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A 5?§JDY OF f‘Av‘J-ééé‘ii EPETERFERESCE
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DEMANDS

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MICM‘GAH STA‘E'E UNEVERSWY
Eéward .i: $9§k
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This is to certify that the

thesis entitled

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ELISE ASSIQEE‘CVFTS FIITJXILIIEG IIOET-WIIFORVT
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presented by

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has been accepted towards fulfillment

of the requirements for

[:85th QM ‘0 ' egree “IMF“ 7”"? ' 91 infineorinff

   

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Major/professor

Date [august E, 1955 ‘

 

0-169

A STUDY OF Iv’ACTiII‘E ILLLRE'E’TEECE IN LULTI-IUXCEEII-L’E

1
H

13'“
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CIE'JG DEE-T713.

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A331 GIFT~EITS WTI'AILIZ’IG NOE? -'JII T ' ()3le

by

Edward J. Polk

A TESIS
Submitted to the College of Engineering,
Michigan State University of Agriculture
and Applied Science in partial fulfillment
of the requirements for the degree of

WSEE‘? OF SCIENCE
Department of .‘vzechanical Engineering

1958

U]

 

”6-9.”

((3
6‘

II.

III.

VVVII .

’3”

’t

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C

TABLE OF CCIJ'IE’I‘TI‘S

Introduction
Direct Measurement of I-Bchine Interference
Statistical Methods of Determining Machine Interference

Limitations of the Dale Jones Machine Interference
Tables

Application of the Dale Jones Interference Table‘

Mathematical Basis of the Dale Jones Machine
Interference Table

The Prdblcm
The Literature Survey
The Thesis Objective
The Experiment Method
Use of Random Number Tables
Selecting the bhchine to be serviced
Determination of Interference
Scope of the Experiments
Experiment Analysis and Results
Standard Deviation.
Control Limits

Correlation Between Experiment Results and the Dale Jones
Interference Table

Page

10
11
11
in
11+
17
l9
19
22

2h

VIII.

IX.

X.

TABLE OF cormmrs (cormmrED)

V
C

The Interference Estimation Adjustment Factors --
Interference Prdblem.Example

Summary
Recommended Further Related Research

Appendix
Bibliography

11

Page
25

3h

35
36

37

Figure
Number

1

2

4r

(13wa

10
ll
12
13
1h
15
16
17
18
19
20

21

 

TABLE OF ILLUSTRATIONS

Dale Jones Machine Interference Table

Use of Random.Tables

Experiment Results -- lO machines @ 9%?)

Interference Graph -- lO machines @‘90%

bhximum Standard Deviation Values,(71n

Machine Interference Graph
Machine Interference Graph

Machine Interference Graph

Standard Deviation
Control Limits for
Experiment Results
Interference Graph
Experiment Results
Interference Graph
Experiment Results

Interference Graph

. Experiment Results

Interference Graph
Experiment Results
Interference Graph

Experiment Results

(Maximum Possible),

Machine Interference Curves

-- h machines @ 80%
-— h machines @ 80%
-- h machines @‘90%

-- h machines @ 90%

-- 1} machines @ 100%
-- h machines @ 100%
-- h machines @2120%
-- h machines<Q 120%
-- 7 machines @ 120;;

-- 7 machinesl@ 120%

iii

—- h machines
-- 7 machines

-- lO machines

10 mchines @ 60%

Page

13
16
21
28
3O
31

37

bl

1*3

M;

1&5

1+7

la

50

51

Figure
Number

22

TABLE OF

Interference Graph
Experiment Results
Interference Graph
Experiment Results
Interference Graph
Experiment Results

Interference Graph

IILUSEI'RATIOIIS (Goren-rum)

10
IO
10
10
10
10

10

machines
machines
machines
machines
machines
machines

machines

iv

e 6053
@ 80,3
@ 8071
@ loo;
@ 100%
@ 1206;?

@120;-

Page

Machine interference is the idleness a machine experiences when it
is non-productive, awaiting servicing by its operator who is servicing
sane other machine in the assignment.

Shasurement of machine interference has long been a perplexing
manufacturing problem when one operator is assigned to several randomly
serviced machines. The measurement of machine interference is necessary
in order to properly schedule production, plan work loads and incentive
pay operators in multi-machine assignments.

The recently deveIOped Dale Jones Interference Tables have proved
satisfactory for closely estimating machine interference in assignments
entailing completely random servicing demands, where the durations of
servicing demands are approximately the same and when the total extent
of servicing demands of all machines is the same.

Since the Dale Jones Interference Tables have been mathematically
Proven to be correct under these uniform conditions, this experiment was
undertaken to expand the tables to include the non-uniform condition where
different machines in assignments have significantly different degrees of
total servicing requirements. This thesis research has evolved a
mathematical method of adjusting the Dale Jones Interference Table values

to accommodate the aforementioned non-uniform condition.

I. INTRODUCTION

Machine interference is the idleness a machine experiences when it
is non-productive, awaiting servicing by its operator who is servicing
sane other machine in the assignment. If two or more machines assigned
to one operator require servicing simultaneously, machine intereference
exists on those machines requiring attention and not being tended by the
operator. Machine interference does not exist on the machine receiving
the attention of the operator, but does exist for those machines waiting
for the services of the operator.

The productive effects of random machine interference are apparent
in cloth weaving, for example, when looms incur yarn breaks simultaneously;
as the operator is tying yarn on one loom, the other idle looms experience
machine interference. Industrial occurrences of random machine inter-
ference are also common in wire drawing, tinning, and covering; winding
operations and automatic screw machine assignments.

The effect of machine-interference delays is to reduce machine
'output. Consequently, all activities concerned with productivity and
work measurement of multi~machine or multi-process assignments must
consider the extent of such reductions. Management problems concerned
with machine interference are: production scheduling, work load planning,
incentive paying of the operator, machine scheduling, labor standards for
cost estimating, machine efficiencies, and economic assignment of machines

to Operators.

When there is one machine for an Operator to run, the standard
machine cycle before allowances is the sum of machine running time plus
the operator servicing time during which the machine is idle. When there
are several machines for an Operator to run, the above machine cycle time
is made longer by the additional machine interference time.

If two machines require the services of an operator simultaneously,
one machine must wait due to machine interference until the Operator
completes his work on the first machine. As more machines are assigned

to the operator, it follows that the interference time delay will increase.

Direct Measurement of Machine Interference

 

Direct measurement of interference delays for a specific work
situation can yield accurate results. However, certain difficulties exist
which make direct measurement undesirable. The stopwatch Observations
must be made over long and continuous periods Of time. Not only does it
take considerable time to Observe and summarize a representative sample
of the assignments, but the studies require an adeptness, alertness, and
persistence that will overtax most Observers. It would be difficult to
Observe and record the activity and inactivity of several machines and the
Operator. As the number Of machines assigned to an operator is increased,
the amount of data that must be recorded is also increased, thereby making
the time study difficult for the Observer.

After the studies have been taken, analyzed, and calculated, the
obtained machine interference is applicable only for the specific situation
that was under study. New assignments involving different numbers of

machines, different work loads, etc., must be studied separately.

It therefore follows that this method of determining machine interference

allowances can be very time consuming and uneconomical.

Statistical NEthods of Determining Machine Interference

 

PrObability assumptior 5 provide the basis for mathematical solutions.
PrObability solutions proceed from one of three possible approaches: the
binomial, the normal curve, and the Poisson exponential. The early attempts
employed the binomial expansion. These pioneering efforts suffer in their
final results because Of omitting interference delay itself when taking I
ratios to the total cycle. Recent binomial solutions by Dr. Dale Jones
have rectified the error.1

The Dale Jones machine interference values are based on certain

requirements the t must be satisxied before the tables are valid or Closely

estimating machine interference.

Limitations of the Dale Jones PT chi.e Interference Tables
The interference table is valid when the following conditions prevail:
1. One Operator tends the machines unassisted.
2. The servicing demands of the machines are random and cannot
be coordinated to permit a fixed servicing sequence that

would minimize or eliminate machine interference.

3. The duration of the individual servicing times for all of
the machines must be equal.

h; The total extent of servicing demand, i.e., the "work load"
must be the same for all of the machines.

As previously mentioned, this thesis considers assignments in which
requirement No. b is not fulfilled.
l

Nmynard, H. 3., Industrial Engineering Handbook, McGraw-Hill Book
Company, New York, 1956.

1:...

Application of the Dale Jones Interference Table

The application of the Dale Jones Interference Table will now be
illustrated. Assume one operator is to tend eight carpet looms, each Of
which would randomly require one minute servicing time per ten minutes
elapsed time if individually tended. Assume also the durations of the
machine servicings are equal. Now, to estimate the per cent of elapsed
time each of the eight looms will experience machine interference,

a. Determine the total work load on an individual attention

basis. This is 8 l min. ’lOO or 80¢.
10 min. (

b. Locate the 80% Work Load column and project downward
vertically to the row of interference values representing
eight machines (see left vertical column) to obtain 6.5
per cent interference per machine. Thus, according to the
Table, each of the eight looms will eXperience machine
interference approximately 65 out of every one~thcusan
minutes of elapsed assignment time.

TABUEI

AVERAGE PERCENTAGE INTERFERENCE PER MACHINE VERsus
Tom. PERCENTAGE WORK LOAD 01-~ Ass1CNED MACHINES

 

 

N0. Operator's Total Percentage Work Load" on Individual Attention Basis
Maths. 50 55 60 65 70 75 80 85 90 95 [00 105 110 115 120

_______.__,__..—_—______._—

 

 

 

 

 

 

4 1.2 4.0 4.1 1.1 6.9 1.0 9.4 10.9 12.1 14.1 11.9 17.9 19.1 21.7 21.7
1 2.1 1.1 4.2 1.1 6.1 7.2 1.1 9.9 11.4 11.0 14.1 16.7 11.6 20.1 22.6
6 2.1 1.1 1.7 4.1 1.1 6.1 7.1 9.0 10.1 12.1 11.7 11.7 17.7 19.6 21.7
7 2.2 2.7 1.1 4.1 1.0 6.0 7.1 1.1 9.7 11.1 11.0 14.11 16.1 11.1 20.9
1 1.9 2.4 1.0 1.7 4.1 1.1 6.1 7.7 9.0 10.6 12.2 14.0 16.0 11.2 20.2
9 1.7 2.2 2.1 1.4 4.2 1.1 6.0 7.2 1.4 9.9 11.1 11.4 11.4 17.6 19.7

10 1.1 2.0 2.6 1.2 1.9 4.7 1.6 6.7 7.9 9.4 10.9 12.9 14.9 17.1 19.4
11 1.4 1.9 2.4 1.0 1] 4.4 1.1 6.1 7.1 1.9 10.1 12.4 14.4 16.7 19.0
12 1.1 1.1 2.2 2.1 1.1 4.1 1.0 1.9 7.1 1.1 10.1 12.0 14.0 16.1 11.6
11 1.1 1.7 2.1 2.6 1.2 1.9 4.7 1.6 6.8 1.1 9.7 11.6 11.6 16.0 11.1
14 1.2 1.6 2.0 2.4 1.0 1] 4.4 1.1 6.4 7.7 9.1 11.2 11.1 11.7 11.0
11 1.2 1.1 1.9 2.2 2.1 1.1 4.2 1.1 6.1 7.4 1.9 10.1 11.0 11.4 17.1
16 1.1 1.4 1.1 2.1 2.7 1.1 4.0 4.1 1.9 7.0 1.1 10.1 12.7 11.0 17.6
17 1.1 1.1 1.7 2.0 2.1 1.1 1.1 4.6 1.6 6.7 1.2 10.2 12.4 14.1 17.4
11 1.0 1.2 1.6 1.9 2.4 1.0 1.6 4.4 1.4 6.1 7.9 9.9 12.2 14.7 17.1
19 1.0 1.1 1.1 1.9 2.1 2.9 1.1 4.2 1.2 6.2 7.7 9.6 12.0 14.6 17.2
20 0.9 1.1 1.4 1.1 2.2 2.1 1.4 4.1 1.0 6.0 7.1 9.1 11.1 14.1 17.1
21 0.1 0.9 1.2 1.1 1.1 2.1 2.1 1.4 4.2 1.2 6.6 1.4 10.1 11.7 16.9
10 0.7 0.1 1.0 1.2 1.6 2.0 2.4 2.9 1.7 4.6 1.9 7.7 10.2 11.1 16.1
40 0.1 0.6 0.1 1.0 1.2 1.1 1.1 2.1 2.9 1.7 1.0 6.1 9.4 11.2 16.6
10 0.1 0.1 0.6 0.1 0.9 1.2 1.1 2.0 2.1 1.2 4.2 6.1 9.1 11.2 16.6
71 0.2 0.1 0.4 0.1 0.6 0.1 1.0 1.1 1.7 2.2 1.1 1.2 9.1 11.1 16.1
100 0.2 0.2 0.1 0.4 0.1 0.7 0.9 1.1 1.1 1.9 2.1 1.1 9.0 11.0 16.1

Figure 1. Dale Jones Machine
Interference Table

Lethematical Basis of the Dale Jones Machine Interference Table

 

Let 3d equal the expected ‘external“ servicing time (Operator‘s
walking, working and any necessary relaxing time that must be taken at
an expense of lost production) per unit of product on any given machine,
i.e., that servicing which must be done while the machine is non-productive.

Let Sr equal the expected “internal" servicing time (Operator's
walking, working and any necessary relaxing time) per unit of product on
any given machine, i.e., that servicing which can be done while the machine
is productive. Those internal duties which normally can be economically
interrupted and/or deferred in order to avoid interference are not to be
considered in this category.

The walking time in both Sd and Sr is based on the average walking
that would be necessary if the number of machines in the assignment were
tended together.

let R equal the average machine's running time per unit of product.
Then S, the portion of overall time any machine would need servicing, if
individually tended from a point involving average walking when the number
of machines in the assignment are tended together, i.e., the machine's
work load on an individual attention basis, is:

(Sd + Sr) 1 (Sd + R)

When one operator tends "n“ machines having running cycles that
cannot be coordinated, machine-interference idleness will occur. Let ”1“
equal the average portion of overall time that each machine would be non-
productive because of machine interference if all "n" machines were tended

by one operator. Since their average servicing ratio is ”S”, the

01

average portion of overall time that each of the machines would require

servicing when tended together is 8(1 - i).

 

Let "d" equal the average portion of overall time that each of the
”n” machines in an assignment is idle because of ”S“ duties and inter-
ference. Then,

das(l-i)+i (l)

The probability that a machine will require servicing at any given
moment is ”d“. The probability that it will not require servicing at any
given moment is l - d. The probability that none of the "n" machines will
require servicing at any given moment is (l - d)n, while the prdbability
that one or more machines will require servicing at a given moment is
1 - (l - a)“.

As previously mentioned, these statements of prdbability are exactly
true only where the ”"8 for each machine in the group is the same as for
every other machine in the group. However, the use of the average “S"
for the machines in the group introduces only a small error when applied
to typical multi-machine assignments, according to the interference-computer
experiments and subsequent research findings.

The average ratio of servicing time per machine to overall time when
"n" machines are tended together can be expressed as follows:

S(l-i)-l-(l-d)n+n (2)

Equations 1 and 2 are the basis for the Dale Jones Machine
Interference Table. The values in the table were determined in the
following Harmer. Convenient "d” and “n" values were substituted in

Equation 2 in order to obtain the respective (l - i) values. Then the

respective "i” values were determined by substitution in Equation 1, and
the respective S values were obtained in the same way. Finally, ”n5”
products versus respective ”i“ values were plotted graphically for various
”n” values, thus obtaining the values presented as average percentage
interference per machine (100 1) versus total percentage work load (100 ns)
of assigned machines in the Dale Jones Interference Table. The proof of
this Table is presented in the Appendix.

Practical conditions do not generally correspond fully to prdbability
laws or any other theoretical conditions; therefore, a small error is
inherent in the statistical measurement of machine interference due to the

assumption that all of the four aforementioned conditions prevail.

The Problem

 

The Dale Jones Machine Interference Table is applied to many multi-
machine operations in industry. However, the Table is not valid for
estimating interference in assignments where there are great differences
in work loads of individual machines comprising the assignments. Since a
significant proportion of multi-machine assignments are of this type, the

need of this thesis research was suggested.

II. THE LITERATURE SURWBY

"A Study of Machine Interference in Multi-Hachine Assignments

Entailing Non-Uniform Servicing Demands” is the title of this thesis.

From the inference of the thesis title, it is evident that the search

has been for writings dealing with the establishment of machine inter-
ference times where the servicing demands of the machines comprising the
assignments are not uniform. Machine interference allowances for non-
uniform servicing demands could not be found in the search of the literature.

It was soon evident that there were many complicated ways of predict—
ing machine interference and that probability assumptions provide the basis
for mathematical solutions. However, all of the tables assumed uniform
servicing demands of individual machines where the Work loads were the
same, as in the case of the Dale Jones Machine Interference Table. None
of the tables provide for estimating average interference where the servicing
demands of the machines comprising the assignments are not uniform.

Those that have made major contributions in the field of machine
interference are Bernstein, Jones, Wright, Sandberg, Benson, Brunnschweiler,
Field, Palm (Sweden), Muller (Holland), Ashcroft and O'Connor (England).
Ashcroft believes that the machine interference time stays approximateiy
the same even if the servicing demands of the machines comprising the
assignments are non-uniform. The author of this thesis will show that

non-uniform servicing demands of machines in an assignment will cause the

machine interference allowance to vary greatly even though the total work
load of the operator is the same in each case.
Recent articles are ”Machine Interference" by H. Holmes in Time and

Motion Study, February, 1958. Sawell Publications Limited, London, and

 

“The Assignment of Workers in Servicing Automatic Machines” by Palm in

the January-February, 1958 issue of the Journal of Industrial Engineering.

 

These writings, in addition to those previously written, do not establish
values to cover non-uniform servicing demands that are being investigated
by the author.

Of the various proposed solutions to the problem of estimating
machine interference, only that evolved by Dr. Dale Jones is accompanied
by proof, presented in the Appendix. However, it is noteworthy that the
interference values of Jones and Ashcroft are in quite close agreement.
This thesis writer's preliminary experiments verified the validity of
the Dale Jones (and therefore the Ashcroft) Interference Tables when
applied to assignments having the aforementioned uniform servicing

demands.‘

III. THE THESIS OBJECTIVE

The Objective of this thesis is to study machine interference in
randomly serviced multi-machine assignments tended by one operator where
different machines randomly require different total degrees of servicing

but where the duration of individual servicings is always the same.

10

IV. THE EXPERIMENT AND METHOD

After many experiments had been conducted without knowing what
variable was causing the machine interference values to vary, a correlation
appeared to be evident. It seemed that, for any given total assigned work
land, there was a direct relationship between the average per cent machine
interference and the dame of variation of individual work loads of the
machines canprising the assignment. This, then, led to a whole new set
of experiments that had to be conducted in order to determine if a

relationship existed .

Use of Randan Number Tables

 

The objective of the many experiments conducted in behalf of this
thesis was to simulate representative multi-machine assignments having the
aforementioned non-uniform servicing demands. Random number tables were
used to simulate the desired conditions for the sake of the experiments.

Numbers fran 00 to 99 were selected from the randan tables to
represent percentages of from 1 to 100 for the various assumed service
loads fix the machines. The results of a typical experiment are illustrated
in Figure 2. Since the experiment assumes four machines are assigned to the
operator, four columns of numbers are used with each column representing a
machine. Machine 1 was assumed to r6qu1re thirty per cent servicing if
individually tended. Thus, the numbers 00 through 29 are circled in the

column representing the activity of Machine 1, to represent the times that

11

12

service was randomly needed. The same thing was then done for the remain-
ing machines in the simulated assignment, depending on the assumed servicing
per cent demand for each individual machine.

Still referring to Figure 2, forty numbers are shown in each column
which indicates that forty observations were made as to whether the machine
required service or not. The total size of the sample in the experiment was
250 Observations. In other words, for each machine, 250 numbers were
Observed to see if servicing was required; if service was required, the
numbers were circled .

After the required numbers were circled in each column which represents
a machine, i.e., after the random shut downs of the assumed assignment were
established as indicated by the circled numbers, the next step was to start
with the top row of numbers and go thrOugh each row and select the machine
that was to be serviced. If no circled numbers were present in a row, no
service was required and this meant that the operator was idle for this
simulated interval of time. If one circled number is present in a row,
then service was required for that machine during the interval of simulated
time by that row. When two or more circled numbers were present in a row,
machine interference existed on all of the circled numbers except the one

that was selected for servicing.

 

 

 

 

 

 

 

 

 

Figure 2.

Service Per Cent 30 S 20 25'
Service Numbers 0-29 0- 0-19 O-2h
Machine #1 i2 ,4} 3 iii;
50 . 67 70 1+8 59 7h 78 ll
50 68 2h 66 93 51 6h 35
11+ 1h 07 no 15 8h % 82
92 21 08 h 61 56 88
02 05 25 é 1+3 21 92 56
8h 35 67 91 68 77 70 69
1+9 12 65 82 L1 ® 61 31+
69 73 25 1+8 20 51 91 72
92 117 31 10 59 67 12+
27 31+ 116 92 ° 27 56
711 92 51 21 6% 35 72
10 81+ 61 1&2 52 99 15
1+2 #6 12 b9 5 61 76
96 1+2 27 91 75 52 80
23 75 21, 8 23 ® 9 26
37 31 56 18 23 ® 31+
75 00 2h \ 30 21+ 59 53
93 38 05 1+1 90 61 1+2
, 71 hi o2 h6 98 hi 35 99
35 13 111 38 23 51 90 2o
61 79 83 36 32 o 90
7h 93 87 31+ 06 97 5
83 8o 116 1+3 73 h? 92
05 83 31+ u 58 (g3 67 36
96 ‘30 88 g 113 9 1+1. ch
80 17 33 70 28 35 13
61 28 36 9 06 £39 61* 118
hg 58 5h 86 18 2 56 13
27 141 25 55 33 ® 95
1+3 112 85 1+2 98 S6 67
79 16 51 27 76 96 77
31+ . 92 82 Q9 37 91 78 7o
79 95 5h 1 55 99 66 h1
18 21 10 71+ 68 23 no 15
95 us 92 36. 58 1+3 ()9 90
96 68 73 97 75 6 70 71
21+ 11+ 110 Q 59 27 87
51 81 27 61+ 1+8 95
01 89 67 92 27~ 76 1+8
98 62 32 99 75 81 6%
Service Observ. lO 1 7 EL. 15R
g3 . Gbserv. 2 5 T L13
otals

 

 

 

Use of Randan Tables

selecting the Machine to be Serviced

 

When reading a book we read from left to right. The same system was
used in the experiments when selecting the machine to be serviced when more
than one circled number existed in a row of numbers. After a circled
number has been chosen in a row, the experiment analyst then dropped down
to the next row and selected the next circled number to the right of the
row in which the previous selection (servicing) was made. When, in drop-
ping down to the next row in which a circled number appears, the experiment
analyst finds no circled numbers to the right of the row in which the previous
selection was made, he selects for servicing the circled number farthest to
the left in that row. With this service selection procedure consistently
followed, there is no partiality in the selection of the machine to be

serviced.

Determination of Interference

 

The machines or circled numbers that have not been selected for
service are then crossed out, which denotes interference. However, the
crossed out circles still require service, so the numbers directly below
are circled and reconsidered in the next row along with any other circled
numbers in that next row.

After following through with this system for 250 simulated intervals
of time, the results are then totaled in this manner:

a. The circled but uncrossed numbers are totaled to obtain the
total number of servicings during the period of time simulated
by the experiment.

b. The crossed out circles are totaled to obtain the total number
of machine interference waits.

15

The total service per cent is determined by dividing the total'service
observations by the 250 time intervals (rows) represented in the experiment.
The average interference per machine is determined by dividing the total
interference waits by the product of the total number of time intervals
(rows) and the number of machines assigned. An example of the experiment
results is shown in Figure 3. Note that ten experiments, all involving the
same intended total machine work load (on an individual attention basis)
for the ten assigned machines, have been conducted. In the first experiment
(see column for C': 0) each of the ten machines had a nine per cent work load
on an individual attention basis. Thus, the standard deviation of these
individual assigned machine work loads was zero. In the second experiment
the assigned machine work loads were 10, 8, 7, 10, 9, 8, 9, 9, lO, and 10.
The standard deviation of these work loads was 1.0 per cent unit, as shown.

Note, in the second experiment, that there were 178 servicings in the
250 observations (time intervals) of the experiment involving 10 machines.
Thus, the aparator was engaged in servicing machines 100 (178) e 250, or
77.8 per cent of the elapsed time of the simulated assigmnent. Also, note
in.this experiment there were 136 interference waits. Thus, the average
per cent interference per machine for the ten machines was 100 (136) s 250 (10),

or 5.h5 per cent.

16

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V. SCOE’E OF THE BEERII-EIITS

One hundred experiments, each involving 250 observations, were
conducted. Ten experiments were made for each of ten machine assignments
involving a desired total work load. These ten experiments gave enough
points to determine if a trend existed between the average interference
per machine and the standard deviation of the work loads of the machines
comprising the assignment. The ten basic assignments, in reference to
number of machines and total work load of all the assigned machines, were
as follows:

Number of Machines Total Work Load

 

 

. . . . . . . . . . . . . 80
.......9o
. .. . 100
.............120
.............120
10 . . . . . . . . . . . . . 6
lO . . . . . . . . . . . . . 80
10.............9o
1o.............1oo
10.............120

NtF-F'L"

As previously mentioned, the results of the experiments shown in
Figures 2 and 3 typify all of the experiment results in experiment method
and results calculations. The remainder of the experiment results are in
the Appendix. The use of the random number tables for the 100 experiments
was so extensive that these 600 pages are submitted under separate cover.

Because of the enormous amount of work required for the experiments,

the experiments had to be limited to those machines and assignments shown

17

18

on page 17. However, as will be shown, the degree of correlation between
standard deviation of work loads of individual machines and average inter-
ference per machine is so great that the results and conclusions obtained
in behalf of these experiments would very likely apply to assignments
involving greater numbers of machines than those represented in the

experiments.

VI. WHEN? ANALYSIS AND RESULTS

In addition to this thesis, under separate cover is 500 pages of
random table analysis and 100 pages of summary sheets. There is a summary
sheet for every five pages of random numbers which constitutes one experiment.
Ten summary sheets provide the data that is shown in the Appendix of this
report under the title of Experiment Results. A sample of this, Figure 3,
has already been discussed and explained.

To measure the dispersion of the per cent service load for the
machines comprising each assignment, the standard deviation of the per cent
service loads was calculated and shown in the top row of each of the

Experiment Results sheets.

Standard.Deviation

To measure the amount of variation of the non-uniform servicing

requirements from the uniform servicing requirements, the standard

deviation of the per cent service loads was calculated with the following

formula:

 

G. (xl--3i)2+(1:2--3'E)2+(x3ux)2+(zen-3?)a
N
Where:
6' a standard deviation of the per cent servicing loads
- per cent service load for machine #1

x1

19

20

x2 3 per cent service load for machine #2
i = average per cent service load

N a number of machines tended by the operator

If the per cent servicing load is the same for all of the machines
in an assignment, then the average per cent service load would be equal to
the per cent servicing load of any of the machines. Therefore, the standard
deviation of the per cent servicing loads would be zero. All of the values
shown in the Dale JOnes Interference Table have a standard deviation of zero,
because the Table values assume the per cent servicing load is the same or
equal for all of the machines in any given assignment.

Referring to the curve shown in Figure h, each of the points on the
graph represent the results shown in Figure 3. The per cent average
interference per machine is plotted against the standard deviation of the
Per cent service loads. Referring again to Figure h, the Dale Jenes
Interference Table value of 7.9 per cent can be seen where the line
intersects the vertical axis. The Dale Jones Interference Table values,
which assume G'of assigned machine work loads is zero, is the starting
Point for all of the curves in all of the experiments. The other point
that determines the line is the maximum sigma value or standard deviation
of the per cent service loads which is the point of intersection with the
horizontal axis. The maximum sigma value of 27 was calculated by assigning
one of the machines the total service load of 90 per cent, and the remaining
machines in the assignment were given zero per cent service loads. This,
of course, 1. an extreme and theoretical possibility. This method of

determining the curve end points was used in establishing all of the curves

for the rest or the experiments.

 

 

 

 

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As can be seen in Figure b, all of the values fall within the
control limits bounding the curve. This is also true of the results of

all of the other experiments shown in the Appendix.

Control Limits

 

In order to determine if the experimentally determined inter-
ference values were significantly different frrnxthe respective curve

values, control limits were established with the following formulas:

 

U.C.L. . P + 2‘43,1 _ p2

 

L.C.L. P - 2Yp’l - £2

n
where :
p . per cent average interference per machine
n . number of observations (250)
U.C.L. - upper control limit

L.C.L. a lower control limit
Referring to Figure h, when the standard deviation of the per cent
service loads is zero, the per cent average interference per machine reads
7.9 per cent (where the interference line intercepts the y-axis). Since
the number of observations is 250 in every experiment and the per cent .
average interference per machine is 7.9 per‘cent, the substitution into

the formula is made as follows:

 

U.C.L. = .079 + 2 / .079 (l - .079f .113 or 11.37%

7 250

 

L.C.L. . .079 - 2V .079 (I - .0793— =- .Oh5 or 14.5%
250

The upper control limit of 11.3 per cent and the lower control limit
of h.5 per cent can be read on the Y-axis of Figure h. The formula provides
95 per cent confidence interval, i.e., results of the experiments will fall
within the upper and lower control limits 95 times out of 100.

In addition to the sample of results shown in Figure h, the other

experiment results are shown in the Appendix.

. V“. n“..-‘F

“—123“.
.

VII. CORRELATION BETWEEN EXPERIMENT RESULTS AND
THE DALE JONES INIERFERENCE TABLE

In order to make use of the Dale Jones Interference Table values
as a determining point for the lines that were established in determining
the per cent average interference per machine, it must also be proven
that the Table values are correct. As stated before, the Dale Jones
Interference Table value is shown at the point of intersection of the
machine interference curve with the Y-axis, where the standard deviation
of the total service load per cent is zero. Upon examination of the_
results of the experiments shown on the graphs where the standard deviation
of the total service load per cent is zero, it can be found that all of
the points fall within the control limits. The experiment values can be
checked on the Interference Graphs shown in the Appendix and on the sample
graph in Figure h.

Considering the points that were established from the experiments,
the line of best fit would closely approximate the line between the two
points (the Dale Jones Interference value point and the maximum standard
deviation point). Figure b shows the Dale Jones machine interference
value of 7.9 per cent (at zero standard deviation) and an interference
value of 0% at the maximum possible standard deviation of 27.

On the basis of all of. the experiment results, typified in Figure u,
it can be definitely stated that there is close correlation between the
results of the experiments (when the servicing demands are equal) and the

Dale JOnes flhchine Interference Table values.

2h

VIII. TEE WNCE ESTIMATION ADJUSTI‘vfiE'NI' FACTORS

The interference estimation adJustment factors can easily be
determined, because a straight line relationship exists between the standard
deviation of the per cent work loads of the individual machines and the
average per cent interference per machine. Since the striight line
relationship exists, the straight line formula can be applied to determine
the average per cent interference per machine when non-uniform servicing

demands exist. The straight line formula is:

y :- mx + b
where:
y .- the unknown value on the line
m a the slope of the line
x a the value along the X-axis

b - the intercept on the Y-axis

It now seems suitable to convert the terms used in the straight

line formula to those terms that have been used consistently when discussing
Ptoblems dealing with machine interference. Referring again to Figure 14,
and considering the straight line formula, the following symbols can be
. used in the development of the formula for determining machine interference
when non-uniform servicing requirements are necessary.

37 - represents "1", the per cent average interference per machine

m - represents the slope which is always negative

x - represents "0' ", the standard deviation of the per cent
service loads

25

26

b - represents “J”, the Dale Jenes Machine Interference
Table value
By substituting the preceding code letters into the straight line formula,
the formula becomes:
1 . J - mCT
Since the slope is always negative and can be represented by __£__, where
0"

(Tm is the maximum standard deviation where the interference lige

intercepts the X-axis, the formula then becomes:

iaJ- JG
(7m

 

iIJ l- 6
Wm

 

The formula is now in its finalized form where,

i a the per cent average interference per machine to be
calculated

J u the Dale Jones Interference Table value of the per cent
average interference per machine

(5 . the calculated standard deviation of the non-uniform
per cent service loads

6h a the maximum standard deviation of the non-uniform per
cent service load where the machine interference line
intercepts the X-axis.
Interference Prdblem Example
In calculating the average per cent interference per machine, the
following simple method is used. Assume that the following assignment

exists:

27

Machine Number 1 2 3 h

 

_ Per Cent Service Load 17 5 33 25

The total service load for the four machines is 80 per cent, so when the
80 per cent total service load is divided by the four machines, the average
per cent service load, i, is 20 per cent. The standard deviation of the

total service load per cent is calculated first as follows:

 

 

C; :\( (xl - E02 +’(x2 -'i)2 + (x3 -‘§)2 + (xh - §)2

7.
L‘

 

6 'Y (17 - 220)2 + (5 - 20);); (33 - 20)2 + (25 - 201?

6 a 10.3 per cent units of the service loads

The maximum standard deviation, (Tm, for four machines with a total
service load per cent of 80 is already known to be 3h.6 from the maximum
standard deviation table in Figure 5. Various values were calculated to
establish the graph for easy reference when maximum standard deviation
values were needed for four, seven, or ten machines.

Referring to Figure l, the J'value from.the Dale Jones Interference
Table for four machines with a total service load of 80 per cent on an
individual attention basis is 9.h per cent. The values are now ready for
substitution into the formula.

1 a J 1 - 6 a 9th 1 - 10.3 a 6.7%
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The average per cent interference per machine would then be 6.7
per cent by making use of the formula method. The steps in Obtaining
the solution were:

1. Calculate the standard deviation of the total per cent

work load,67.
2. Obtain the maximum standard deviation of the total service f}
load per cent, cm, from the graph in Figure 5. I
1
3. Cbtain the J'value from the Dale Jones Interference Table i
in Figure l.
h. Calculate the average per cent interference per machine 5
using the formula, ' ’

l=J(—6)
O’m

There is a second method (a graphical method) for determining the
average per cent interference per machine that is a little simpler than
the method Just described. Using the same data in the prdblem Just solved,
the standard deviation of the total per cent work loads would have to be
determined with the same formula. The answer would again be 10.3 per cent
units of the service loads for step one above. Steps two and three would
be eliminated in this solution method and the final answer would be
determined by referring to Figure 6, where the graphical solution is shown
for four machines at various total work loads. Since the 10.3 per cent
units of the service loads (standard deviation) has been calculated and
the total work load of 80 per cent is known, the intersection of the 10.3
per cent standard deviation of the total work loads with the 80 per cent
total work load line, will give the answer of 6.7 per cent average

interference per machine.

 

 

 

 

 

 

 

 

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33

The steps for the graphical method solution for the average per
cent interference per machine are:

1. Calculate the standard deviation of the total per cent
wark load, 0".

2. Determine the average per cent interference per machine
from the machine interference graph.

14 machines - Figure 6
7 machines - Figure 7
lO machines - Figure 8
The family of curves developed for the various total work loads
for four, seven and ten machines was easily established. The Dale Jones
Machine Interference Table value is used for determining one point at the
Y—axis, and the maxim standard deviation, o’m, determines the other point
to establish each line for the various total work loads.
Even though the servicing time for the machines vary, the machine
interference time can be easily determined by following through the two

simple steps above .

. -. :——_.——.—-— :‘T—I?

_. , .9-
.. __.. ...,,,,

IX. SUMMARY

The problem involved in this thesis was to find a simple method
of determining machine interference times when different machines in an
assignment have different work loads and where the servicing was of a
random nature. Various solutions are available where the work loads do
not vary, and the statistical method was used for the solutions. An
example is the Dale Jenes Fbehine Interference Table shown in Figure 1.
This is the onLy proposed solution to the prdblem of estimating inter-
ference where machines have uniform servicing demands which is accompanied
by proof of the solution. Because of this, and because of the agreement
of the experiments of this thesis and the Jenes values for assignments
entailing uniform machine servicing demands, the Jones Interference Table
was the foundation or starting point of these experiments.

The research conducted for this thesis has yielded a tool for
expanding the Dale Jones Machine Interference Table to include estimates
of machine interference for assignments where different machines have
significantly different operator work loads. The methods of determining
the machine interference when the work loads are non-uniform can be

found on pages 29 and 33 of this thesis.

3h

 

X. RECOI‘fl‘IEI‘IDED FURTHER REIATED RESEARCH

The experiments conducted for this research considered only four,
seven and tan machines; therefore, further experiments are necessary to
confirm the straight line relationship for any number of machines. Since
the same relationship is expected to exist for any number of machines, it
is recommended that experiments be conducted to include four through one
hundred machines.

Due to the enormous amount of worh that is necessary to conduct
GXperiments where many machines are involved, it is further recommended
that the experiments be set up so that they can be programmed into a
canputer. After sane investigation, it is firmly believed that this
tYDe Of experiment can be programmed into a computer.

After further investigation, it seems likely that these experiments
can be done at the Buick Motor Division or at the General Motors Technical

Center where these computers are available.

35

APPENDIX

 

 

E IBLI OGRAPH‘Y

Benson, F. Machine Interference, Textile World, Dec. 1953.

 

Bernstein, P. How Marv Automatics Should a Man Run, Factory Management
and Maintenance, March 1913f.

 

Brunnschweiler, D. Machine Interference, Textile World, Dec. 1951+.

 

Denholm, D. H . , How Many Machines per Operator, Factory Management and
Mainteance, July 1951;.

 

Field, J. W. Machine Utilization and Economical Assignment, Factory
Management and Maintenance, August 1915.

 

Heard, J. H. Machine Interference Problem, Michigan State University, 1955.

 

Holmes, H. Iviachine Interference, Time and Motion Study, Sawell Publications
Limited, London, February 1958.

 

Jones, D. Cuick Way to Figure Machine Interference, Factory Management and
Maintenance, July 1951+.

 

Wage Incentive Payment forgiultiple Machine Assignments, Georgia
Institute of Technology, 1939.

Maynard, H. B. Industrial Engineering Handbook, McGraw Hill Book Company.
New York, 1956.

 

O'Connor, T. F. Allocation of Machines to Operators, Inst. MeChanical
Engineering Process, 1952.

 

Easy Way to Allow for Machine Interference, Textile World, Dec. 1952.

__

gov Four Factors Affect Ashcroft Interference Tables, Textile World,
Dec.“1955.

Palm. The Assignment 0f Workers in Servicing AutomaticI Machines, Journal
of Industrialfngineering, January» .‘ebruary 195B.

 

Vaughn, W. B. Report on Random Number Machine Interference ExPeriment,
Michigan State University, I955.

Wright, W. R. Machine Interference, Mechanical Engineering, August 1936.

 

37

_< ___——.._..—-_—--=—s

._ ...“...

PROOF OF THE DALE JONES INTERFERENCE TABLE

The accuracy of the average machine interference values shown in
the Table can be proved as follows:

1.

Assume one operator randomly tends 6 machines, each of
which would randomly require 20 per cent servicing if
individually tended. Assume the durations of the servicing
are equal. The total work load on an individual attention
basis (i.e., in absence of machine interference) for the
assignment is 6 x 20% or 120%.

Referring to the Dale Jones Interference Table, Figure l,
the average per cent interference per machine for 6 machines

having a 120 per cent total work load is 21.7 per cent of
elapsed time.

When all 6 machines are tended together the per cent
servicing time per machine is 20% (1 - i) or 20% x (1 - .217)

or 15.66%.

When all 6 machines are tended together, the per cent down
time per machine is this 15.66 per cent servicing plus
21.7 per cent interference, or 37.36 per cent.

The probability of any given machine running at any given
moment when the 6 machines are tended-together is 100% -
37'3“ a 06261;.

The prdbab%lity of all 6 machines running at any given moment

is (.626h) , according to the general law of compound probability.
Therefore, the prdbability of one more machines being down at
any given manent is l - (.62616) or .9396. This is the
portion of elapsed time the operator is servicing the machines.

The per cent servicing time per machine is therefore, 93.96% 9 6

or 15.66%.

An interference value of 21.70 per cent shown in the Table is
the only value which will cause the values in Step 3 and Step 7
to agree. This checking procedure applies to all interference
values shown in the Table.

38

73

_.___i_— ___'i

Total Machine

Number of Machines

 

 

Load Per Cent h 7 16
60 26.0 21.0 18.0
80 3t.6 28.0 2u.0
90 39.0 31.6 27.0
100 h3.3 35.1 30.0
120 52.0 u1.6 36.0

Figure 9. Standard Deviation
Maximum Possible)(0;)

39

into}; ...-..«a

Total Per Cent

 

 

 

lechine Load h 7 lO
60 U.C.L. .075 .056 .0u6
L.C.L. .021 .010 .006

80 U.".L. .131 .10h .085
L. .L. .057 .039 .027

90 U.C.L .167 .13t .113
L.C.L .083 .060 .ous

100 U.C.L. .205 .173 .1u8
L.C.L. 113 0087 m0

120 U.C.L. .291 .260 .2hu
L.C.L. .183 .158 .1hh

Figure 10. Control Limits for Machine
Interference Curves

 

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