from score line allowed. Box blank slots must be completely removed and must not be ragged. Box blank slots must be centered on the vertical score lines. There must be enough glue on the joint surface. Joint must not pull apart easily. Tape must adhere to the joint surface sufficiently. Joint must not pull apart easily. Tape length allowed - 3/8" to + 1/8" variation from horizontal score line. 21. Stitching spacing 22. Quantity 23. Special instructions 24. Delivery approval 25. Due date 26. Buffer sheets 27. Load tags 28. Number of straps 29. Strapping tension 30. Delivered products 31. Delivery location 46 Maximum spacing between stitches allowed is 1 1/2". Stitches must be at least 1" from either edge. Quantity manufactured must be within _-I_- 25% of ordered quantity. Must be followed completely. Call customer 24 hours before delivery for specified customers. Goods must be delivered within i 2 days of due date specified to the customer. Top and bottom buffer doublewall corrugated sheets or two pieces of corrugated board must be used. Conect load tag must be used with the conect quantity entered. Unit must have at least two straps. Product must not be tom and straps must not be too loose. Unit must be intact with rrrinimal fork lift damage. Correct products must be delivered to the correct shipping address. When a customer had strict quality requirements, the assumption that the machine operators would check product quality could not reliably be made. In such a case, the first item produced in the order was double checked. Specifically, when such a customer placed an order, a quality sticker (Q sticker) was attached to the production worksheet and sent to the production plant to be produced. The Q sticker was actually a piece of paper saying: 47 "Quality Check - show either owner, production manager or salesperson before running". This alerted the machine operator to have the machine setup inspected and approved before the entire quantity was produced. In this way, operator errors were caught before they affected the entire order. The inspector checked for accuracy of the following: Length, width and depth dimension Printing readability, accuracy, location and color Scoring accuracy and depth Slotting accuracy and depth Ragged board edges Flute type Mullen burst strength type SP‘S‘PP’N!‘ When the product was a container, it was folded up to its final shape and inspected for squareness and overall quality. If any defect was detected, the problem was corrected and the machine setup inspected again until the setup was finally approved. Once approval was obtained, the Q sticker was initialed by the inspector and the entire order was produced. Pgligy 3 - Satisfy the quality needs and requests of the customer in a helpful manner. When a customer had an extraordinary quality request or specification, additional instructions were included in the "Special Instructions" section of the worksheet and listed for all the production employees to see. In this way, each machine and shipping operator was informed of each customer's special requests and was expected to execute each instruction that pertained to his area of responsibility. 48 Pgligy 4 - Prevent defects by confronting the individual responsible and explaining the seriousness of the defect. Each time a defect occurred, an attempt was made to trace it back to the individual responsible. Only when there was definite proof of the individual's responsibility was this procedure employed. The error was shown to the operator and an attempt to remedy the problem was made. It was believed that when the operator saw his error and understood its significance that the defect would be prevented in the future. In this way, the operators learned to avoid serious defects. This behavior was reinforced by requiring the operator to use a die to print his name on the bottom end flaps of the corrugated containers he produced. This made it possible to trace a defect back to the responsible operator and make him concerned for the quality of the output because his name appeared on the product. 2.4 Analysimtmhtahility The top management at Valley Container considered their manufactured products to be of good quality. In their opinion, product quality was neither excellent nor poor but was satisfactory and suitable for the needs of the customer. The quality of the products compared to those of other manufacturers within the industry was at least equal to or better than the competition. The effectiveness of the original quality program was considered mediocre to good. The quality procedures were not always found in practice and there were several reasons for the variation: 49 1. Lack of documentation and enforcement of quality checks made on the shop floor. It was difficult to trace a defect back to the responsible individual and take conective action. The system erroneously assumed that the machine operators were performing the quality checks without a final product inspection to ensure product quality. 2. Informal and personal judgments made about product quality. Many quality characteristics had vague and ambiguous specifications and were checked at random. The operators were forced to make subjective quality decisions. 3. Inadequate first piece inspection for the more critical customers. Quality problems or defects that occurred in the middle or end of the production run often went undetected. 4. Lack of feedback from quality problems. No system existed to analyze trends and repeated quality problems in order to improve quality. This resulted in firefighting rather than problem solving. 5. Inadequate spot-checks on raw materials. Poor quality raw materials entered into the production system if not "spotted". A machine operator could not be expected to produce high quality products from defective materials. Prior to this study, the average quality had been tolerable. By increasing the product quality level, customer value would not have increased proportionally to justify the increased quality costs. However, in the present economic environment where quality has become the major factor in deciding the share of market, the mediocre quality program and moderate product quality was no longer acceptable. As Ford Motor, Hewlett- Packard, General Motors, Xerox, AT&T and other major US. companies have adopted and implemented the Deming Management Method with SPC [7], a ripple effect in American business has required higher quality for all products and services. Valley Container had experienced pressure from key customers to implement SPC in order to qualify as their supplier. Not only 50 customers to implement SPC in order to qualify as their supplier. Not only did this mandate the implementation of SPC but more importantly a change in the company's attitude about quality. The implementation of SPC at Valley Container had an excellent foundation for success because it was initiated by the chief executives of the company whose management philosophy moderately resembles that of the Deming Management Method. The management philosophy of defect prevention through process checks instead of defect detection by final inspection provided the framework for statistical techniques. It was found that SPC would satisfy this company's needs by providing more objective, effective and efficient process checks with documentation with which to analyze and improve the process. Management’s philosophy supported problem solving instead of firefighting but was hindered by the inability to trace defects back to the responsible individual. SPC techniques would provide a data tracking system to improve quality. The Q sticker policy in the original quality control program, however, will become unnecessary with Deming's management philosophy and SPC. \Vrth a wide range of quality requirements from customers for relatively similar products, the company had been reluctant to produce high quality goods for any customers except those who required or demanded high quality. The time and money spent to provide high quality for those customers who were unconcemed with quality seemed wasteful. However, according to Deming, as quality improves, costs go down [4]. It is therefore necessary to strive toward high quality for all customers. With the help of SPC, it was determined that the Q sticker policy would be eliminated and a high level of quality sufficient to satisfy the highly critical customers 51 Finally, the raw material inspection procedures in the original quality control program were determined to be unacceptable since the Deming management philosophy requires that the production system extend to the vendors. High quality input of raw materials was necessary for high quality output of finished products. Unless the raw material inspection procedure was improved to ensure high raw material quality, SPC could never provide the highest attainable quality at the lowest cost. 3W 3.1“ 'E . {5' 'fi 0 l' E I] The first step in the implementation of SPC was to identify the most significant quality problem areas with respect to frequency and cost. A Pareto analysis of credit/rejection reports, quality inspection reports, documented customer complaints or customer performance appraisals would have identified the vital few quality problems in need of attention. Unfortunately, quality information was never recorded in this company and these documents did not exist. The identification of the significant quality problems was forced to be done through employee interviews involving selected representatives of the company (plant manager, sales manager, production manager, office manager and several salespeople). During each of the interviews conducted, the employees were asked to rate the list of possible defects in Figure 15 on a scale of 1 to 3 according to their frequency of occurrence based on their knowledge of complaints, rejected shipments and lost customer accounts. A rating of 1 indicated the defect rarely occurred and a rating of 3 indicated the defect occurred very frequently. This was not an accurate appraisal based on historical data since the ratings were based solely on individual opinions, memory and experience with the company. However, with no documented information available, the only way to determine the most serious problems in the company was to consult the individuals involved. 52 53 Defect W Liner separation Open conugation Warped board Ragged edges Crushed board Overhangin g liner (feather edge) 5.9mm Inaccurate score Cracked score False score Crooked score Starring Incorrect slot depth Inaccurate slot Ragged edge litmus Insufficient ink cover up Incorrect printing register Ink smear Incorrect ink color Lack of printing sharpness Incorrect prinwd information Misaligned glue joint (fishtail) Glue adhesion separation Misaligned tape joint (fishtail) Tape adhesion separation Inaccurate tape length mm Incorrect carton dimensions Carton dust Late delivery Special instructions not followed Quantity overrun or underrun Figure 15. List of defects 54 Figure 15 also classifies the defects as major or minor according to the plant and sales managers. A major defect was defined as any nonconformance to specification that reduced product usability for its intended purpose. Specifically, since the corrugated containers manufactured by Valley Container were intended to provide protection, utility and communication, a defect that caused the product to fail in providing any of these functions was considered major. A minor defect was any deviation from specification which did not greatly reduce product usability. The interviews provided the defects frequency ratings in Figure 16. Due to the diverse ranges of experience of the individuals interviewed, more importance was given to the individuals with more experience in the company. A weight of 3 was given to the two owners' ratings (interviews #1 and #2) because they had started the company from scratch 25 years ago and had the most experience and knowledge about the quality problems in the company. In this way the opinion of each owner was really counted as the opinion of three individuals. The production manager, office manager and first salesperson's ratings (interviews #3, #4 and #5) were given a weight of 2 because of their experience with the company and the last two salespeople's ratings (interviews #6 and #7) were given a weight of 1 because of their limited experience with the company. Figure 17 shows the employee weighted average frequency rating for all defects. Defect importance was also considered. A second weighting system was used in Figure 17 which gave more importance to the most serious and costly defects. A weight of 2 was given to the employee weighted total for all major defects and a weight of 1 was used for all minor defects. 55 Interview number Cgrrugated Board Liner separation Open corrugation Warped board Ragged edges Crushed board Overhanging liner (feather edge) Scoring Inaccurate score Cracked score False score Crooked score mung Incorrect slot depth Inaccurate slot Ragged edge Insufficient ink cover up Incorrect printing register Ink smear Incorrect ink color Lack of printing sharpness Incorrect printed information Maaafagmr's jam 1; Misaligned glue joint (fishtail) Glue adhesion separation Misaligned tape joint (fishtail) Tape adhesion separation Inaccurate tape length mm Inconect carton dimensions Carton dust Late delivery Special instructions not followed Quantity overrun or underrun HHy—emp—ep—e NHmHN HNHwHN NNN HHHH wwwu—u— HHHH HwHHHH t-u—IUJUJUJ Hut—n—I—u—I HNt—t cannon-IN NNNl-‘H commun— HNHHNN [Qt—H r—u—H—u—t NNNWr-H-d Hme—ih-lw I—‘NHNI—i Figure 16. Defects frequency ratings p—Ap—eg—rp—r HHHHHH NHN p—ey—ep—ep—ep—r mourn—n— HHh‘NN HI—H—dt—at-dr—I v—H—u—t t—INI—u—I l—II—iP—INI—Ip—A r—ANh—ANt—I WUJUJI-‘H r—Ih—IN HNNH h—lb—ib—lb—tt—It—i Hp—er—rp—rp—r UJNHHN 56 Employee Mighted Average Defect 13194114939! Tram Bank W Liner separation 1.00 2.00 13 Open corrugation 1.00 1.00 19 Warped board 1.93 1.93 14 Ragged edges 1.14 1.14 18 Crushed board 1.57 3.14 6 Overhanging liner (feather edge) 1.14 1.14 18 Inaccurate score 1.00 2.00 13 Cracked score 1.07 2.14 11 False score 1.14 2.28 10 Crooked score 1.00 1.00 19 Slotting Incorrect slot depth 1.57 3.14 6 Inaccurate slot 1.57 3.14 6 Ragged edge 1.64 1.64 15 Printing Insufficient ink cover up 1 64 3.28 5 Inconect printing register 1 14 1.14 18 Ink smear 1.57 3.14 6 Incorrect ink color 1.36 1.36 16 Lack of printing sharpness 2.07 2.07 12 Incorrect printed information 1 00 2.00 13 Misaligned glue joint (fishtail) 1.71 3.42 4 Glue adhesion separation 1.71 3.42 4 Misaligned tape joint (fishtail) 1.86 3.72 3 Tape adhesion separation 1.36 2.72 8 Inaccurate tape length 1.21 1.21 17 Inconect carton dimensions 1.29 2.58 9 Carton dust 1.14 1.14 18 Late delivery 2.71 5.42 2 Special instructions not followed 2.78 5.56 1 Quantity overrun or underrun 2.86 2.86 7 Figure 17. Defects ranking The third column in Figure 17 ranks the defects in order of importance. The most serious and frequent defect involves special instructions and was given a ranking of 1, indicating that it was of first priority to be investigated. The following is the list of the most important defects in 57 decreasing order. m 1 Defect Name and Exphaation WM - A Special instmction specified by the customer is not followed. Wm - Order is delivered on a date later than the date promised to the customer. Migaljgaed tap; joint - Commonly called a crooked box or fishtail, horizontal score lines on the box do not line up at the tape joint. Final box does not fold up square. Misg'gaed glue join - Commonly called a crooked box or fishtail, horizontal score lines on the box do not line up at the glue joint. Final box does not fold up square. Glue agfllgsign saparag' on - Manufacturer's glue joint separates easily. Final box falls apart. i ' - Ink is transparent or light. The printing is difficult to read. Calm - Corrugated board flutes are crushed and deformed. Final box has less compression strength. - Slots on a box blank are either too short or too long. Final box does not fold up square. Inaccurate slot - Slot is not in the correct location or not centered on the vertical score line. Final box does not fold up square. Mm - Ink on surface of the box is smeared or smudged. The printing is indistinct, messy and difficult to read. ' v r - Final quantity shipped to customer is beyond the limits of the allowable industry standard of 25 % maximum overrun or underrun. 58 It was decided that SPC was to be applied to the first, second and fourth quality problems. Although the third ranked quality problem was misaligned taped boxes, the fourth problem of misaligned glued boxes was chosen instead. This was mainly because the machine operator for the Flexo folder-gluer machine which manufactured the glued boxes was the only college educated employee on the shop floor. This operator was more likely to participate and understand the control charting techniques. It was critical that the pilot program on the shop floor prove successful since most employees were doubtful of the new techniques and needed practical proof of real quality improvement in order accept SPC. The following sections discuss the steps taken to implement SPC for quality improvement in each of the three chosen quality problem areas. Each section will include a definition of the process, establishment of a sampling plan and data collection. The data will be analyzed and corrective action will be determined using the SPC tools described in Chapter 1. A second collection of data will take place following the implementation of corrective actions along with a secondary data analysis in order to determine the extent of quality improvement. 59 3-2 WW4 Customer specified special instructions were often honored to accommodate the individual needs of each customer. Figure 18 is a list of the general areas in which special instructions were most frequently specified. Each special instruction specified by a customer was considered a necessary requirement. When just one of these requirements were not met, the defect was considered major since the customer found it impossible to use the delivered products. Number per unit Unit overhang limit Maximum unit height No underrun 10% maximum overrun 2 straps in each direction Skid dimensions Delivery day No ovenun Must use small delivery truck Call before delivery Do not ship when raining Number per bundle 5% maximum overrun Delivery time Mark bundles with ID number Must be on skids Unit dimensions Figure 18. Special instructions frequently specified 3.2-1 Warren Special instructions were listed in a small box on the left side of the production worksheet for each customer's order as illustrated in Figure 19. At each critical operation, the operator read the entire list of special instructions and executed only those that pertained to his area of responsibility. The number of special instructions listed on a worksheet ranged from 0 to 12 with approximately 30% of the orders having no special instructions at all. 2000 TEST TEST , 2‘” x 25" x 12" 1111 100 Meta Street 100 Mela Street ““u "‘ "V "W- Bridgeport. CT 06610 Bridgeport. CT 06610 99 X 37 1 [SC Ill/89 —_ .00“ ‘ 273 C 1112/89 Here eech bundle with to! end P0! or will reject. "Glue 1 W ..J. Hue: be on eklde. Uo overrun. Shtde no higher thee Tee: '0' 2222 62" tnc'd ektd. Cell one dey before delivery or ..- 32 llue “w a" ”W ebb-5335 end uee epeclel leed rege. Deliver been 0-2 ’I. . 1 111 2000 one” one We...” 1112/09 IlllS/89 11 200 2200 3333 .— SL ' IL! ‘ GIT ' FLT ' ear 1 1/6" 24 5’16" 2‘ $116" 24 3/16" 26 3/16" 12 3/16” 12 3116" 12 3/16' ""“‘ 2...... mane—-JHL— V. e. m 1999 w 275 c - I Q I ISC 'OL POL H80 _ 0" FULL TEL IIAV _ PAD 56-8" 5 fl OIC T I?!“ Figure 19. Production worksheet with special instructions 3.2.2 Dataficlleciicn The sampling plan established for data collection is shown in Figure 20. It was decided that attributes data would be collected to acquire the average number of special instructions not completely followed. Since attributes data was used with a p chart, many more observations per subgroup were needed in order to provide a comprehensive representation of the process. It was determined that 15 samples of special instructions could be taken every day with moderate searching time and effort. The subgrouping method was designed to measure special instructions performance for each day. Data was collected for two months according to the established sampling plan. The raw data and the percent special instructions not followed for each subgroup appear in Table 1 of Appendix A. 61 S .11 . S 1' El Purpose: To determine the average proportion of defective products over time with respect to special instructions. To declare the seriousness of this defect to the employees by introducing an inspection system to monitor the special instructions quality level. Critical Characteristic: Attributes data: One special instruction (conforming or not conforming to specification). Inspection Location: All 15 critical operations. Measurement Method: A special instruction is considered defective if at least one item of the order does not conform to the special instruction specified. Subgroup: Sample size: 15 special instructions Time period: 8 weeks, daily sampling Subgroup Size: 40 subgroups Subgrouping Method: Daily random selection of 15 special instructions at random critical operations between 12:00 pm and 1:30 pm. Type of chart: Frequency histogram and p chart Record: 1. Sampling date 2. Special instructions in subgroup 3. Special instructions defective in subgroup 4. Percent defective 5. Special circumstances Figure 20. Special instructions sampling plan 3.2.3 §p_ecial Instructigns Staa'stigl Amlysig After two months of data collection, it was determined (Appendix A) that the average special instructions percent defective was 30%. This meant that 70% of the special instructions were being followed. The control limits for 62 the p control chart are calculated in Appendix A. The p control chart in Figure 21 indicates that the data was in control so that the special instructions process was stable and predictable. S '11 . El Il-S 1233 70% ._ UCL = 65% 60%" 50% «- Smal 4% d- e H e e Instructions Not h“. . /\ ./\ _ Followed 30% \ A I I I :6 = 30% 20%. \__/'\_I ' \/_/ V L'\./ r..\./,__z 1 6 1 1 16 21 26 31 36 Subgroup Number Figure 21. Special instructions p control chart The frequency histogram in Figure 22, however, indicates that the process spread was much larger than the allowable specification spread. Specifically, the process was estimated to range from 0% to 65% of the special instructions not followed virtually all of the time while a maximum of only 10% was allowed. In fact, only one subgroup representing 3% of the entire sample data provided a special instructions percent defective of less than 10%. Therefore, although the special instructions process was in control, it was operating at an unacceptable level. Action was required to decrease the process spread and bring the process performance closer to specification. LPSL = 0% Average = 30% UPSL = 65% e LSL = 0% <——-h USL =10% 9... 8- 7- 6- Frequency 5 ////////////1 WI -----------------------.!-- § 31‘ §s l.— I I kI §AI §§% 0 6.7 14 20 27 33 40 47 53 Percent not followed Jul-Aug1989 Figure 22. Special instructions frequency histogram 3.2.4 Camus The statistical analysis revealed that the special instructions process was stable and that there were no special causes of variation to correct. Therefore, merely asking the employees to follow the special instructions more carefully would not have brought about process improvement because the normal operating process was determined to be capable of following only 70% of the special instructions. Process improvement could have only taken place through management action on the system. It was necessary to investigate problems in the system that were causing the special instructions not to be followed. Informal interviews were conducted with the employees 54 involved and some specific problems in the special instructions system were identified: 1. The special instructions were written in small print in a small area on the production worksheet as one continuous sentence with confusing abbreviations. Employees found them very confusing to read and follow. 2. Machine and shipping operators were not clear as to who was responsible for executing each special instruction. Many times one operator thought that another operator would cany out the special instruction and vice versa, resulting in no one executing the special instruction. 3. Some special instructions were ambiguous and the operators often did not understand what was required. 325 We The first action taken was to improve the quality of the special instructions information. The entire list of customers' special instructions was examined and ambiguous instructions were redefined more clearly. Similar special instruction phrases were standardized into simple, consistently worded phrases. With the aid of the salespeople, managers, shippers and truck drivers, the list of special instructions was updated by correcting errors and removing obsolete instructions. The most serious problems with special instructions were identified through the Pareto analysis illustrated in Figure 23. The first 6 special instructions which comprised 60% of the special instructions not followed were reviewed during short informal sessions with the employees. It was found that the proper measuring devices had not been provided to measure the specified maximum unit height and skid dimensions. These measuring devices were made available to improve the process. In addition, it was necessary to assign responsibility to certain employees for ensuring the specified maximum overrun. 16% 14% 12% 10% Defect Frequency 8% (Percent of Total) 6% 4% 2% 0% S\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\V \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\‘ t\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\‘. '\\\\\\\\\\\\\\\\\V S\\\\\\\\\\\\\\\V H N U) h 65 cial Ins ti ns Pare h W S\\\\\\\\\\\\\‘3 LI! 0\ \l 8 910111213141516171819 Special Instructions Code Code Special Instruction :33:55:50mqaquN— Number per unit Maximum unit height 10% maximum overrun Skid dimensions No overrun Call before delivery Number per bundle Delivery time Must be on skids Unit overhang limit No underrun 2 straps in each direction Delivery day Watch bundle counts Must use cabover Ship 10 bottoms only Do not ship when raining Special load tags 5% maximum overrun Order material West Mark bundles with ID# Number of bundles per layer Mark units with ID# and PO# Unit dimensions Figure 23. Pareto analysis of special instructions 66 Finally, management was involved in redesigning the production worksheet to improve the presentation of the special instructions. Although 4000 worksheets were still in stock, management decided it was more important to immediately begin redesigning and ordering new worksheets to improve the special instructions process. By rearranging the worksheet layout, the special instructions area was doubled as illustrated in Figure 24. In addition, all special instructions were broken down into five critical areas of responsibility within the production facility (production, planning, unitizing, loading and delivery). Management defined the areas of responsibility to the respective employees and required them to begin initialing their section upon completion of their special instructions in order to be able to trace a defective special instruction back to the responsible individual. rcsr ‘ TEST 2‘" x 2'." x 12" 1111 100 Halo Street 100 Hell! Street “""‘“ "‘ ""' w.-.“ Irldgeporr. CT 06610 Irldgeport. CT 06610 99" X 37" 1 45C Ill/69 V .-—.J'I “.0" "“""’ or... 273 c 1112/59 Prod 1. No overrun 3" ' ¥ -. e- - Plea 1. Cell before delivery I." ’9' '32 blue 2222 2. Dellver between 6-2 p. m- — one u.- Gee-u- Unlt 1. Keri bundlee vlth 1M + PM 1 I r 1 2000 Loed l. Hue: be on ehlde r-I—I-nm—u r. 2. Heel-u- ekld helghr - 62" 3333 Del 1. Dellver beeveeo 6-2 p- 51. ' er ‘ urn ' 7LT ' SI? 1 Illa" 24 5/16" 26 3/16" 26 SI16" 24- 3/16" 12 3116" 12 3116” 12 3/16" * -- _- - m m- Sunller A 2222 I “In!!!“ .. - ., 20710 __T "ooo"'— fl—‘wmmm, 1115/» 11 200 2200 I- 175 c - ' ' manure l — — _r T‘... -- -—I m -- -- .0“.- I M“ Figure 24. New production worksheet with special instructions 67 32.6 W After the improvement action had been taken, data was again collected according to the established sampling plan. The purpose of the sampling this time was to measure the effectiveness of the improvement action on decreasing the average percent special instructions not followed. The raw data and the special instructions percent defective for each subgroup appears in Table 2 of Appendix A. After the four weeks of data collection, it was determined that the average special instructions percent defective had decreased to 15%. This meant that ‘ 85% of the special instructions were being followed which is a significant improvement from 70%. The control limits for the p control chart (Appendix A) and the p control chart in Figure 25 indicate that the data was in control and the process was still stable. 70% «- 60%4- 50% r- UCL = 42% Special 40% ‘- Instructions Not Followed 30% .- 20% -- /-/\-/.\- /'\_/\ p=15% /\ [V 10% ..\/ \/ V \./ \/ (fl 1 e e r J 1 r e e r - J 1 1 e 1 e 1 4 0 ' ' ' U U I U I I ' e I ‘ ' ‘ ‘ V I ' Subgroup Number Figure 25. Special instructions p control chart 68 The frequency histogram in Figure 26 indicates that the process spread had reduced significantly. The improved process variation was estimated to range from 0% to 42% defective special instructions virtually all of the time, whereas the process had initially ranged from 0% to 65% defective special instructions. However, the process spread was still larger than the specification spread of 0% to 10%. Only 3% of the initial sample data fell within this specification before, whereas the improved process showed 5 subgroups or 25% of the entire sample data within specification. Even though significant improvement had been realized, the process was still operating at an unacceptable level. Further improvement action was required to decrease the process spread and bring the process performance even closer to the 10% specification. LPSL = 0% Average = 15% UPSL = 42% e SL = 10% I. LSL = 0% 9- 8.. 7 _ Frequency 6— 5- 4- 3.. 2... 1 - A ///// f///////////l __----_-_....-_..___ --r-.. —/////// § I 3 4 Number not followed % ~—7/////A o o-I N 6.7 14 20 27 Percent not followed Dec-J an 1989 Figure 26. Special instructions frequency histogram 69 From Table 3 in Appendix A, it is evident that only 25% of the special instructions were initialed after improvement action had been taken. It is expected that the special instructions process will continue to improve as the initialing procedure becomes more established. 70 3.3 gram Valley Container had trouble meeting customer delivery time requirements. It was determined that lead time error, the difference between actual lead time and promised lead time, was a more serious problem than long lead time. This was because it was more important to the customer that the products were delivered consistently and reliably on the promised delivery date given a reasonable lead time. Therefore, SPC was implemented with the purpose of reducing lead time error instead of length of lead time. 3.3.1 Qalivary Mss Descnp’ tign The problem with the delivery process involved more than the physical delivery of the products to the customer. The total product delivery lead time included the time elapsed from the time at which the customer placed an order to the time at which the customer received the order. It was necessary to construct a process flow diagram as illustrated in Figure 27 depicting each event that contributed to the total product delivery lead time. The following departments were involved in the process flow diagram: administration, sales, design, purchasing, scheduling, receiving, manufacturing and shipping. This diagram provided an understanding of the factors that contributed to the problem of late delivery. 3.3.2 Data Collection The data collection on delivery lead time was required to cover at least a period of one month in order to include inventory management methods which increased shipments of finished goods inventory at the end of the month to increase monthly sales totals. It was decided that the data would be collected over a period of three months in order to establish a reasonable 71 Valley Container Total Delivery Lead Time Process Flow Diagram I Customer places an order Is the order No ~ for a repeat item? 4' Design/Redesign the item XI N 0 Y Doe th Enter order k es customersapgrove of * e design? . scthe order No A scstgtjk? 4| Order the raw material Yes th re s k N — V Sma‘Ieri 0c 0 [ Receive the raw material available? Yes Schedule order Manufacture order Yes need to bew ifirpused ,l Warehouse or store order Ship order I Customer receives order I Figure 27 . Total delivery process flow diagram 72 history of delivery performance according to the sampling plan shown in Figure 28. Delivery information was easily retrieved from existing computer shipping reports which virtually eliminated the cost of obtaining this large amount of data. Samplineflm Purpose: To determine the natural tolerances of the delivery times and the average delivery lead time error. To estimate the common cause variation that occurs under normal operating conditions and establish controls to insure the customer's delivery requirements are satisfied. Critical characteristic: Variables data: Time lapse between actual and promised delivery date (days). Inspection location: Critical operation number: 15 Critical operation name: Delivery Measurement method: Determine number of days lapse between actual delivery date and order due date from "Shipping Log" computer report (excluding all weekends and holidays). Subgroup: Sample size: 5 orders Time period: 12 weeks, daily sampling Subgroup size: 60 subgroups Subgrouping method: Daily random selection of 5 orders from "Shipping Log" at 3:00 pm. Type of chart: Frequency histogram and X, R chart Record: 1. Order ship date 2. Order due date 3. Order number 4. Lapse between actual ship date and order due date 5. Special circumstances Figure 28. Delivery sampling plan 73 The lead time error data was collected for three months according to this sampling plan. The raw data along with the X and R for each subgroup appears in Table 4 of Appendix B. 3.3.3 Wars The first step in the delivery process capability analysis was to determine whether the delivery process was in a state of statistical control. The X, R and trial control limits were calculated in Appendix B and the corresponding X and R control charts are shown in Figures 29a and 29b . It was evident that one point (subgroup 43) was outside the control limits on the Xchart. In addition, subgroup 45 was a point of instability since it was the second out of three successive points to fall in Zone A or beyond. Five points (subgroups 21, 34, 43, 45 and 50) were outside the control limits on the R chart. Finally, subgroup 29 was the eighth consecutive point that was either in Zone C or below and also a point of instability. It was concluded that the process was out of control and special causes for late delivery existed. The process data was therefore unpredictable and could not be used to determine the delivery process capability. Nevertheless, a frequency histogram was constructed in Figure 30 for this unstable process to get an indication of the central tendency and spread of the lead time error sample data. X Lead Time Error (dayS) 161116212631364146 Subgroup Number Figure 29a. Lead time error X control chart W x 40 .. X I 30 R Lead 20 . Time Error (days) 10 . 0 .1 '10 :iigviiiii 1 61116212631364146 Subgroup Number Figure 29b. Lead time error R control chart 75 ‘N‘N‘Sbs‘bfi VNNNNe l 1.- 24" l 6“ 8“ 56- 48— 404 32- Frequency Lapse Between Actual and Promised Delivery Date (days) May-July 1989 Figure 30. Lead time error frequency histogram 76 33.4 W The next step was to determine the assignable causes of late delivery and whether or not they could be eliminated. The control charts and frequency histogram were used to identify the points where assignable causes were evident and worthy of investigation. Each closed order whose delivery performance contributed to either the large frequency distribution spread or a point beyond the upper control limit on either the X or R control chart was retrieved. The cause of excessive late delivery for each order was determined with the help of the salesperson. Except for subgroup 29, it was discovered that every point out of control on the X and R charts was caused by the late delivery of raw materials from the supplier. An analysis of past delivery performance for the two major suppliers was necessary to measure supplier delivery quality. The raw materials for corrugated boxes were separated into two categories with different lead times; Singlewall kraft corrugated board with a lead time of 5 days (12 days allowance) and doublewall, oyster and other corrugated board types with a lead time of 6 days (3:2 days allowance). Delivery lead times for every order received in the previous three months were retrieved from the computer records in Tables 5 and 6 in Appendix B. The lead time average and standard deviation for each material category are also shown in Appendix B. The frequency histograms for Singlewall kraft board lead times and doublewall, oyster and other board type lead times are shown in Figures 31 and 32. The supplier delivery performance analysis proved that supplier late delivery was definitely a problem. Although both suppliers delivered the Singlewall kraft corrugated sheets within approximately 5 days on the average, their lead times often exceeded the 3 to 7 day allotted range. The extreme case of 15 and 18 days lead time for Suppliers A and B respectively 77 SI'ES'I IIKEC IE 1121' May -Jul 1989 50 45 40 35 30 Frequency 25 20 15 10 u. ”Ill VIII/IIIIIII/I/IIIIA VII/Ill/I/Il ax ”III/III,” " VIII/ll 00 ”III. “I NI 0) & Ur :11 I 9101112131415161718 LeadTime (days) 50 -- 45 .. 35 4. 30 4. Frequency 25 .. 20 .. 15 .. 10 .. 'I/I/I/I/I'l. 'II/I/II/I/A Ur ”IA 1‘ e‘ .- L‘ -- .- 9101112131415161718 Time (days) \V. use 456 p—e N W \3 00 E Figure 31. Singlewall kraft corrugated board lead time frequency histograms S 8 mm mm. a. 7 3 v” u. .S\\\\\ w \\\\\\\§ w s M Q\\\, r..v. n\\\s m ‘\\\\\\§ ‘\\\\\\\\\\\\\\N\\\u V .“““~“‘.“~‘---~L \\\\\\\\\\\\\\\\h ‘N\\\\\\\\h N\\\. \S mgaum arahm Frequency 5 .. 12 3 4 5 6 7 8 91011121314151617181920 Lead Trme (days) May-Jul 1939 s S 8 mm %1 as 6 3 = = .X s «N‘\\\\\s V\\\‘\\\\. ‘8 N‘\\L‘“\\§ g\\\\\\\\\\\\\\§ .““~““-~k §\\\u‘\\\\k g\\\‘\\\\\\§ §\\\\\.‘L Q‘s. nnnnnnn ddddddddddd wan/876543210 Frequency 12 3 4 5 6 7 8 91011121314151617181920 Lead Time (days) Figure 32. Doublewall and other corrugated board lead time frequency histograms 79 was highly unacceptable.. In addition, both suppliers delivered doublewall, oyster and other board types beyond the specified 8 day allowable lead time. The extreme case of 17 and 20 days lead time for Suppliers A and B was also highly unacceptable. Even though Supplier B had a slightly shorter average lead time for this material type, its range of lead time was larger. It was concluded that the poor delivery performance of both suppliers prevented the company from delivering corrugated boxes on time. 3 .3 .5 Improvement Action Two different actions were initiated to improve supplier delivery performance. First, management brought the above frequency histograms and diagnosis of poor performance to the attention of Supplier A since Supplier B was thought to be less receptive. The production manager of Supplier A suggested the purchase orders be faxed directly to the production planning office, thereby skipping the order entry operation and reducing total delivery lead time. A new system of placing orders with Supplier A was implemented as a result. This required purchaser training, fax machine utilization and a redesign of the production worksheet layout. Another inexpensive corrective action to prevent late delivery was suggested by the sales service employees. It was found that long overdue raw materials frequently went unnoticed until the finished products were overdue. A new system which checked computer generated open purchase orders daily for all suppliers was adopted. Specifically, for each purchase order which was 1 to 3 days late, a revised promised delivery date was requested from the supplier. Those orders that were more than 3 days late were brought to the sales manager's attention who in turn pressured the supplier to expedite the raw materials. 80 33.6 W The company's delivery performance was monitored for three more months after initiating the improvements. The trial control limits for the Y and R chart would no longer apply since the process would be affected by the improvement action. It was possible to recompute the control limits since an assignable cause had been detected and action had been taken to eliminate this cause. The revised control limits are calculated as shown in Appendix B by removing those subgroups that showed a lack of control on the 7(- and R chart and whose assignable cause had been detected and removed (subgroups 21 ,34,43,45,50). A point excluded on the R chart was not used to estimate 0 for the 32 chart. However, an assignable cause that affected a need not have had any effect on u, and vice versa [42]. Nevertheless, an out of control point was excluded from both X and R charts to simplify the hand calculations. The revised 7 chart had an UCL of 7.2 and a LCL of -3.4 and the R chart had an UCL of 19.4 and a LCL of O. In addition, the centerlines for these charts changed to a process average of 1.9 days and a range average of 9.2 days. Next, a rough estimate of the company's delivery process capability was made from the revised data with the out of control values eliminated. This was the value of a that might conceivably be obtained if the special causes of variation were eliminated and the process was brought into control. Since there was no previous measure of capability, this estimate based on the early unstable pattern in the study was the best available. Given that specification was to deliver within 4 business days of the promised delivery date, the process capability, Cp, was found to be 0.33 (see Appendix B). Since the minimum standard acceptable CI) is 1.33, it was concluded that delivery 81 performance would not be capable of conforming to specification even with the special cause eliminated. Even if the process was brought into statistical control, the process spread would still exceed the specification spread and further improvement would be required to improve capability. 33.7 W Delivery lead time data for every order received in the three months after improvements were made is shown in Tables 7 and 8 in Appendix B along with the lead time average and standard deviation for both material categories. ' The frequency histograms for Singlewall kraft board and doublewall, oyster and other board types are shown in Figures 33 and 34. Significant improvement in supplier delivery performance was realized in these three months. Supplier A's lead time for Singlewall kraft corrugated sheets dropped from 5.56 days to 4.50 days, and for doublewall, oyster and other types of corrugated sheets, from 7.67 days to 5.77 days. In addition, the standard deviations were smaller indicating that there was less variation in the delivery lead times. Therefore, the action taken to fax orders directly to Supplier A's production planner proved highly effective in reducing average supplier delivery lead time and variability. The average delivery lead time for Supplier B had also reduced, although not as significantly as Supplier A. The lead time for Singlewall kraft corrugated sheets dropped from 5.36 days to 4.66 days and the the lead time for doublewall, oyster and other types of corrugated sheets dropped from 6.96 days to 6.06 days. The standard deviation was also smaller. Therefore, the action taken to check overdue purchase orders proved effective in eliminating extremely late supplier deliveries. 82 lir ' w l D liv Aug-Oct 1989 60 -- 50- 40 -- Frequency 30 . 3:43;) ((11:31: 20.1 S \ 10- s V 0 :.:I:E:’3'.m.:::::::. 6 7 8 910111213141516171819 Lead Time (days) 51.133] HKEL‘ 1E 1121' Aug-Oct 1989 60 -— 50 .. 4O -- Y:4.66days Frequency 30 .- ‘ V s = 2.05 days s s 20» \ § i i 1... i NE 0 =41. 1”. :Elm :—: 12 3 4 5 6 7 8 910111213141516171819 Lead Time (days) Figure 33. Singlewall kraft corrugated board lead time frequency histograms 83 5152]! HE III: IE ”:1. Aug-Oct 1989 Frequency §§ s $3 §s - ii 0 _es.§e es 1234567891011121314151617 LeadTime(days) '0 01-1 JLLI.'-, v.0: Aug-Oct 1989 Frequency 7 8 91011121314151617 Lead Time (days) Figure 34. Doublewall and other corrugated board lead time frequency histograms 84 The next step was to determine whether a state of control over the delivery process had been established as a result of the attempt to eliminate the special causes of variation. Using the revised 75 and R control limits, it was found that not one data point was out of control. However, these revised control limits were only an estimate of how the process would behave after the improvement action was implemented. Therefore, the control limits for the actual data collected in the subsequent three months in Table 9 of Appendix B were calculated to determine whether the process was actually in a state of statistical control. Figures 35a and 35b show the i and R control charts and reveal that although one of the 52 subgroups was beyond the R chart UCL, the process had generally been brought into control. This point was assumed to be a random chance occurrence and part of the common cause variation. The control charts in Figures 35a and 35b reveal a significant improvement in delivery process performance. First, the assignable causes of variation were no longer present. In addition, the lead time error process average was reduced from from 2.2 to 1.5 days and the average range was reduced from 11.6 to 7.6 days. Since the improved delivery process was operating as a stable and predictable system, it was possible to use the process data to estimate the process capability. The frequency histogram in Figure 36 revealed the reduced process spread. It followed that in Appendix B the process capability index increased from 0.33 to 0.40. Although the process capability improved with the reduced process spread, the delivery process was still not capable of adhering to the specification since the Cp was still less than 1.33. 85 Lead Time Error 3? Congo] gran Aug-9c; 1282 Time Error (dayS) ,4 .. -3 : ID P l l l l l L l j j j 1 1 I I 161116212631364 4651 Subgroup Number Figure 35a. Lead time error X control chart 4O .. 30 ._ R Lead 20 UCL _ 16 3 Time Error ——————————————— (days) 10 O . ________________ 3517-- -10 I l J I l J J l l l 1 1611162126 31364146 51 Subgroup Number Figure 35b. Lead time error R control chart 86 N‘“-~‘---“ L ‘--~‘~‘--~‘~§---s I1 48-“ 32% Frequency 24— 16" 8 33 17 21 25 29 913 5 -ll -7 -15 Lapse Between Actual and Promised Delivery Date (days) Aug-Oct 1989 Figure 36. Lead time error frequency histogram 87 Even though the process had been brought into statistical control by removing the special cause of variation, it was still not capable of meeting the specification. The action required to continue the never-ending cycle of process improvement was only started. It is recommended that the company perform the following steps in order to detect and remove additional special causes of delivery trouble. 9‘ SAPS” P!" Take a random sample of 5 orders shipped for the day. Record the number of days lapse between actual and due delivery date, excluding all weekends and holidays. Determine the average and range of the 5 values. Plot the points on the appropriate chart. If the chart shows the sample is within the control limits and follows no special pattern, take no action. If the sample point is outside the control limits or follows a special pattern of variation, determine the cause and alert the plant and production managers to prevent the the problem in the future. Every month summarize all late delivery causes using Pareto analysis and discuss this with plant and production managers to determine appropriate conective actron. As long as a stable system exists, management is responsible for the implementation of changes for process improvement. Since only common causes of variation will prevail, management must also take action to investigate and determine potential improvements in the system. 88 3.4 39; Join]; Misalignment Box joint misalignment was a serious quality problem for Valley Container the since the joint often had a large variation in gap width between the top and bottom flap scorelines as illustrated in Figure 37. For quality measurement purposes, joint misalignment was defined as the largest misalignment between the bottom edges of a knocked-down box. On the production floor, this defect was commonly referred to as "fishtailing" because one end of the knocked-down box fanned out like a fish tail. Box width Box length Figure 37. Misaligned glued box joint 3.4.1 MW Glued box joint misalignment occurred in the Flexo folder-gluer operation. The follOwing steps were taken by the Flexo machine operator to convert corrugated board appropriately scored in the horizontal direction into 89 a finished box: W 1. Set up scoring heads and yoked slotting knives to specified vertical score lines. Set up slotting knives to coincide with horizontal score lines. Set up glue lap knives to specified blank length. Clean fountain and ink rolls from previous job and fill ink fountains with specified color. Set up printing plates according to specified print layout. . Set up electric compensators for proper location of printing dies and slotting knives. Set up understacker for blank width. Select bundle count. Set electric eye to set strap in middle of the bundle. . Continually feed hopper with appropriately scored and cut sheet blanks. . Score vertical score lines, slot, print and glue sheet blanks. . Fold box blank panels to align them parallel and glue them together. . Accumulate folded glued boxes in stack until specified bundle count is reached, then square bundle and push off to strapper. 14. Strap bundles and transport bundles on powered conveyon 15. Repeat steps 10-14 until specified quantity :10 has been processed. 5‘5”!" HHr—Iv—t m N H opws a 9 When a blank sheet was not lined up when fed into the machine, all subsequent machine operations were performed on a biased blank and the box joint was misaligned. The accuracy of the machine setup was equally critical in producing an aligned box joint. The vertical scoring and slotting knives must be properly aligned and the scoring knife must contact the corrugated board with enough pressure so that the board is easily folded by 90 the standard tension of the folding belts. In addition, insufficient or excessive tension in the folding belts caused one side of the box blank to drag as it passed through the Flexo machine and resulted in fishtailing. 3.42 W Box joint misalignment data was collected directly at the Flexo operation in a pilot program which introduced control charts on the shop floor. The sampling plan is shown in Figure 38. Rational subgroups were obtained by sampling a series of consecutive boxes from the Flexo machine that were produced as nearly as possible in time. Daily samples were taken at approximately hour intervals by the first shift machine operator for a period of one month. The box joint misalignment was measured to the nearest 1/ 16" since the accepted tolerance in the corrugated industry is 1/16" and since the machine operator cannot be expected to consistently read a scale which is any finer than this with any accuracy. In addition, insistence on more precise measurements in the early stages of SPC would have hindered its success. The raw data for joint misalignment along with the“)? and R values for each subgroup appear in Table 10 of Appendix C. 91 Samplingflan Purpose: To determine the natural tolerances of the box joint misalignment and average box joint misalignment. To estimate the common cause variation that occurs under normal operating conditions. Critical Characteristic: Variables data: Box joint misalignment (1/16"). Inspection Location: Critical operation number: 8 Critical operation name: Printing/Slotting F olding/Gluing Measurement method: Measure the largest difference between the bottom edges of a knocked-down box to the nearest 1/16". Subgroup: Sample size: 4 boxes Time period: 4 weeks, daily sampling, 4 times a day Number of subgroups: 64 subgroups Subgrouping method: Daily sampling every two hours (9:00,1 1 :00 am,l :00,3:00 pm) of 4 consecutively produced boxes. Type of chart: Frequency histogram and Y, R charts Record: 1. Sampling date 2. Order number 3. Joint misalignment for each box sample 4. Special circumstances Figure 38. Box joint misalignment sampling plan 3.431.“.1. S"l!l' The control charts for the initial joint misalignment data are shown in Figures 39a and 39b. The average joint misalignment was 0.77/16" and the average range between joint misalignment values was 0.6/16". As expected, both the X and R chart had many points out of control that were not part of the common cause variation in the system. Given this complex pattern, it 3.50 X x 3.00 2.50 _ 2.00 X Joint 1.50 Misalignment (1/16") . UCL=1.2 0.50 0.00 -050 -100, . . - - g - g - -; I I I I I I 16111621263136414651 Subgroup Number Figure 39a. Joint misalignment 7 control chart Joint Mi li R l A 9 R Joint 2 i' n Misalignment ———————————————— .__ “"6” 71H m nn 0 ........Ll..L_ U__LlllJl.lJJ_—l—:§f:, -1 CL: 1.4 H l l l l l J j l l I I I I I r I 16111621263136414651 ‘ Subgroup Number Figure 39b. Joint misalignment R control chart 93 would have been impossible to identify the assignable causes for each out of control data point. Therefore, the control charts were analyzed to isolate problems with process behavior. The nine data points above the 3? chart UCL were certainly noteworthy but the pattern of variation between the points on the control charts provided more valuable information. Specifically, the wide erratic fluctuations on the i chart indicated that over-adjustment was a problem. The process was investigated in order to determine the adjustment that affected the joint alignment the most. First, it was discovered that the folding belt tension on the Flexo machine was frequently adjusted to prevent fishtailing. It was decided that action would be taken to eliminate this process variable followed by the collection of new data. A frequency histogram for this process was constructed in Figure 40. The distribution revealed that a small number of boxes had a joint misalignment beyond the specified allowable 2/16". However, since the process data was erratic, it was impossible to predict whether this process behavior would repeat itself. Although based on unnatural process data, the process spread was estimated in order to establish a reference point for comparison. It was estimated that the process had a spread of $0.87/ 16" about a central value of 077/16". 94 1201- 100 -- ‘ § 80 ~- Frequency 60 .. 40 .. 20 ~- om exam—.- Box Joint Misalignment (1/16") Figure 40. Joint misalignment frequency histogram 34.4 W Following the decision to eliminate the wide fluctuations in joint misalignment caused by the folding belt tension adjustments, it was discovered that the folding belts on the Flexo machine were so worn and stretched that abnormally frequent tension adjustments were required. The folding belts were replaced in order to eliminate the need for adjustment. Management's willingness to invest time and money in an entirely new folding belt system was not based solely on the control chart information however. A second opinion from the machine mechanic confirmed the suspicion that folding belt replacement was long overdue and could have been causing the fishtailing. Data was again collected according to the established sampling plan in order to measure the effectiveness of the action taken. The raw data along with the 3(— and R values for each subgroup are in Table 11 of Appendix C. The effect of eliminating the folding belt adjustment can be seen in the control charts of Figures 41a and 41b. The Y chart indicates that although the average joint misalignment increased from 0.77/16" to 1.2/16", the wide erratic fluctuations were reduced. The process was more stable. In addition, although the average range had not changed, much of the instability on the R ' chart disappeared since significantly less data points were out of control. Unfortunately, the stabilization of the process did not establish statistical control and the process spread had actually increased to ;I-_1/16" about the central value of 1.2/16". Further action was required to detect and remove the special causes of variation apparent in the process in order to achieve statistical control. 3.50 3.00 2.50 2.00 - 7 Joint 1-50 - Misalignment 1.00 . (1/16") 0.50 . 0.00 4 -0.50-- -1.00 :::::::4 1611162126313641 Subgroup Number Figure 41a. Joint misalignment X control chart iMili X X X R Joint __________ _.__- ———UCL=1.6 Misalignment ‘ (“16> “ fl . a u n L . i=0-69 o.._' _”_U '_ In I xem fl 1 l 1 l l J -1 "l" 8 8 1 I I I I 1 1 611162126313641 Subgroup Number Figure 41b. Joint misalignment R control chart 97 34.6 W VVrth the aid of the Flexo machine operators, production manager, and plant manager, the cause and effect diagram for joint misalignment in Figure 42 was developed. 3.4.7 WWW Even though the process was still out of control, the machine operator was trained in the use and interpretation of control charts due to time constraints. The established cause and effect diagram was used to aid in the identification of special causes of variation. Since the control limits previously derived were unreliable since they were derived from an unstable process, a conservative UCL of 2/16" for the Y chart was established with the help of the plant manager. Judging from previous process behavior, this was determined to be the appropriate limit which would alert the operator to investigate special causes of variation. There was no LCL for the Y chart since the smallest joint misalignment possible was most desirable. These estimated control limits were to be used until the process was brought into statistical control and the operator was more experienced in the identification and elimination of special causes. The plotting of data points on the control chart was simplified in order to eliminate the need for a calculator on the shop floor since it was expected that a calculator would have been lost or stolen. However, hand calculations were also not desirable since a higher probability of error would have resulted. Therefore, instead of requiring the operator to sum the four sample joint misalignments and divide by the constant sample size of four to chart the sample average, the UCL and LCL were multiplied by four and the operator was instructed to merely plot the sum. The UCL for this version of the X 98 Man Flexo Folder-Gluer Machine Adjustment of Poor maintenance folding belts Large scorehead of folding belts Training clearance Too many sheets Insufficient fed into hopper pull roll pressure Sheets fed Kicker feed pressure crooked mechanism Improper scoring Worn gripper or slotting setup component Folding belts _ not positioned \Full stripper correctly X Fishtail Corrugated board does not score Lengtthepth easily proportion too Last sheet large fed Biased blank / No extended Small box glue tab dimensions Corm gated Board Box/Design Figure 42. Joint misalignment cause and effect diagram 99 control chart was 8 and the LCL was 0. Assuming that the 3(— chart would detect any large joint misalignments that would have been indicated on the R chart, an R chart was not initially used by the machine operator to maintain simplicity. 3.4.8 fireman 19m 1 Misalignment Statistical Anflysis The control charts for the first month of charting by the machine operator are shown in Figures 43a and 43b. The process average of 1.2/16" had hardly changed from the previous month and the average range was still approximately 0.7/16". The fluctuations in the data points had again substantially reduced however. The pattern indicated that special causes were definitely affecting the process but because it was only the first month of control charting by the machine operator, few of the special causes had been identified and eliminated. The lack of action taken by the machine operator was understood as a normal setback in the implementation of SPC. This particular employee had been working on this Flexo machine for 10 years and was very proud of his work. It could not have been expected that he would immediately change his normal method of quality control in favor of SPC. Therefore, management agreed to actively encourage the investigation and elimination of special causes as well as stress that SPC and the actions required were a necessary job requirement. Figure 44 is the frequency histogram for the out of control process and shows that the process average had increased and the process spread had decreased. Whereas the original distribution indicated a small amount of boxes had a joint misalignment beyond the specified allowable 2/ 16" misalignment, this distribution indicates that virtually none of the boxes had a 3.50 -- 3.00 .. X 2.50 -b 2.00 -- YJoint 1.50 —-I ------ Misalignment “Ad i = 1.29 (1/16") 1.00 ~- 0 50 -------------- - LCL = 0.81 0.00 .. -0.50 -- -1.00 : : t : : 1' : : 1611162126313641 SubgroupNumber UCL = 1.77 Figure 43a. Joint misalignment 7C control chart RJoint 2 '- Misalignment -— —— ___ (MW) 1 1 6 11162126313641 Subgroup Number Figure 43b. Joint misalignment R control chart 101 joint misalignment beyond the specified allowance. In addition, the distribution follows the normal distribution more closely indicating that more normal data was obtained without the erratic large and small joint misalignments. Although the distribution range reduced from 5/ 16" to 3/16" the process spread for this unnatural process had hardly changed since the process had a spread of i0.96/16" about the central value of 1.29/16" joint misalignment. 1 M' 11 l 120 q- ‘ V 100 .. 80 .1. Frequency 60 ~- 40 In- 20 .. \ 0 m : \ + URN : . 0 1 2 3 4 5 Box Joint Misalignment (1/16") Figure 44. Joint misalignment frequency histogram 3.4.9 Revi ed oint Mis li ent ta istical Anal sis The revised process average and distribution were calculated in Appendix C by removing those subgroups that showed a lack of control on the X and R charts in Figures 43a and 43b (subgroups 6,7 ,13,22,23,24,25,28,38,41). It was determined that a process average of 1.2/16" and an average range of 0.56/16" for joint misalignment might conceivably have been obtained if the 102 special causes of variation had been eliminated and the process had been brought into statistical control. An estimate of the company's box joint misalignment process capability was also made from the revised data. Since there was no previous measure of joint misalignment process capability, this estimate based on the unstable pattern was the best estimate available. Given the maximum joint misalignment allowance of US", it was determined that the Cp was 1.23, just slightly under the accepted minimum Cp of 1.33. It is expected that once this process is brought under control through further identification and elimination of special causes, the process will conform to ' specification. 4.1 Manual/smart Although this company was still in the initial stages of SPC implementation, significant quality improvement was realized in several quality problem areas. First, as a result of the special instructions SPC analysis and corrective action, the number of special instructions not followed decreased by 50%. In addition, the process distribution spread was reduced by 35% since the initial process ranged from 0% to 65% special instructions not followed and the improved process ranged from only 0% to 42% not followed. Second, as a result of the action taken on the delivery process to bring it into statistical control, delivery performance was improved. Specifically, the average number of days late was reduced by half a day which translated into a reduction of 21%. Had this process not been investigated and improved, deliveries would still be an estimated average of 1.9 days late instead of 1.5 days late. In addition, the delivery process spread reduced from the estimated initial process spread of 24 to a process spread of 19.8 for a 17.5% reduction. Since the process variation reduced and statistical control had been achieved, the improved delivery process was more consistent and reliable. 4.2 W The measured quality improvement was not expected to translate into improved productivity and increased profits within the first year of SPC implementation. During this initial stage, there were more significant benefits of SPC that were realized. The intangible gains of increased customer 103 104 satisfaction, better understanding of processes, increased quality awareness and improved communication were realized within the first year. 42.1 MW Customer satisfaction increased within the first year of SPC implementation since quality improvement in selected areas resulted in fewer defects reaching the customer. Specifically, the 50% decrease in special instructions not followed resulted in significantly fewer reported complaints and unsatisfied customers. In addition, because the variations in both the special instructions and delivery processes were reduced, a more uniform and consistent product was supplied to the customer. Since consistency and reliability were paramount to the customer, a reduction in variation brought increased customer satisfaction. The mere fact that Valley Container had introduced SPC into their quality program brought increased customer satisfaction since the customer was assured of receiving high quality products in the long run. During this initial stage, customers were pleased even though out of control situations were detected with the control charts since they saw evidence of improvement action being taken. In the long run, increased sales should occur as a result of increased customer satisfaction because of the multiplier effect on sales from a happy and satisfied customer [2]. As the company acquires a reputation for high quality, new customers should be attracted their low cost, high quality products. In addition, since many customer have required suppliers to implement SPC, Valley Container should win orders over its competitors who have not implemented SPC. Therefore, increased customer satisfaction will ultimately result in the tangible returns of increased market share and 105 increased profitability. 422 WWW Before SPC implementation, the quality levels and capabilities of these processes were not fully understood. Specifically, all that was known was that defective special instructions were causing customer complaints and that late deliveries and excessive RSC joint misalignment were jeopardizing customer accounts. With SPC, however, once a process was found to be in control, it was possible to estimate the process capability indirectly from quality control checks done on the actual products. For example, the special instructions process was found to be capable of following only an average of 70% special instructions and the delivery process was found to be 1.9 days late on the average. Given these estimates, it was possible to predict future process performance and conformance to specification. Finally, it was possible to quickly and reliably measure the effectiveness of corrective action taken to improve quality using the predictable process data. The control charting system used to monitor RSC joint misalignment on the Flexo folder-gluer machine provided a better understanding of the process. Although an accurate process capability could not be estimated, the chart indicated that the process was out of control and had special identifiable causes in need of corrective action. Before SPC implementation, the operator used his own personal judgment in machine adjustment and never completely understood the effect the adjustment had on product quality. Using a control chart however, the machine operator had a better understanding of the presence of assignable causes and as a result, more accurate adjustments were made on the machine. Therefore, even though no quality improvement had yet been realized in RSC joint misalignment, a valuable understanding of 106 the process had been achieved. Above all, the control charts indicated when an adjustment of the process was necessary to improve process performance. Specifically, the special instructions process analysis revealed that this process was stable and dominated by common cause problems in the system which could only be corrected by management through fundamental improvements in the system. Without such a statistical analysis, management might have continued to blame the workers for not following special instructions when in fact there were basic imperfections in the system. Management would have continued adjustment of a stable process and further increased variation without ever really improving quality. SPC successfully diagnosed the type of process adjustment required and quality improvement resulted from a better understanding of the process. The ability to accurately measure and understand the process capability of the Flexo machine was critical since the company was considering investment in a new Flexo machine. Due to the high capital investment of such a machine, it would be advantageous to understand the current equipment’s capability of conforming to specification. As soon as the box joint alignment process is brought into statistical control, an accurate estimate of the process capability can be made. This process capability index estimate will then be used to establish a performance specification requirement for a new machine and select between competing Flexo machine vendors. 4.2.3 Increased mafia Awareness Increased quality awareness was realized mainly because SPC was a very visible quality tool on the shop floor. Control charts at the Flexo folder-gluer operation and special instructions quality inspections were used all throughout the production and shipping operations. These were easily seen 107 by all the shop floor employees instead of being hidden at the end of the production line in a final inspection. The employees quickly learned that quality was an integral part of their performance since it was evidently important enough for management to get involved and take action to improve quality. Management support and involvement achieved more quality awareness than any motivational or promotional campaign could. The production atmosphere changed from one where average quality was accepted as the norm and quality was a hardly a topic of conversation to one in which quality concerns and problems were frequently discussed. 4.2.4 Improved ngmm'gatjgn Communication between management and shop floor employees significantly improved since SPC forced them to work together to solve quality problems. Instead of perceiving the workers as the problem, management consulted the workers for quality improvement suggestions since they knew more about the problems and faults in the system. When a process was found to be stable and predictable, as in the special instructions process, management consulted the workers for ways in which the system could be changed so that the workers could do their job better. After management acted on their suggestions, the workers overcame their fear of blame and rejection and began to participate more actively in quality problem solving. 42.5 W The productivity index used by Valley Container was the ratio of output to input for each critical operation; Initially, no significant increase in the productivity index was evident. The improvements in productivity as a result 108 of SPC implementation were too small in the initial stages to be measured. Nevertheless, there were important changes made in the process that allowed tasks to be done better, faster and easier. First, the changes made in the production worksheet layout made it possible for the workers to read the special instructions more quickly and more accurately. The improved system allowed the Flexo folder-gluer machine operator to quickly identify only those special instructions that applied to his area of responsibility. Finally , the initialing procedure allowed management to take corrective action more efficiently by saving time in identifying the responsible individual. A reduction in rework resulted in increased productivity since the number of defective special instructions reduced by 50% which meant that half the amount of rejects resulted. Instead of wasting time and effort picking up the rejected order, reworking it and shipping it out again, more time could be spent on the production of goods, thereby promising increased productivity. 4.3 Iimcandcarzitaunmmmmuimmems Management’s time commitment was one of the more expensive requirements of successful implementation of SPC. However, it was imperative that top management support and participate in SPC since no quality improvement would have resulted otherwise. Quality simply would not have seemed important to the workers. In addition, without management’s participation with the workers in quality problem solving, communication would not have improved. Therefore, an organization whose management cannot commit itself to motivate, support and take action for quality improvement should not consider implementing SPC. It was found that putting an effective quality improvement program into 109 practice need not be a capital intensive operation to achieve realistic gains. The two examples where measurable quality improvement was found were not very costly. The major part of the effort in SPC implementation must be directed at changing the attitudes of the workers toward their jobs. This involved training and education in the SPC defect prevention philosophy and statistical techniques. It was not new machinery or gadgets that brought improved quality but employees taking pride in their work and cooperating with management to solve quality problems with simple and inexpensive solutions. 4.4 Long Term Commitment It is important to realize that a full scale SPC program cannot be achieved after only one year. As more quality characteristics are controlled and improved with SPC, it will be possible to virtually eliminate the need for inspection. The next step to be taken is to improve the current raw material inspection procedure since the quality of the finished goods and services is highly dependent on the quality and consistency of the raw materials supplied. This study confrrrned that SPC is not a short-term quality control program but rather a long-term commitment to continuous quality improvement. Patience is the key to successful SPC implementation. It was easy to become discouraged and frustrated when the quantitative gains were not immediately recognized. However, by recognizing the importance of any improvement, no matter how small, and appreciating any gains, whether tangible or intangible, the entire organization was encouraged. Instead of deciding to abandon SPC after no substantial quantitative gains were realized in the first year, Valley Container has prepared for a long journey of never-ending 1 10 quality improvement. This company will be far ahead of its competition when its competitors finally realize SPC is critical to the survival of an organization in this new economic era. APPENDICES APPENDIX A SPECIAL INSTRUCTIONS ANALYSIS 111 APPENDIX A Table 1. S illn c'nNoFllwed Jul-Aug 1989 Subgroup Date Number Number Fraction 'v f iv 1 July 17 1 15 0.067 2 18 5 15 0.33 3 20 5 15 0.33 4 21 5 15 0.33 5 24 3 15 0.20 6 26 3 15 0.20 7 27 4 15 0.267 8 28 3 15 0.20 9 31 7 15 0.467 10 Aug 1 6 15 0.40 11 2 8 15 0.533 12 3 4 15 0.267 13 4 6 15 0.40 14 11 6 15 0.40 15 14 7 15 0.467 16 15 2 15 0.133 17 16 3 15 0.20 18 17 5 15 0.33 19 18 3 15 0.20 20 22 5 15 0.33 21 23 6 15 0.40 22 24 4 15 0.267 23 25 4 15 0.267 24 28 3 15 0.20 25 29 5 15 0.33 26 30 6 15 0.40 27 31 4 15 0.267 28 Sept 1 4 15 0.267 29 5 3 15 0.20 30 6 4 15 0.267 31 7 4 15 0.267 32 8 5 15 0.33 Total 143 480 112 Special Instructions Defective Jul-Sept 1989 p = _43 = 0.30 480 op= /m=/0.10x010= 0.118 n 15 p chart: UCL = 0.30 + 3(0.118) = 0.654 LCL = 0.30 - 3(0.118) = -0.054 APPENDIX A 1 13 APPENDIX A Table 2. Smcial Insguctjons Not Followed Dec-Jan 1989-90 Subgroup Date Number Number Fraction Number Defeggye Inspected Bfegive 1 Dec 5 2 15 0.133 2 6 l 15 0.067 3 7 3 15 0.20 4 8 4 15 0.267 5 ll 2 15 0.133 6 12 4 15 0.267 7 13 2 15 0.133 8 14 l 15 0.067 9 15 3 15 0.20 10 18 2 15 0.133 11 19 3 15 0.20 12 20 0 15 0.0 13 21 2 15 0.133 14 22 2 15 0.133 15 26 1 15 0.067 16 27 3 15 0.20 17 28 l 15 0.067 18 29 3 15 0.20 19 Jan 2 2 15 0.133 20 3 3 15 0.20 Total 44 300 1 14 APPENDIX A C H . . C l l . Special Instructions Not Followed Dec-Jan 1989-90 fi=ii= 0.146 300 GP = [m =[Q,14§1X5 0,854 = 0.09 n p chart: UCL = 0.146 + 3(0.09) = 0.416 LCL = 0.146 - 3(0.09) = -0.124 115 APPENDIX A Table 3. Smcial Instructions Initialed Dec-Jan 1989-90 Date Number Number Fraction Initialed 111W Dec 5 2 15 0.13 6 6 15 0.40 7 4 15 0.27 8 3 15 0.20 11 2 15 0.13 12 5 15 0.33 13 3 15 0.20 14 7 15 0.47 15 3 15 0.20 18 2 15 0.13 19 0 15 0.00 20 0 15 0.00 21 6 15 0.40 22 3 15 0.20 26 4 15 0.27 27 7 15 0.47 28 8 15 0.53 29 3 15 0.20 Jan 2 5 15 0.33 3 2 15 0.13 Total 75 300 Average Special Instructions Initialed = 11 X 100% = 25% 300 APPENDIX B DELIVERY PERFORMANCE ANALYSIS 116 APPENDIX B m D C N a D d 6 mm 4.Pm.., C mm. T .w. M A n m B Range R Average X 345 Time (days) 2 Sample Number 1 Subgroup Date Mmmr 8.4727716825327929 1 1 11 11111 1 1 1963795600347224908 1 11 111 21 3606040224402303663402220646242404026 0.0320232223231121321521323200230.10112 6224421012440424438446120102302040743 0 01 0 3329 6468016614M04111432435420910 .1 O1I... . 52 31...59420.00000255140005515604.2401.000442 323310101n44n04n71443045640144w404 2 . 5 2403795800H45120H55m451450140551M3 6 1 134590115 111 16 17 9356 1222 m m 112345670090 1 117 APPENDDCB Table 4. (cont’d) 38 6 0 1 14 1 1 3.4 14 39 10 l 6 0 3 -1 1.8 7 40 11 1 1 17 -2 2 3.8 19 41 12 2 4 -1 2 -3 0.8 7 42 13 3 0 0 4 1 1.6 4 43 17 0 2 32 2 15 10.2 32 44 18 l 4 5 -10 2 0.4 15 45 19 -1 2 0 34 2 7.4 35 46 20 -1 1 11 1 3 3.0 12 47 21 0 -6 0 5 6 1.0 12 48 24 0 0 2 5 -2 1.0 7 49 26 2 0 0 2 1 1.0 2 50 27 0 -l -16 29 0 2.4 45 Total 110.8 578 Tri n lLimi u ti n Lapse Between Actual and Promised Delivery Date May-Jul 1989 X = 110.8 = 2 2 50 R = 518: 11 6 50 X Chart: UCL = 2.2 + 0.58(11.6) = 8.9 LCL = 2.2 - 0.58(11.6) = —4.5 R Chart: UCL = 2.11(11.6) = 24.5 LCL = 0.00(ll.6) = 0.0 1m APPENDIX B d m o B W m w L...» m% irl kmm 108qu n w... M m T r e h u S hrA 45429 45457 55446 86466 4363m 63864 44444 44454 44567 44568 53575 54545 My 6646 000041 H846 98H47 44H54 84344 U8355 36667 76084 1 65046 1 65344 36145 km 449 955 3004 694 757 744 555 6764 5766 3776 9576 4477 July N 7573344 7573445 8393446 4494746 4553434 5563234 5556234 2366646 2B66743 2466854 55772553 4 550079154 W M 4635 6142 6H62 6663 6663 4775 5756 67M4 6833 38454 3w685 004655 km 5576 4572 5637 7747 47474 44684 44675 44645 34754 35755 35866 75786 July 119 APPENDIX B Supplier Lead Time for Singlewall Kraft Board May-Jul 1989 51121211214 Time (days) Frequency . x f 1x 1x2 1 1 1 1 2 1 2 4 3 11 33 99 4 48 192 768 5 28 140 700 6 28 168 1008 7 16 112 784 8 11 88 704 9 6 54 486 10 4 40 400 11 3 33 363 15 1 15 225 Total 158 878 5542 x = 8.2.8 = 5.56 s = 42 - (5.56;; 2.04 158 158 E n 11' .1 . C l l i Supplier Lead Time for Singlewall Kraft Board 3? 120 APPENDIX B May-Jul 1989 53mm Time (days) Frequency x f 1x 1x2 2 9 18 36 3 24 72 216 4 42 168 672 5 37 185 925 6 35 210 1260 7 26 182 1274 8 10 80 640 9 3 27 243 10 2 20 200 11 1 11 121 14 2 28 392 15 1 15 225 18 1 18 324 Total 193 1034 6528 = 103 = 5.36 s = 6528 - (5.36)2 = 2.26 193 193 Su lier Lea Time da 8 f rDou lew May-Jul 1989 June July June July \l\l \000 MON #00 05: 0‘83 p—r #Qh 88610111011 “0‘ one 4:3: 7 l 0 mr-I U.) p—r No x)“, 7 8 121 Table 6. Sppplier A VIA So 045: \OQ p—r qU) 00 Cho‘ Uta: 055‘, 00% \100 mm p—t °°O\ OH.» Ostr APPENDIX B d Other Board 5548 31088 O‘xl Sq J>0~ 651111 5244 5620 5377710263 122 APPENDD( B E 12' 'l . C l l . Supplier Lead Time for Doublewall, Oyster and Other Board May-Jul 1989 Sum Time (days) Frequency x 1 1x 1x2 2 1 2 4 3 2 6 18 4 5 20 80 5 8 40 200 6 10 60 360 7 8 56 392 8 10 80 640 9 4 36 324 10 2 20 200 11 2 22 242 12 l 12 144 13 4 52 676 15 3 45 675 17 l 17 289 Total 61 468 4244 x = 468: 7.67 s =fl244 - (7.67)2 = 3.30 61 61 m1, 123 APPENDIX B i ' i 1 i n Supplier Lead Time for Doublewall, Oyster and Other Board May-Jul 1989 W Time (days) Frequency x f fX 1x2 2 2 4 8 3 4 12 36 4 6 24 96 5 5 25 125 6 6 36 216 7 8 56 . 392 8 5 40 320 9 1 9 81 10 4 40 400 11 4 44 484 17 1 17 289 20 1 20 400 Total 47 327 2847 x = m = 6.96 s 75847 - (6.96)2 = 3.48 47 47 124 APPENDIX B vi . . l . Lapse Between Actual and Promised Delivery Date May-Jul 1989 (Eliminating subgroups 21,34,43,45 and 50) f: 85,4 :19 45 R = 412: 9.2 45 X Chart: UCL = 1.9 + 0.58(9. 2) LCL = 1.9 - 0.58(9. 2) = R Chart: UCL = 2.ll(9 2.) = LCL = 0.00(9 2.) = May-Jul 1989 Estimate of o = 9.2 = 4.0 .326 UPSL=1.9+3(4.0)=13.9 LPSL = 1.9 - 3(4 0.)=1 Cp= 4-(-4)=0.33 6(4.0) 125 APPENDIX B ft Board Table 7. her Lead Time d s for Sin lewall Aug-Oct1989 Su Supplier A 765634 326244 453424 653434 554444 793334 4352243 6352443 55m3425 453M255 4636625 4655648 me A 0093455 603234 744434 334435 3344563 5444666 3345335 .3340435 3345145 3252545 3552565 4432515 M. 375684 576357 576359 766455 303758 404659 304674 304774 6357556 533247mw 733558H 7355888 5544 6737 6322 6334 6341 4333 4364 4435 74344 65396 05394 75354 Aug 77 7004 354 356 356 256 536 544 434 535 435 Sept 334 336 324 545 574 4D4 755 9445 4555 00455 7334 Oct 126 APPENDD( B ' 1 l i n Supplier Lead Time for Singlewall Kraft Board Aug-Oct 1989 WA Time (days) Frequency x j fX 1x2 0 6 O O 1 2 2 2 2 15 3O 6O 3 50 150 450 4 52 208 832 5 52 260 1300 6 25 150 900 7 16 112 784 8 8 64 512 9 4 36 324 10 2 20 200 11 2 22 242 Total 234 1054 5606 X‘ = 1054 = 4.50 s = 5606 — (4.50)2 = 1.93 234 N U.) 4:. 127 ~ APPENDDC B n Di ' ' 1a i Supplier Lead Time for Singlewall Kraft Board Aug-Oct 1989 1i r Time (days) Frequency x f rx fX2 O 1 O O 1 1 1 1 2 4 8 16 3 29 87 261 4 33 132 528 5 29 145 725 6 13 78 468 7 12 84 588 8 2 16 128 9 3 27 243 19 1 19 361 Total 128 597 3319 X = 521: 4.66 s = 1 - (4.66;: 2.05 128 128 128 APPENDIX B f rDo lew 11 O ster and ther Board 9 00 .9 811 e t l m m u A a d m .T d m cm 1 u lier A 565 5003 665 7007 775 332 952 962 576 8n1U.I8 O 5133 00643 Aug 44 69 69 63 610 11 386 973 646 653 28B 272 754 Oct 31055105 2 4 3 Sept Oct 9751135561734 129 APPENDD( B E E' .1 . C l l . Supplier Lead Time for Doublewall, Oyster and Other Board Aug-Oct 1989 mm Tune (days) Frequency )1 f fX fXZ 0 1 0 0 l 1 1 1 2 7 14 28 3 13 39 117 4 11 44 176 5 12 60 300 6 19 114 684 7 13 91 637 8 8 64 512 9 7 63 567 10 5 50 500 11 1 11 121 13 2 26 338 Total 100 577 3981 X = 511: 5.77 s 732816.779 = 2.55 100 100 130 APPENDD( B E D' 'l . C l 1 . n Supplier Lead Time for Doublewall, Oyster and Other Board Aug-Oct 1989 311121251113 Tune P (days) Frequency ‘- x 1’ DC 1x? 1 1 1 1 t 2 1 2 4 3 4 12 36 4 4 16 64 5 7 35 175 6 3 18 108 7 2 14 98 8 3 24 192 9 2 18 162 10 2 20 200 11 1 11 121 17 1 17 289 Total 31 188 1450 )‘Z’ = 1_&8_= 6.06 s = 4go- (6.06)2 = 3.17 31 31 131 APPENDIX B Promised live Date 'mma Aug-Oct 1989 La se Between Ac Average Range X R Time (days) Ehmkamr 3 4 5 12 Number Subgroup Date 4704635497084440876137464505615058386 11 11 1 2 1 1 1 ..l. 11 8400424022626606426880228600624220020 1110102140400013410312033032000002101 307950.“..564514222150.]..H12423400544400351.. n4140441441oa133914236272413420328205 4383122164144442140024415014134710061 01032.301.12.520a022220115263322313444.47..1002.50 650500043403201H6440000464N4440032000 123 7890 567234589115 23 8 4 1H1112222223t 7H11fimwmflfl%flww45 u w m A S 12345678901234567890123456789 23 11111111112222222222m4fl33aflafiwafl 132 APPENDIXB Table 9. (cont’d) 38 6 -2 0 0 2 2 0.4 4 39 10 0 -1 -4 5 10 2.0 14 40 11 -1 3 1 2 3 1.6 4 41 12 -1 3 O 0 8 2.0 9 42 13 4 2 -l 1 8 2.8 9 43 16 5 -1 3 1 l 1.8 6 44 17 l 0 7 l 1 2.0 7 45 18 4 0 0 4 4 2.4 4 46 19 -l -4 7 3 l 1.2 11 47 20 9 O l 1 5 3.2 9 48 23 5 0 5 5 7 4.4 7 49 24 -1 0 -4 3 7 2.6 8 50 25 2 2 7 12 0 4.6 12 51 30 2 2 6 6 -2 2.8 8 52 31 0 -6 4 4 0 0.4 10 Total 79.8 399 C 11' . C l l . Lapse Between Actual and Promised Delivery Date Aug-Oct 1989 if = 19.5 = 1 5 52 R = 322 = 7.7 52 X Chart: UCL = 1.5 + 0.58(7 LCL = 1.5 - 0.58(7 R Chart: UCL = 2.ll(7. 6) LCL = 0.00(7. 6) 77 .7 1.36 0.0 ) ) 6.0 3.0 133 Aug-Oct 1989 Estimate of o = 2.6 = 3.3 2.326 UPSL = 1.5 + 3(3.3) = 11.4 LPSL = 1.5 - 3(3.3) = -8.4 = 4-(-4) =0.40 Cp 6(3.3) APPENDIX B APPENDD( C BOX JOINT MISALIGNMENT ANALYSIS ON THE FLEXO MACHINE Subgroup N r—u—a HOOOOQONUIJ>UJNH NHHHt—H—H—AHH O\OOO\)O\M4>~UJN NNN 0)th 24 N UI Dt Aug \O\O\OOOOOOO\I\)\)\I 134 Table 10. Box int Mis ' Aug 1989 ent n Flexo Misalignment (1/16") Tim 9:30am 11:45 am 2:00 pm 6:40 pm 11' 3.0 am 3:00pm 5:00 pm 9: 30am 11:00am 3:15 pm 9: 00am 11:30 am 4:00 pm 6. 30 pm 9: 15 am 10: 05 am 4:00pm 5:00pm 9: 00am 9. 45 am 12: 45 pm 2:00pm 3: 20pm 4:00 pm 6:05 pm 8: 35 am 10:45 am 1:00 pm 3:00pm 9:00am 11:003m 1:00 pm 3:00pm 8:30am 11:00am 2:30 pm 9:00am 1 OOHooov—IOHOHt—u—u—IHHHOHOHmHt—IHNQOHOOOHHNHO OHOQQOOOHOHHHt—aHHt—IOHOOhNt—IHNHHHOOOv—u—Nt—tt—s OOHOOOOOOOHHOOOOOOHHHMHHHNv—HHOOOt-H-th-H-t 2 34 ODHOOOOOOOHHOHCHOOHHOWNHHNOOHOOOHHNHH a m Pppprrpppppprppwrrrwpprppprrwro 8888888d8d38888888888888888888 0.00 APPENDIX C Sample Number Average Range R OHHOOOHOHOOOHHHHHOOHHHHOOOHHOOOOOOOOH 135 APPENDIXC Table 10. (cont’d) 38 25 11:00am 1 1 1 1 1.00 0 39 25 1:30pm 1 1 1 1 1.00 0 40 28 8:30am 2 3 3 1 2.25 2 41 28 10:50am 1 l 3 2 1.75 2 42 28 1:10pm 0 0 0 0 0.00 0 43 29 11:35am 0 0 0 0 0.00 0 44 29 1:30pm 1 l 1 1 1.00 0 45 29 2:50 pm 1 0 l 0 0.50 1 46 30 6:20am 0 1 0 l 0.50 1 47 30 8:30am 1 0 l 0 0.50 l 48 30 10:10am 1 0 0 0 0.25 1 49 30 10:503m 2 0 0 0 0.50 2 50 30 11:30am 1 1 2 1 1.25 1 51 30 2:00pm 1 1 1 l 1.00 0 52 30 3:00pm 1 2 1 2 1.50 1 53 31 9:00am 3 5 3 2 3.25 3 54 31 5:45 pm 1 0 l 0 0.50 1 55 31 8:20pm 1 0 1 O 0.50 1 Total 42.50 33 Box Joint Misalignment on Flexo Aug 1989 X=42.5Q=0.77 55 R=fl=0.60 55 X Chart: UCL = 0.77 + 0.73(0.60) = 1.208 LCL = 0.77 - 0.73(0.60) = 0.332 R Chart: UCL = 2.28(0.60) = 1.368 LCL = 0.00(0.60) = 0.0 Subgroup Number NHt—tr—u—I—ar—ih-H—dh-dr—a OOWQQm-thHOOOOQGM-kmNr—a‘ NNN AWNB Date Sept \IQQQQO‘QMUIUIUIU. 136 Table 11. Box Joint Misalignment on Flexo Sept 1989 Misalignment (1/16") Sample Number Av§rage Range 3 4 Time 9:00 am 11:00 am 1:30 pm 3:00 pm 5:00 pm 9:00 am 11:00 am 1' .30 pm 3:00 pm 9:00 am 11:20 am 2' 30 pm 9:30 am 11:45 am 4:00 pm 9:00 am :00 pm 1 : "553 pm am :30pm 3. 30pm 9:00am 11.20am 1:00pm 3:30pm 9:30am 1:00pm 3: 10pm 1:00pm 2:30pm 10:00am 1:00pm 3:00pm 9:20am 83288 1 o HHmr—IHUJt—I 12 Noh—ih-lh—fih-II-iHWHNHWHHNNHHHHNHONNNHHHHHHHHHN NOHHt—iHHNNoHer—AHv—n—OHHHHHr—sNt—r—INt—H—tNr—at—Itov—H—Ih HHHHHHHt—imor—iHNHHHHOHt—IOHHHNh—iI—it—INNHNHD—INt—fim OOHHv—H—n—u—tmOt—Ar—ih-H—aHHNHHHONHr—INNNNNNHHHNNNh 7‘97‘7‘7‘2‘7‘1‘NPT‘T‘PFT‘T‘I‘.°T‘!‘.OE‘E‘.OPE‘1‘7‘2"?!"I"E"!"!"f".m assessssduuessassassaasssaaaaaussaaus APPENDIX C NHOOOOOt—lHHHONOOI—IHHOOHHOHor—lHHh—IHHHOHHHN “'1”: 137 APPENDIXC Table 11. (cont’d) 38 27 11:00am 2 1 1 1 1.25 1 39 27 3:30pm 1 1 1 0 0.75 1 40 27 5:45pm 2 1 1 l 1.25 1 41 28 9:20am 1 1 1 1 1.00 0 42 28 11:00am 1 1 1 1 1.00 0 43 28 2:30pm 1 l 0 0 0.50 1 44 28 4:30pm 1 1 1 l 1.00 0 45 Oct 2 11:00am 1 l 1 1 1.00 0 Total 54.50 31 Box Joint Misalignment on Flexo Sept 1989 55:54.5:121 45 R=31=0.69 45 2 Chart: UCL = 1.21 + 0.73(0.69) = 1.71 LCL = 1.21 - 0.73(0.69) = 0.70 R Chart: UCL = 2.28(0.69) = 1.57 LCL = 0.00(0.69) = 0.0 tr" ' - 138 Table 12. Box Joint Migfligmnent on Flexo Oct 1989 Misalignment (1/16") APPENDIX C Subgroup Sample Number Average Range Number Date Time 1 2 3 4 X 1 Oct 6 9:00am 1 2 1 1 1.25 1 2 6 10.00am 1 2 1 2 1.50 1 3 6 1:00pm 1 1 1 1 1.00 0 4 6 3:30pm 1 1 1 1 1.00 0 5 9 11:00am. 1 l 1 1 1.00 0 6 9 2:00pm 3 3 3 3 3.00 1 7 10 9:00am 3 3 2 1 2.25 2 8 10 11.20am l 1 1 1 1.00 0 9 10 1:00pm 1 2 1 1 1.25 1 10 10 3:00pm 1 1 2 2 1.50 1 11 11 9:30am 1 2 l 2 1.50 1 12 11 4:00pm 1 1 l 1 1.00 0 13 11 5:10pm 2 2 1 0 1.25 2 14 12 11: 30am 1 1 1 1 1.00 0 15 12 1:00pm 2 l l 2 1.50 1 16 12 2:30pm 1 1 2 2 1.50 1 17 16 11:20am 2 1 1 1 1.25 1 18 16 1:30pm 1 1 1 1 1.00 0 19 16 3:30pm 2 2 1 1 1.50 1 20 16 4:30pm 1 1 1 1 1.00 0 21 16 6:00pm 1 1 1 1 1.00 0 22 17 2:30pm 2 3 1 2 2.00 2 23 18 1:00pm 2 2 2 2 2.00 0 24 18 3:00pm 1 0 0 1 0.50 1 25 19 9:30am 0 0 0 0 0.00 0 26 19 11:45am 2 1 1 1 1.25 1 27 19 2:30pm 1 1 2 1 1.25 1 28 19 4:30pm 2 2 2 2 2.00 0 29 20 11:45am 2 1 1 1 1.25 1 30 20 3:10pm 1 1 1 1 1.00 0 31 20 5:00pm 1 2 1 1 1.25 1 32 24 11:00am 1 l 1 1 1.00 0 33 24 1:20pm 1 1 1 1 1.00 0 34 24 3: 30 pm 2 1 1 2 1.50 1 35 24 5.00pm 2 1 1 1 1.25 1 36 25 11' 3.0am 1 1 1 2 1.25 1 37 25 1:20pm 1 1 1 1 1.00 0 139 APPENDD(C Table 12. (cont’d) 38 25 3:00pm 2 2 3 2 2.25 1 39 26 1:00pm 1 1 1 1 1.00 0 40 26 3:00pm 1 1 1 1 1.00 0 41 26 5:30pm 1 1 0 0 0.50 1 42 30 10:00am 1 1 1 2 1.25 1 43 30 2:30pm 1 1 1 2 1.25 1 44 31 3:00pm 2 1 2 2 1.75 1 Total 56.75 29 C 11' . E1 l . Box Joint Misalignment on Flexo Oct 1989 35:35.15: 1.29 44 fi=22=066 44 X Chart: UCL = 1.29 + 0.73(0.66) = 1.77 LCL = 1.29 - 0.73(0.66) = 0.81 R Chart: UCL = 2.28(0.66) = 1.51 LCL = 0.00(0.66) = 0.0 thrmf-‘fi'fimj 4 1 L h'.—‘ __._._-_ _ ' 1 40 APPENDIX C 1 . Box Joint Misalignment on Flexo Oct 1989 (Eliminating subgroups 6,7,13,22,23,24,25,28,38 and 41) X=fl= 1.2 34 E = 12: 0.56 34 Estimate of o = _jS = 0.27 2.059 UPSL = 1.2 + 3(0.27) = 2.01 LPSL = 1.2 - 3(0.27) = 0.39 Cp = 2 - Q = 1.23 6(0.27) BIBLIOGRAPHY 10. 11. 12. BIBLIOGRAPHY J uran, J .M., Japanese and Western Quality - A Contrast, Quality Progress, December 1980, Volume XI, #12, p. 10. Deming, W. Edwards, Out of the Crisis, MIT: Cambridge, MA, 1986. Tribus, Myron and Tsuda, Yoshikazu, W New Economic Era, MIT: Cambridge, MA, 1985. Walton. Mary. Welt/1mm, Pedigree Booksz New York, 1986. Gitlow. Howard S..M1mng_GJnde_tLQna1mLend_Cempetme Position, Prentice-Hall: NJ, 1987. Ryan. Thomas R, Went John Wiley & Sons: New York, 1989. Katz, Donald R., We, Business Month, October, p. 57. Crosby, Philip B., W, McGraw-Hill Book Co.: New York, 1984. Messina, William S., Mm, John Wiley & Sons: New York, 1987. Moen, Ronald D. and Nolan, Thomas W., W, Quality Progress, September, 1987, p. 62. America's Quality Coaches, Excerpted from "Quality Coaches", sponsered by Dow Chemical Company, CPI Purchasing Magazine, 1 986. Bartnik Allan C W, Journal of Packaging Technology, May 1988, p. 198. 141 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 142 Sinha, Madhav N. and Willborn, Walter, W, John \V11ey & Sons: New York, 1985. Juran J...M Gryna.FrankM QualimlilanningendAnalxsis. McGraw-Hill Book Company: New York, 1980. Harrington, Dr. H.J., MW, McGraw-Hill Book Company: New York, 1987. Bhattacharyya, Gouri K. and Johnson, Richard A., W W, John W11ey & Sons: New York, 1977. Grant, Eugene L. and Leavenworth, Richard 8., ° mm, McGraw-Hill Book Company: New York, 1988. Ott, Ellis R., W, McGraw-Hill Book Company: New York, 1975. Carlson, David A., W, Tappr Journal March 1988, p. 75. Cowden Dudley J W. Prentice-Hall: Englewood Cliffs, NJ, 1964. “Estern Electric Co.. WWW Mack Printing Co.: Easton, PA, 1956. Juran, J.M., WW, McGraw-Hill Book Company: New York, 1962. HICHIGRN STATE UNIV. LIBRRRIES 1|HIWIINWWWIWWI"HI"llWlWll‘llHll 31293006122620