Factors influencing ship repair part consumption

FACTORS INFLUENCING SHIP REPAIRPART CONSUMPTION

Richard Alan Lippert

LIBRARYNAVAL POSTGRADUATE SCHOOt

MONTEREY, CALIF. 93940

NAVAL POSTGRADUATE SCHOOL

Monterey, California

THESISFACTORS INFLUENCING SHIP ]REPAIR

PART CONSUMPTION

by

Richard Alan Lippert

William Thomas Lee

Thesis Advisor: J. K. Hartman

Approved Ion. pubtic KoXoxubd; d-istnibLutcon untvrUXtd.

T > - j

Factors Influencing

Ship Repair Part Consumption

by

Richard Alan Lippert. Lieutenant, Supply Corps, United States Navy

B.A., Middlebury College, 1966

and

William Thomas LeeLieutenant Commander, Supply Corps, United States Navy

B.A., University of Utah, 1964

Submitted in partial fulfillment of therequirements for the degree of

MASTER OF SCIENCE IN OPERATIONS RESEARCH

from the

NAVAL POSTGRADUATE SCHOOLSeptember 1973

LIBRARYNAVAL POSTGRADUATE SCHOOL

MONTEREY, CALIF. 93940

'

ABSTRACT

An investigation was made of possible linear relation-

ships between several specific factors concerning ships of

the Navy and the actual repair part consumption dollar fig-

ures for a two year period for the purpose of using such

relationships for planning and budgetary aids. Factors con-

sidered included steaming hours, fuel consumption, overhaul

schedules and overhaul mandays, and ship age. Overall Navy-

wide linear models were developed for NSA (odd cog) stock

numbered items, for APA (even cog) stock numbered items, for

Other (odd cog) manufacturer's part-numbered items (items

without a Federal Stock Number assigned) , and for a combined

overall repair part model. In addition, some of the same

models were developed for the Pacific and Atlantic fleets

and for certain ship types.

TABLE OF CONTENTS

I. INTRODUCTION .7

II. DESCRIBING THE SYSTEM HA. MAJOR ASSUMPTIONS xl

B. PARAMETERS AND VARIABLES '. H

III. DEVELOPMENT OF MODELS 16

A. NAVY-WIDE MODELS 16

B. "OCEAN" MODELS 27

C. SHIP TYPE MODELS 29

IV. RESULTS, CONCLUSIONS AND RECOMMENDATIONS. ... 32

APPENDIX A - CONSTANT VARIANCE (HETEROSCEDASTICITY)TEST AND RESULTS 4 5

APPENDIX B - AUTOCORRELATION TEST AND RESULTS. ... 48

APPENDIX C - TESTS FOR NORMALITY OF RESIDUALS ANDEXAMPLE 51

APPENDIX D - SHIP LISTING 52

APPENDIX E - MODEL DATA 60

APPENDIX F - DATA COMPILATION PROGRAM 95

APPENDIX G - FIRST PARTIAL MASTER OVERHAUL PROGRAM . . 99

APPENDIX H - SECOND PARTIAL MASTER STEAMING HOURSPROGRAM 104

APPENDIX I - FINAL MASTER PROGRAM 107

APPENDIX J - MATHEMATICS OF PREDICTION INTERVALCOMPUTATIONS HO

BIBLIOGRAPHY 113

INITIAL DISTRIBUTION LIST H 4

FORM DD 1473. ... H 5

TABLE OF SYMBOLS AND ABBREVIATIONS

RPC Repair Part consumption, dollars consumed.

NSA Navy Stock Account (odd cognizance classes)Federal Stock Numbered items; the Navy StockAccount is financed by the Navy Stock Fund, aworking capital or revolving fund whose capitalto acquire replacement stock is provided byreimbursement for all issues to the customer fromthe Operation and Maintenance appropriation fundsin the hands of the consumer.

APA Appropriations Purchases Account (even cognizanceclasses) of Federal Stock Numbered items; APA con-sists of the following appropriations: Procurementof Aircraft and Missiles, Navy (PAMN) , used toacquire aircraft, aircraft engines, variousmissiles, certain high value spares and repairparts, and related support equipment and facilities;Ship Construction and Conversion, Navy (SCN) , whichpays for the construction and initial outfittingof new ships and major conversion and outfittingof ships already completed; and Other Procurement,Navy (OPN) , which consists essentially of high valueship spares and repair parts, convential ammunition,nuclear weapons, and materials handling equipment.

OTHER (Odd cognizance classes) manufacturer's part-num-bered items (items that have not been assigned aFederal Stock Number) ; these repair parts arefunded by the Navy Stock Fund.

OVERALL , . , „_„ __, , ^mTT„„COMBINED Combined NSA, APA, and OTHER items.

AGE Ship age, in months, from the month of commissioning

TSLOH Time, in months, since the last overhaul.

SHIN Steaming hours in port, monthly.

LMSHIN Previous month's steaming hours in port.

SHUW Steaming hours underway, monthly.

LMSHUW Previous month's steaming hours underway.

FCIN Fuel consumption in port, monthly, gallons consumed.

LMFCIN

FCUW

LMFCUW

TOTMDY

RMDY

SMDY

TMDY

UMDY

VMDY

Y

s2

X

da

e.<a.2

w

b

t

n

X'

-1

Previous month's fuel consumption in port.

Fuel consumption underway, monthly, gallonsconsumed

.

Previous month's fuel consumption underway.

Total mandays expended during the last overhaul.

Repair mandays expended during last overhaul.

Ship and Facility Support (S&F) mandays expendedduring last overhaul.

Ship Construction and Conversion (SCN) mandaysexpended during last overhaul.

Ordnance mandays expended during last overhaul.

Other mandays expended during last overhaul.

The independent variable (RPC) in the models.

The predicted RPC from the models using test data.

The unbiased estimate of the variance of a model.

The matrix of dependent variables in a model.

The disturbance for month a for any model.

The residual for month a for any model.

Coefficient of Determination; a measure of goodnessof fit of the model.

A column matrix of the test data.

A column matrix of the constant and coefficientsof a model

.

The t-distribution.

The number of data points.

The inverse of a matrix.

The transpose of a matrix X.

ACKNOWLEDGMENT

We wish to thank those who provided assistance in the

collection of data and the follow-on development of this

thesis: Professor J. K. Hartman for his assistance concern-

ing the details of the thesis as well as his encouragement

throughout its development; Professor M. 0. Sovereign for

his assistance; The Center for Naval Analysis, Washington,

in particular LT C . F. Snyder and the CNA computer center,

for providing portions of the data; the Maintenance Support

Office, Mechanicsburg ,particularly Mr. Ben Barrouk, for

extracting and providing the repair part consumption data in

the unique and detailed format required; the W. R. Church

Computer Center of the Naval Postgraduate School and its

personnel, particularly Mr. Gerald Learmonth whose aid made

our task much easier; and finally, and gratefully, Mrs.

Barbara Lippert, who spent many hours assisting in the pre-

paration of the COBOL programming functions - without her

aid our task would have been immeasurably more difficult.

I. INTRODUCTION

For some time, Navy budget managers and operators have

been concerned with the costs of supporting ships. Of parti-

cular concern is the consumption of repair parts; what factors

most affect this consumption, and what are the repercussions

of budget cuts in this area. Many managers generally feel

that repair part consumption should be related to such things

as ship age, time since last overhaul, and other operating

factors of this nature. To the present time, however, no

known studies have been made to either prove or disprove this

hypothesis.

The object of this thesis was to develop linear models

using least squares regression techniques to attempt to deter-

mine if repair part consumption was actually related to

various operating factors. Linear models only were developed

and no attempt was made to determine the "best" model to

explain repair part consumption. This was done primarily to

determine if simple linear models did exist which explained

repair part consumption. Linear models are relatively simple

to use and are easily understood by managers.

The models of this thesis were developed for possible use

by Navy repair part managers as budgeting and planning aids

for estimating consumption of NSA, APA, other and Overall

Combined repair part dollars. Monthly, quarterly, or yearly

estimates of repair part consumption on a Navy-wide scale,

Pacific or Atlantic fleet scale or a certain ship type scale

would be possible using models developed for this thesis.

Repair part consumption models may possibly be used for

planning inventory policies or estimating overhaul repair part

consumption, but these uses were not investigated by this

thesis

.

In developing the models of this thesis, repair part con-

sumption data in dollar figures as reported under the 3M

system for a twenty-four month period (July 1970 through

June 1972) for 474 ships were evaluated. Data for the same

period and the same 474 ships concerning operating factors

that might influence consumption were similarly evaluated.

Factors evaluated included ship age, time since last overhaul,

steaming hours in port and underway, fuel consumption in port

and underway, mandays expended during the last overhaul, ship

type, and Pacific and Atlantic fleets. Of the 474 ships, 326

ships remained for consideration after this initial evaluation

phase. The others were eliminated from the study because of

obvious inconsistencies in their reported data. Data con-

cerning the operating factors for the same period were obtained

from the Center for Naval Analysis, Washington, D.C. from

overhaul departure reports, ships' logs, and other reports of

the Navy system. A more detailed discussion of the data

sources and data is contained in Appendix E.

In developing all the models of this thesis, the step-

wise linear regression procedure as developed by the Uni-

versity of California at Los Angeles (UCLA) , BIMED02R was

utilized (1) . Step-wise linear regression, as accomplished

by BIMED02R, considers all the variables to be included in a

model and mathematically chooses the variable that is most

important in explaining the variation of the data of a model.

A coefficient is computed for that important variable and then

the next most important variable is chosen. This process is

continued until all variables have been considered or until

the contribution of the next variable is not significant in

explaining the remaining variation. BIMED02R allows com-

putations of coefficients for variables with or without a

constant term appearing in the model. The models of this

thesis all include a constant term since it was decided to

designate these constants as the "fixed portion" of repair

part consumption. BIMED02R mathematically computes the

standard deviations of the coefficients of the variables and

calculates a test statistic for performing acceptance testing

of the models. A 95% significance level t-test was used for

testing significance of the coefficients in the models of

this thesis. The models of this thesis are shown with the

most important variables occurring first and those variables

of lesser importance occurring later, as determined by the

BIMED02R procedure. More detailed information concerning

BIMED02R, the test statistics, and the mathematical compu-

tations involved in the procedure are contained in reference

(1).

Section II of this thesis considers some assumptions

about the repair part consumption data and contains the

factors used in the development of the models of the thesis

and discusses the criteria used to allow inclusion into

consideration for the data.

Models developed within the thesis include models for

overall Navy-wide repair part consumption, for NSA (odd cog)

stock numbered items, for APA (even cog) stock numbered

items, and for Other part-numbered (odd cog items without a

Federal Stock Number assigned) items. Additionally, models

were developed for the four categories (Overall, NSA, APA,

and Other) for the Pacific and Atlantic fleets, and for

certain ship types. xThe models developed are discussed in

Section III of the thesis.

The results and conclusions of the thesis are discussed

in Section IV. Tests performed on the models and the results

are contained in Appendixes A, B, and C. A listing of the

ships considered in the models is included in Appendix D and

the data used in the models is included in Appendix E. The

COBOL computer programs to extract the required information

from the master tape are included in Appendix F, and the

COBOL computer programs to construct a master tape for use

with the models are included in Appendixes G, H, and I.

Appendix J contains the mathematics of prediction interval

computations for the models.

10

II. DESCRIBING THE SYSTEM

A. MAJOR ASSUMPTIONS

The following major assumptions were made concerning the

data received and evaluated and concerning the Navy reporting

systems.

1. The reporting of repair part consumption to the

Maintenance Support Office, Mechanicsburg was a requirement

for all ships considered in the models of the thesis. Data

received from MSO and CNA, Washington were assumed accurate

and up-to-date, subject to the criteria contained in Part B

of this section. Appendix H contains a more detailed dis-

cussion of the data and data sources.

2. The repair part consumption data were samples from an

underlying normal distribution of consumption data. For each

of the operating factors, data were also assumed to be samples

from underlying normal distributions.

3. The figures for repair part consumption data for all

models were independent random variables.

The assumptions of normality and of independent random

variables for the repair part consumption data are required

for the model development, test statistics, and prediction

intervals of the models of the thesis.

B. PARAMETERS AND VARIABLES

The parameters and variables of this thesis consisted of

those listed below. For each variable, the criterion used

11

for determining whether the reported data for a particular

ship would be considered reliable so that the ship would be

included in the models is shown in the listing as well. The

parameters and variables were:

1. The dollar value of repair part consumption (RPC) for

NSA, APA, Other (manufacturers 1 part-numbered items which

have no Federal Stock Number assigned) and Overall Combined

(the combined figures for NSA, APA, and Other) . The figures

obtained from MSO, Mechanicsburg were assumed correct and

utilized if the operating data for the ship in question met

the criteria for inclusion into the models. If, however, '

zeros were obtained as reported data from MSO for three suc-

cessive months, the repair part consumption was assumed

erroneous and the ship was excluded from consideration.

2. The age of the ship (AGE), in months, computed from

the month of commissioning.

3. The time since the last overhaul (TSLOH) of the ship,

in months. This variable was computed as follows:

a. The month following the end of the last overhaul

was determined to be month "one" for computation of the time

since last overhaul.

b. If the ship was actually in overhaul during any

month, the time since last overhaul was computed by determining

the months since the overhaul prior to the one the ship was

now actively engaged in.

4. The steaming hours in port (SHIN) during the month

under consideration. This variable was obtained by accepting

12

the figures contained in the data obtained from CNA, Wash-

ington if_ there existed data for both steaming hours in port

and fuel consumption in port (FCIN) , or zeros for both in

which case the data was also assumed correct and acceptable.

5. The steaming hours underway (SHUW) during the month

under consideration. This variable was obtained in a manner

similar to that of steaming hours in port (SHIN).

6. The fuel consumption in port (FCIN) for the month

under consideration. This variable was reported in gallons

consumption data, as was fuel consumption underway for the

month under consideration. This variable was obtained as

follows

:

a. If the steaming hours in port (SHIN) was other

than zero and the reported fuel consumption was other than

zero, or if both variables were reported as zero, then the

data was accepted as correct.

b. If the fuel consumption in port (FCIN) data was

reported as zero for four successive months and the ship was

not actively engaged in an overhaul, the ship was excluded

from consideration in the models.

7. The fuel consumption underway (FCUW) for the month

under consideration. This variable was reported in gallon

consumption data. This variable was obtained in a manner

similar to that for fuel consumption in port (FCIN)

.

8. The total mandays (TOTMDY) expended during the last

overhaul. Mandays during the last overhaul were reported in

five categories (Repair, Ship and Facility Support (S&F)

,

13

Ship Conversion and Construction, Navy (SCN) , Ordnance and

Other) plus the combined total mandays expended figure.

These figures were accepted as correct as obtained through

reports provided by CNA, Washington. The total mandays ex-

pended (TOTMDY) figures were used in determination of the

models instead of the five categories of mandays for reasons

discussed in Section IIIA of this thesis.

9. The last month's steaming hours in port (LMSHIN) . As

discussed in Section III. of the thesis, lagged variables were

considered in the determination of the models. Lagged vari-

ables means that the previous month's data might have some

effect on the prediction of the current month's repair part

consumption. As shown in Section III, the only lagged vari-

able that was significant in any model was the previous month's

steaming hours in port. The data for this variable was ob-

tained in a manner similar to that for the current month's

steaming hours in port (SHIN)

.

The resulting data, which was used in estimating the

models of Section III, consisted of 24 observations on each

of the variables listed above - one observation for each of

the 24 months in the data reporting period. The observation

for a particular variable in a particular month was obtained

by summing that variable over all ships included in the sample.

The parameters and variables listed above were those

utilized in the determination of the models of this thesis.

Much more detailed parameters and variables were reported by

MSO and CNA, however. MSO reported dollar figure repair part

14

consumption data by NSA, APA, and Other as used in this

thesis; also reported was the consumption within each of

these categories by the two most important digits of the

Equipment Identification Code (EIC) for the different types

of equipment aboard each ship. CNA reported, in addition to

those variables used in the thesis, the types of overhauls

the ships underwent, the type commander of each ship, and

several other more detailed categories of operating factors

concerning each ship. These more detailed reportings were

not used in the models of the thesis primarily because of the

time involved in evaluating and utilizing such detailed in-

formation and, secondarily, it was the purpose of this thesis

to attempt to find simple linear models that could be easily

and readily used and understood. For these reasons, the more

detailed categories of reported data were not considered in

the determination of the models. Such detailed study may,

however, be a profitable area of further research.

15

III. DEVELOPMENT OF MODELS

A. NAVY-WIDE MODELS

As a first attempt to determine linear models for repair

part consumption the data available for all 474 ships was

utilized without eliminating the cases of obviously poor data

reporting as discussed in Section II of the thesis. The

parameters for each month for all 474 ships were totaled.

The summed total figures of the parameters for each month

were used in the determination of models. These attempts

failed to generate acceptable models for use. There was sig-

nificant correlation among several of the variables, notably

ship age (AGE) and repair part consumption (RPC) , between

ship age (AGE) and the time since last overhaul (TSLOH) , be-

tween ship age (AGE) and the different categories of mandays

expended in the last overhaul, and between the different

categories of mandays expended. The models so attempted did

not explain the variance of the models to any significant de-

gree. The approach of using all data reported to determine

models was abandoned.

The second approach was to eliminate obviously bad data

utilizing the computations for the various parameters as

listed in Section II of the thesis. For example, only those

ships which had by the computation decisions of Section II,

"good" APA reported repair part consumption were utilized in

attempting to determine the Navy-wide APA model. Similarly,

16

for the NSA, Other and Overall Combined models, only "good"

data was utilized. In each of the models, only those ships

that met the computation criteria for fuel consumption and

steaming hours were utilized in the models. After eliminating

bad data, there remained a smaller number of ships to be used

in determination of the models. Specifically, the numbers of

ships to be used in each model were: Overall Combined: 126

ships; NSA: 251 ships; APA: 182 ships; and Other: 134 ships.

As a result of these computations, the ships included in the

models were all types of ships on which data was available

with the exceptions of Aircraft Carriers (CVA) and Auxiliary

Fast Support (AFS) ships. No ships in these classes of ships

met the criteria for model inclusion. In particular, little

or no repair part consumption data was available for any CVA

or AFS.

Using this second approach, model determination was again

attempted. Better results were obtained but again no signi-

ficant acceptable models were generated. Again there was

significant correlation between variables, largely between

ship age (AGE) and the other variables. Determinations of

the models then was attempted without using the variable of

ship age (AGE) . The reasons for this approach were that ship

age (AGE) , computed as the sum of the ages of all the ships

in a model, seemed to create the correlation problems and to

cause the models to be unacceptable since, in the step-wise

linear regressions used, ship age (AGE) entered the model as

the first variable in all cases and caused the models to

"blow-up". That is, no other variable could enter in a

17

significant manner and the ship age variable by itself did

not adequately explain the variances of the models. It was

reasoned that the computation of ship age as being the total

number of months since commissioning date may have been an

erroneous computation. The reasoning was that many, if not

most, of the older ships commissioned prior to 1960, which

was a significant portion of the 474 ships on which data was

available, had undergone some sort of conversion or updating

since 1960. An example would be the FRAM (Fleet Rehabilita-

tion and Modernization) conversions of most of the older de-

stroyer type ships. Because of the conversions and/or up-

dating of equipment aboard the ships, the question arose as to

how to acceptably compute the "age" of a ship. Several

possible alternative computations were proposed, but none

was acceptable in that all entailed such arbitrary decisions

as had been originally made. Defining the variable ship age

(AGE) to be the sum of the ages of all ships in a model seemed

to contribute to the problem area as well. In addition, ship

age (AGE) , as computed, did not allow Navy managers much

control over that variable. It was desired that models be

developed with variables that allowed some control by managers

For these reasons, the variable ship age (AGE) was abandoned

as one of the variables for consideration in the models. In

addition, because of the high correlations among the different

manday categories, it was decided to use only the total man-

days expended during the last overhaul (TOTMDY) figures in the

models and abandon the sub-classifications of overhaul mandays

as variables for consideration.

18

As stated above, determination of the models without the

variable ship age (AGE) was then attempted. The use of lagged

variables and a variable to account for trend effects (i.e.,

inflation) was made. Lagged variables means the use of the

previous month's fuel consumption in port (LMFCIN) , fuel

consumption underway (LMFCUW) , steaming hours in port (LMSHIN)

,

and steaming hours underway (LMSHUW) to determine if any of

these previous month's variables contributed to explanation

of the variance of the model. A "time" variable, computed as

the number of months since the beginning of the reported data

period, was used to account for any trend effects in the

models. This variable of "time" was forced to be an addition

to the model; the variable was not allowed to enter as a free

variable. The purpose of this approach was to determine if

any additional variance of the model could be explained by

trend effects in the data. The models generated by this

approach are discussed below.

1 . Discussion of the Models

In the models developed, the only lagged variable

that entered into any model was the previous month's steaming

hours in port (LMSHIN) which entered into the OVERALL COM-

BINED model. The variable "time" did not enter, at a 95%

significance level, into any model. The conclusion was there-

fore reached that there existed no trend effect, due to in-

flation or otherwise, in any of the models. A Coefficient

2of Determination, R , which is a measure of the goodness of

fit of the models to the data that shows the proportion of

19

the variance of the repair part consumption data explained

by the model, was computed for each model. These ranged from

0.5251 through 0.7901; that is, from one-half to eighty

percent of the variance of the data was explained, depending

on the model. The models all contained a computed constant

figure in addition to the variables in the models. These

constants were interpreted as the "fixed cost" of supporting

the ships of the models in the particular type of repair part

consumption the model represented. These "fixed costs" did,

however, have a range of values - that is, a standard devi-

ation for each was computed - and therefore were not strictly

constants. These "fixed costs" may be affected by variables

not considered in the models.

For each coefficient for each variable of all the

models, standard deviations for the coefficients were cal-

culated and are included in the models. These standard

deviations are shown in parentheses directly, below the co-

efficients of the models.

For each model, the last three months of the 24

months of data (for months April through June 1972) were not

used in the development of the models but were used as test

figures to test the predictive powers of the models. Problems

arose with this procedure since, for unexplained reasons,

the last two months* (May and June 1972) data was of an out-

lying nature. That is, May's data was significantly lower

than normal and June's data was significantly higher than

normal. The range of these two months' data was significantly

20

outside that of the other twenty-two months' data used in the

thesis. As will be discussed in Section IV of this thesis,

it is recommended that the models of this thesis not be used

to predict monthly repair part consumption since the range of

possible predictions is too large, but instead to use the

models for quarterly prediction purposes since the range of

average quarterly figures is much less than monthly ranges of

consumption data. In addition, money is allocated for expend-

iture on a quarterly basis vice a monthly basis , so that

monthly predicted figures are not as necessary as quarterly

average predictive figures to Navy managers. For these

reasons, the average monthly repair part consumption for the

last three months of the 24 month data period is predicted

using the models of the thesis. The average quarterly figure

is obtained by multiplying the average monthly predicted

figure by three. The average monthly predicted repair part

consumptions were computed as follows: (1) the predicted month-

ly consumption for each of the three months was calculated

using the data observations in the models for each of the

three months; and (2) the average monthly repair part con-

sumption for the quarter was computed as one-third the sum

of the three monthly predictions. Additionally, for infor-

mational purposes, the reported repair part consumption for

each of three months was averaged to obtain the reported

average monthly repair part consumption for the quarter. A

95% prediction interval was computed for the average monthly

repair part consumption. Appendix J contains the mathematical

21

computations required to obtain these prediction intervals.

These mathematical computations were based on procedures

contained in reference (3) . The range of prediction interval

as a percentage of the predicted average monthly consumption

was computed for each model. The results for all the models

are contained in the Brief Summary of Models table in Section

IV of this thesis.

It will be noted that two of the models' reported

average repair part consumption did not fall within the pre-

diction intervals for those models. These models were the

Ship Type - Cruiser Overall Combined model and the Ship Type -

Cruiser NSA model. It was felt that this was caused by (1)

2the fact that the R of the Ship Type - Cruiser NSA model

was 0.1962 - that is, the model was not a good prediction

model - caused the reported average repair part consumption

to fall outside the prediction interval for that model; and

(2) the problem of the Cruiser NSA model carried over to the

Cruiser Overall Combined model since exactly the same ships

were included in the two models.

The acceptable variables entering the Navy-wide models

were not fully consistent from model to model but some con-

sistency was found in that the total mandays expended during

the last overhaul (TOTMDY) entered as the most significant

variable in three of the models, in that the time since last

overhaul (TSLOH) entered two of the four models, and in that

fuel consumption and/or steaming hours entered into all four

models in some way. The models and the computed data for each

22

model are listed below with some observations made concerning

each of the models. As previously mentioned, a table con-

taining a summary brief of all the models is contained in

Section IV of the thesis.

a. Overall Combined Model

Model: Y = 373,114,141 + 7 . (FCUW) - 6788 . 9 (LMSHIN)(40526) (1.3) . (1923)

Incremental IncreaseIn and Total r2 : (0.3874) + (0.2507) = 0.6381

Test quarter average reported consumption: $4 30.74 million

Predicted average monthly consumption: $458.40 million

95% Prediction Inverval: ($427.69 million, $489.11 million)

PI as % of predicted consumption: 13.4%

Number of ships considered in the model: 126

Observations: Fuel consumption underway (FCUW) explained

almost 39% of the variance of the model while

the previous month's steaming hours in port

explained an additional 25% of the variance.

A causation statement implied by the model is

that cost reductions might be obtained by de-

creasing the time spent at sea and increasing

the time spent in port by the ships . While

this may be an obvious statement, the feasi-

bility of doing that is questionable. A

caution is made that the statements made in

the observations above, and those made in the

observation sections of the following models,

imply causation while, in fact, only correlation

is observed.

23

b. NSA Model

Model: Y = 367,875,078 - 16.3(TOTMDY) + 5.1(FCIN)(58108) (4.5) (2.4)

Incremental IncreaseIn and Total R2

: (0.4394) + (0.0857) = 0.5251

Test quarter average reported consumption: $241.87 million

Predicted average monthly consumption:- $220.76 million

95% Prediction Interval: ($196.15 million, $245.37 million)



Observations: Only about one-half of the variance of the

model is explained by the variables, and total

mandays expended explains almost 44% by itself.

A causation statement implied by the model is

that cost reductions may be gained by increas-

ing the number of mandays expended during

overhauls, and decreasing fuel consumption in

port. Whether doing so will actually lead to

cost reductions depends on the relative cost

of NSA material and mandays, so that increas-

ing mandays may lead to more cost instead of

less cost.

c

.

APA Model

Model:

Y = 438,912,344 - 53.0(TOTMDY) + 2117.6(SHUW) + 72564 . 8 (TSLOH)(36213) (8.5) (849) (33718)

Incremental IncreaseIn and Total r2 : (0.6726) + (0.0603) + (0.0572) = 0.7901


24





Observations: Of the 79% of the variance explained, total

mandays expended during the last overhaul

explains 67% by itself. This may be partly

explained by the fact that APA material of

high value is usually installed on board ships

during overhaul. Not all APA material is in-

stalled in overhaul, obviously, but a high

percentage is installed then. A causation

statement implied by the model is that in-

creasing the mandays expended in overhaul,

decreasing the length of time between over-

hauls, and decreasing steaming hours underway

might lead to cost reductions in repair part

consumption. Such a statement is not un-

expected, but whether such a schedule could

be followed is highly questionable,

d. Other model

Model:

Y = 130,772,813 - 9.9(TOTMDY) + 4.8(FCIN) - 1522.5(SHIN)(30671) (4.3) (1.3) (381)

- 20807.3 (TSLOH)(9144)

Incremental IncreaseIn and Total r2 : (0.1605) + (0.0946) + (0.2561) + (.1195)

= 0.6307

25






Observations: While 63% of the variance is explained in the

model, no one variable explains a majority of

the variance that is explained. This fact

may possibly be because of the nature of the

items (manufacturers' part-numbered items

without a Federal Stock Number assigned) con-

tained in the model. These items may appear

in very old equipment or in very new equipment,

which may have just been installed during the

last overhaul. In any case, a causation state-

ment implied by this model is very similar to

the statements of the other models - cost

reductions may be gained by increasing the

mandays expended during an overhaul, and de-

creasing fuel consumption. Logical inconsis-

tencies seem to be in the model in that it is

also implied that cost reductions may be gained

by increasing steaming hours in port ( and de-

creasing fuel consumption in port) and by in-

creasing the time since last overhaul. No

explanations are readily available for these

inconsistencies

.

26

B. "OCEAN" MODELS

After development of the Navy-wide models, it was decided

to attempt to develop similar models for the Pacific and

Atlantic fleets. Consequently, the ships for which data was

available were segregated into Pacific and Atlantic fleets.

The criteria for inclusion in the models was exactly the same

as outlined for the Navy-wide models. The data computation

criteria were similarly exactly the same as for the Navy-wide

models. Since, in development of the Navy-wide models, time

and ship age variables had been rejected from consideration,

these variables were again rejected from consideration. An

attempt was made to develop the models for the Pacific and

Atlantic fleets using only the variables that were considered

for the Navy-wide models. A secondary objective for develop-

ing the "ocean" models was to determine if the different

operating characteristics and make-up of the Pacific and

Atlantic fleets had any effect on repair part consumption.

Utilizing the same procedure for development of the models

as outlined for the Navy-wide models, the "ocean" models were

developed. The Overall Combined models were developed for use

by the respective fleet managers. The results obtained for

2each model, the R computed, and the other statistics associ-

ated with the models are included in the Brief Summary of

Models table included in Section IV of this thesis. The

models as developed will not be listed individually in this

section. Discussion of the models and the observations/con-

clusions reached are shown below.

27

Discussion of "Ocean" Models

Acceptable models could not be developed for each of

the four categories for each fleet. Specifically, models

with significant variables to explain the data variance did

not exist for Pacific Fleet NSA and for Atlantic Fleet Over-

all Combined categories. Models were developed for all the

other categories for each fleet, however. The models devel-

2oped had R associated with them ranging from 0.37 through

0.836, so that, in some cases, most of the data variance was

explained by the models. In all cases where models were

developed, the actual last quarter's average consumption

figure was included in the confidence intervals computed for

the predicted figures. As can be seen from the models, fuel

consumption underway (FCUW) and in port (FCIN) is the most

important significant variable in the Pacific Fleet models

while total mandays expended (TOTMDY) in overhaul is the

most important significant variable in the Atlantic Fleet

models. Fuel consumption and steaming hours are secondary

significant variables in Atlantic Fleet models while the

total mandays expended in overhaul variable is secondarily

significant in the Pacific Fleet models. Whether these dif-

ferences are explained by the different operating policies of

the fleets (Viet-Nam versus the Mediterranean) or the much

larger area of ocean covered by the Pacific Fleets than by

the Atlantic Fleet is debatable.

In sum, some models did exist for the different cate-

gories of models for the Pacific and Atlantic Fleets. These

28

models were different in major significant variables which

may be partly explained by the differences in the operating

policies and operating areas of the respective fleets. In

general, the models developed for the separate fleets were

less efficient than the Navy-wide models in explaining the

data disturbances.

C. SHIP TYPE MODELS

It was decided to attempt to develop models for the four

categories of models (Overall Combined, NSA, APA, and Other)

for different types of ships. The objectives of this approach

were (1) to determine if such models did exist which might

be of use to Navy managers (including type commanders) and (2)

to determine if the type of ship in itself was an important

variable in explaining repair part consumption. As with the

"Ocean" models, the same criteria for inclusion into the

models and computation of data criteria as for the Navy-wide

models was used.

Ship types decided upon to be used were:

1. Destroyer types, which included ships classed as DD,

DDG, DLG, DEG, DE and DLGN.

2. Cruiser types, which included CG, CGN and CLG.

3. Submarine types, which included ships classed as SS,

SSN, and SSBN.

4. Amphibious types, which included ships classed as

LSD, LPD, LPH, and LST.

5. Underway Replenishment types, which included ships

classed as AF, AO, AOG, AOE, and AE.

29

Models were developed for the majority of the categories

of models for each type of ship listed above, with the ex-

ception of the Underway Replenishment types. No models with

significant variables existed for Underway Replenishment

types, possibly because of the small number of ships included

in the models or possibly because of the diversity of classes

of ships included in this classification of ship types. Some

other models did not exist for the other ship types classifi-

cations as well, notably, "Other" models existed only for the

destroyer ship types. The results obtained for each model,

2the R computed, and the other statistics associated with the

models are included in the Brief Summary of Models table in-

cluded in Section IV of this thesis and are not listed indi-

vidually in this section. Discussion of the models and

observations reached are shown below.

Discussion of Ship Type Models

Although several models were developed for the

2different ship types, the range of R of the models was from

0.1962 to 0.5655, so that, in general, the majority of the

models did not explain well the variances of the consumption

data. Some of the models are questionable as to accept-

ability because of this fact.

The important variables for the ship type models did

vary according to ship type, indicating that the type of ship

under consideration is an important variable in itself.

Specifically, the most important variable for the destroyer

type models was fuel consumption underway (FCUW) ; for the

30

cruisers, in general , the most important variable was the

total mandays expended (TOTMDY) during the last overhaul;

for submarines each model had a different most important vari-

able including steaming hours underway (SHUW) total mandays

expended (TOTMDY) last overhaul, and fuel consumption in port

(FCIN) , depending on the model under consideration; for amphi-

bious types the important variables were again different for

each model and included fuel consumption underway (FCUW)

,

steaming hours underway (SHUW) , and total mandays expended

(TOTMDY) last overhaul. As previously noted, no models

existed for the Underway Replenishment classification of ship

types.

In sum, models of questionable acceptability existed

for all the ship types (except Underway Replenishment types)

in all categories of models except Other. In general, fuel

consumption and total mandays expended (TOTMDY) last overhaul

were the most important variables of the models, with other

variables important in specific models or of secondary impor-

tance to the models. However, the important variables in the

models did differ from ship type to ship type leading to the

possibility that ship type in itself may be an important

variable in explaining repair part consumption.

31

IV. RESULTS, CONCLUSIONS AND RECOMMENDATIONS

The results of this thesis were the development of linear

prediction models for repair part consumption in each of four

categories of parts (Overall Combined, 'NSA, APA, and Other) .

Models were developed for Navy-wide repair part consumption,

for Pacific and Atlantic fleet repair part consumption, and

for different ship types repair part consumption. Although

significant models did not exist for all categories in each

case, notably the category of Other for some of the ship

types models, and the goodness of fit of some of the models

developed was of questionable acceptibility , it is felt that

the purpose of the thesis, which was to determine if repair

part consumption was linearly related to various operating

factors, has been fulfilled. Sufficient acceptable models

were developed to enable the conclusion to be drawn that re-

pair part consumption is linearly related to various operating

factors. The inclusion into the models of additional oper-

ating factors such as a variable that adequately measures the

age of a ship, or a variable that enters into consideration

the political climate of the world, such as a dummy variable

for Vietnam service, may increase the goodness of fit of the

models developed. In addition, the models and data may be

subdivided into Equipment Identification Codes and linear

models possibly developed for each EIC. These are areas into

which further research can be done.

32

2The models developed within this thesis, the R of each,

the test quarter's actual average repair part consumption,

the predicted consumption, a 9 5% confidence interval for each

prediction, and the confidence interval of each prediction

expressed as a percentage of the predicted consumption are

shown in the following Brief Summary of Models table.

33

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Eh t-H" HHft

ft mft s ft

w ft sg'd H w o < < w H W O <:oa

s £ u CO ft EH ffi > u COCO o S < O CO O 2

39

<*> 1

CD TJCO U CD

fd &< -P 1 1

uh n-i -hP4 XJ

C -nOHM•h nj cP >U r-l -H•H OJH 1 1

-a -ph<D G -HM H gPw ^

,_^

»d co

a> cPU U -H•H pH rH 1 1

^d tf -hO) -Hu gen wid wP cfd o CO a>a u -h in vo

0< rH • •

•P PJ -H «^ oCO -HCD gH "-

CN 1 1

Pi

CO rH*H ft CD CN CNO'H c-a rH rH£ -H O

=*= w 2T3

+J

C +J Pc c

U fd fd•0 o o^ l Eh •H •Hid C 2 «4-4 »W^0 1 CD W •H •HC ^ "g C Cfd u a. S tP cnp w •H •Hco m c H CO to

-H s£ w XJ X!-P w w hH •P -P•H C +> A4 •H •H£ c w £ £W «H CD '-v S CO (0

P -H W rH CD rH CDH d) U-H >H CD rH CD rHCD -H -H CO <: T3 £1 •a xifO > m CD s O fd o rd

O CD M-4 .C « e-H g -HS 'd a) +j w >H M

a o fd fd

53 s > 2 >D

1

CU

ft W '

>1 PUEn

EhrH «CD Pvi w»0 H < K

EC CU Ens CO 3 °

40

Conclusions that can be drawn from this thesis and from

inspection of the models developed include:

1. Repair part consumption dollar figures are linearly

related to various operating factors such as overhaul schedules,

fuel consumption, and steaming hours. In addition, repair part

consumption is linearly related to ship age, but ship age was

eliminated from consideration because of being a variable that

is uncontrollable by Navy managers.

2. Of the variables considered in this thesis, overhaul

schedules - that is, the mandays expended (TOMDY) during over-

hauls and the duration between overhauls (TSLOH) - appear to

be the dominant variables in many of the models developed.

Fuel consumption and steaming hours, both in port and underway,

are important to most models and dominant in some of the models,

notable the ship type models.

3. Several of the models developed are of questionable

acceptability in that the models do not adequately explain the

variances of the data within the models. Inclusion of addi-

tional factors or a larger sampling of data for those variables

considered might alleviate this inadequacy.

4. The models, as developed, may be used for predictions

of monthly repair part consumption for the four categories

(Combined Overall, NSA, APA, and Other) of models. Fairly

good results can be obtained for the Navy-wide models and sev-

eral of the sub-models. It is recommended, however, that if

the models are used for prediction, the predictions be for at

least a quarterly period. The reasons for this recommendation

41

are (1) that Navy managers allocate expenditures on a quarter-

ly basis, (2) monthly repair part consumption varies more

rapidly from month to month than from quarter to quarter, and

(3) therefore, predictions on a quarterly basis would tend to

be more realistic and accurate.

5. In the models of the thesis, the signs (positive or

negative) of the coefficients of the significant variables

imply some causation statements concerning the possibility of

cost reductions and savings. The statements, it is cautioned,

imply causation while, in fact, only correlation is observed

in the models. The statements are:

a. The negative sign of the variable mandays expended

during last overhaul (TOTMDY) in the majority of cases where

that variable significantly entered the models implies that

cost reduction in repair part consumption might be obtained

by increasing the length of and mandays expended during over-

hauls. While this may seem an obvious statement, the increased

cost of longer overhauls may outweigh any cost reductions so

obtained.

b. The positive sign of the variable time since last

overhaul (TSLOH) in the models in which that variable signi-

ficantly entered implies cost reductions might be obtained by

decreasing the time between overhauls. This is another un-

surprising statement, but, as before, the increased cost of

more frequent overhauls may outweigh any cost reductions

realized in repair part consumption.

42

c. In general, fuel consumption underway (FCUW) had

positive signs for the coefficients, and fuel consumption in

port (FCIN) had a negative sign for the coefficients. In a

related manner, the variable steaming hours underway (SHUW)

had, in the majority of models significantly entered, a posi-

tive sign; steaming hours in port (SHIN) had, in the majority

a negative sign. These results imply a statement that de-

creasing the time spent at sea and increasing the time spent

in port by ships may lead to cost reductions in repair part

consumption. The statement may be an obvious one, but Navy

operating policies and/or missions or the world political

climate may not allow such scheduling.

In summary, the variables significantly entering the models

did, in the majority of the models, enter with the sign of the

coefficients the logically expected one, whether it be posi-

tive or negative. There were, in general, no major or unex-

pected surprises in the signs of the coefficients of the signi-

ficant variables of the models.

Recommendations for use of the models of this thesis and

for further research into the linearity of repair part consump-

tion to various operating factors include:

1. As previously noted, it is recommended that the models

of this thesis, if used, be used to predict quarterly consump-

tion instead of monthly consumption, for the reasons noted.

2. The models of this thesis can be used for planning

and budgetary aids, if desired. It is recommended that if

the models be used, they be used as a check and/or test of

43

figures and estimates of budgetary requests or planned allo-

cations of expenditures which were arrived at by the present

methods of Navy managers. The models may, however, be used

to arrive at estimates or predictions by the Navy managers.

Such estimates or predictions would be liable to large vari-

ations if the present models were used.

3. It is recommended that the models be updated prior to

use for periods later than June 1972 because of the possible

changes in Navy operating policies, world political climate,

Navy size and composition, and/or other possible changes from

the 1970-1972 time period.

4. Areas for further research include, as previously

noted, the addition of more variables (such as an adequate

measure of the age of a ship) into the models to try to in-

crease the goodness of fit and predictive powers of the models.

A second approach for further research might be the subdivision

of the present models into Equipment Identification Codes (EIC)

and the development of possible linear models for each EIC.

A final recommendation for further research is the gathering

of more data for more ships in an effort to improve the pre-

dictive powers of the present models. This thesis covered

only a two year period and some of the models of the thesis

were developed considering only a small number of ships (five

in one model, seven in another three models). The inclusion

of more ships and for a longer period of time may lead to

improvements in the current models.

44

APPENDIX A

CONSTANT VARIANCE (HETEROSCEDASTICITY) TEST AND RESULTS

The models of this thesis were tested under the null hypo-

thesis that the variances of the disturbances were constant

over time, with the alternative hypothesis that the variances

of the disturbances either increased or decreased over time.

The observations were divided into two equal groups of ten

months in each group with the eleventh month of the twenty-

one observations ignored. Then the least squares residuals

were computed for both sets of observations separately. The

residual sums of squares for the two sets of observations are

independent and similarly distributed. The ratio of the sums

of squares of the sets of observations was formed as a test

statistic. This ratio is distributed as F (10-K, 10-K) under

the null hypothesis. The ratio was compared to the five-

percent significance level for the appropriate F distribution.

The critical values of the F distributions, the computed test

statistics, and the test results are listed below for the

models of this thesis. A more detailed explanation of the

procedure is contained in reference (3)

.

ModelF CriticalValue

TestStatistic Results

NAVY-WIDE MODELS

OVERALL COMBINED

NSA

3.79

3.79

0.46

0.30

Accept hypo-thesis

Accept

45

F Critical TestModel Value Statistic Results

NAVY-WIDE MODELS Cont 1 d

0.23 AcceptAPA 4.28

OTHER 5.05 1.10 Accept

PACIFIC OCEAN MODELS

OVERALL COMBINED 3.79 0.21 Accept

NSA - - -

APA 3.79 0.37 Accept


ATLANTIC OCEAN MODELS

. .OVERALL COMBINED

NSA 3.79 0.42 Accept



SHIP TYPES - DESTROYEIIS

0.39 AcceptOVERALL COMBINED 3.44




SHIP TYPES - CRUISERS

3.79 0.74 AcceptOVERALL COMBINED


APA 3.44 0.62. Accept

OTHER - - -

46

F Critical TestModel Value Statistic Results

SHIP TYPES - SUBMARINES




OTHER - - -

SHIP TYPES - AMPHIBIOU S




OTHER - - -

SHIP TYPES - UNDERWAY REPLENISHMEN r

, .OVERALL COMBINED - -

NSA - - -

APA - - -

OTHER - - -

47

APPENDIX B

AUTOCORRELATION AND TEST RESULTS

The models of this thesis were tested for autocorrelation

in the disturbances. The null hypothesis tested was that no

autocorrelation existed, and the alternative hypothesis was

that the successive disturbances were positively correlated.

The starting point was the following identity:

E(da+ 1 " V 2

" E(d2a+ 1>

+ E(d2a> " 2E(da<W'

where d is the disturbance for month a. When successivea

disturbances are positively correlated, the left-hand expect-

tation will be smaller than when they are uncorrelated be-

cause of the negative sign of -2E (d d . ) . To the extent that

the residuals are satisfactory approximations to the corres-

ponding disturbances, there will be a smaller result for

2(d

, . - d ) . These considerations lead to the Durbin-Watsona+1 a

statistic

:

n-12

E (ea+l " e

a }

. , a=l , where e is the residuald = ' a

n2

I ea=l

for month a. The null hypothesis is rejected in favor of the

alternative hypothesis that the disturbances are positively

autocorrelated when d takes a sufficiently small value. When

the alternative hypothesis states that the disturbances are

either positively or negatively autocorrelated, the critical

region consists of both small and large values of d.

48

Durbin and Watson (1950, 1951) formulated bounds (d , d )J_i U

for each significance limit. The procedure is then to reject

the null hypothesis in favor of the alternative hypothesis if

d < d T , to draw no conclusion if d falls in (d , d ) and toL Li U

declare the null hypothesis as acceptable if d > d ) . A more

detailed explanation of the test is contained in reference (3)

.

The upper and lower limits, the test statistic calculated

and the results of the test are included below for each model

within this thesis:

DURBIN-WATSON TESTS AND RESULTS

ModelLowerLimit

UpperLimit

TestStatistic

Results

NAVY-WIDE MODELS

OVERALL COMBINED 1.13 1.54 1.83 Accept nullhypothesis

NSA 1.13 1.54 2.59 Accept

APA 1.03 1.67 2.03 Accept

OTHER 0.93 1.81 1.82 Accept

PACIFIC OCEAN MODELS

1.54 1.50 No conclusionOVERALL COMBINED 1.13

NSA - - - -

APA 1.13 1.54 1.37 No conclusion


ATLANTIC OCEAN MODELS

OVERALL COMBINED -

NSA 1.13 1.54 2.46 Accept

APA 1.03 1.67 2.50 Accept


49

ModelLowerLimit

UpperLimit

TestStatistic Results

SHIP TYPES - DESTROYERS

1.42 1.26 No conclusionOVERALL COMBINED 1.22

NSA 1.22 1.42 1.82 Accept

APA 1.13 1.54 1.69 Accept


SHIP TYPES - CRUIS;ers

OVERALL COMBINED 1.13 1.54 1.80 Accept

NSA 1.22 1.42 2.81 Accept

APA 1.22 1.42 1.26 No conclusion

OTHER - - - -

SHIP TYPES - SUBM2lRINES

1.54 1.73 AcceptOVERALL COMBINED 1.13

NSA 1.22 1.42 2.28 Accept

APA 1.03 1.67 2.36 Accept

OTHER - - - -

SHIP TYPES - AMPH3 BIOUS

1.54 2.07 AcceptOVERALL COMBINED 1.13

NSA 1.22 1.42 2.10 Accept

APA 1.13 1.54 2.77 Accept

OTHER - - - -

SHIP TYPES - UNDEFMAY REPLENISHMENT

OVERALL COMBINED - - -

NSA - - - -

APA - - - -

OTHER - - - -

50

APPENDIX C

TESTS FOR NORMALITY OF RESIDUALS

Since most assumptions used in the models of this thesis

depend on the normal distribution of the data and residuals,

chi-square goodness of fit tests were performed to ensure the

normality assumption was acceptable. The results were that

the normality assumption was acceptable in the models of this

thesis. An example of one of the tests performed on one of

the models of the thesis is contained below.

A chi-square goodness of fit test was performed on the

residuals of the model for Navy-wide Overall RPC . The pro-

cedure used is contained in reference (2)

.

Interval Theoretical Observed (f. - F.)2

l l(in millions) Frequency (F .

)

Frequency (f .

)

F.l

less than -50 0.4 0.0 0.40Between -50 and -40 0.6 0.0 0.60Between -4 and -30 1.0 3.0 4.00Between -30 and -20 2.0 0.0 2.00Between -20 and -10 3.0 5.0 1.33Between -10 and 3.5 4.0 0.07Between and 10 3.5 2.0 0.64Between 10 and 20 3.0 2.0 0.33Between 20 and 30 2.0 2.0 0.00Between 3 and 40 1.0 2.0 1.00Between 4 and 50 0.6 1.0 0.27More than 50 0.4 0.0 0.40

11.045% Critical chi-square value: 16.92

Result: Since 11.04 is less than 16.92, the hypothesis ofnormality was accepted.

51

APPENDIX D

The attached list of ships is that actually used in the

development of the models. Although data was originally

collected for 474 ships, only these 326 satisfied the arbi-

trary RPC data reporting requirements established for use in

this thesis. Any ship not in overhaul with three or more

consecutive months of zero RPC data in all three categories

(APA, NSA and Other) has been excluded from this listing.

This action eliminates two significant classes of ships,

Carriers and AFS's, from consideration and reduces the AD *

s

considered to one ship. This data purification action was

taken as an attempt to insure that only relatively consistent

and presumably accurate reporting units were considered, thus

improving confidence in study conclusions.

The three codes are defined and interpreted as follows:

1. RPC - Designates categories of repair part consumption

data (APA, NSA, Other) for which the ship has less than three

consecutive months of zeros during the 24 month period con-

sidered (i.e., "good" report categories).

A = APA only G = APA, NSA and Other

B = APA and NSA N = NSA only

C = APA and Other = Other only

D - NSA and Other

52

2. F£ - Fuel consumption data code indicating ships

missing fuel consumption data for four or more consecutive

months (both FCIN and FCUW missing for each month considered)

1 = Good FC data

= Incomplete ("bad") FC data

3. 0/H - The overhaul code is used to identify ships

that underwent some form of overhaul during the reporting

period considered (July 1970 - June 1972)

.

Y = Ship was in overhaul during the period

N = Ship was not in overhaul during the period

53

SHIP LISTING

TYPE HULL # RPC FC 0/H TYPE HULL # RPC FC 0/H

UNDERWAY REPLENISHMENT

AE 21 G 1 N AE 22 N O Y

AE 23 G 1 Y AE 24 G O Y

AE 25 B N AE 26 G O N

AE 27 G 1 N AE 28 G 1 Y

AF 52 G 1 N AF 56 B 1 N

AF 58 D 1 Y AF 59 G Y

AO 51 D Y AO 98 D 1 N

AO 99 G 1 N AO 106 N N

AO 107 D N AO 108 G 1 Y

AO 109 G 1 N AO 143 B 1 Y

AO 144 G 1 Y AO 145 N 1 Y

AO 146 B N AO 148 G 1 N

AOE 1 G Y AOE 2 G Y

AOG

AOG

50

56

N

N

1

1

N

Y

AOG 55 N 1 Y

CRUISERS

CG 10 G 1 N CG 11 G O N

CG 12 G 1 Y CGN 9 G 1 Y

CLG 4 G 1 Y CLG 5 G 1 Y

CLG 6 G 1 Y CLG 7 G 1 N

DESTROYERS

DD 714 G 1 Y DD 715 G 1 Y

DD 717 B O Y DD 718 N O Y

DD 719 B O Y DD 743 B Y

DD 782 N N DD 783 B N

DD 786 B N DD 817 G 1 Y

DD 818 G 1 Y DD 824 G 1 Y

54

TYPE HULL # RPC FC O/H TYPE HULL # RPC FC O/H

DESTROYERS Cont'd

DD 826 G N DD 827 B 1 Y

DD 837 G 1 N DD 840 G 1 N

DD 845 G N DD 849 G 1 Y

DD 851 B Y DD 853 G 1 Y

DD 865 G 1 N DD 866 G 1 Y

DD 867 G 1 Y DD 868 G 1 Y

DD 873 G 1 Y DD 875 B 1 Y

DD 876 B Y DD 878 G 1 N

DD 881 G 1 Y DD 886 B Y

DD 890 G 1 Y DD 931 G 1 Y

DD 933 G 1 Y DD 938 G 1 Y

DD 941 G 1 Y DD 942 G 1 N

DD 943 G 1 Y DD 944 G 1 N

DD 945 G Y DD 946 B 1 Y

DD 948 B 1 Y DD 951 B Y

DDG 2 G 1 Y DDG 3 G 1 Y


DDG 6 G 1 N DDG 7 G Y

DDG 8 G 1 N DDG 9 G N


DDG 12 G N DDG 13 G 1 Y

DDG 14 G 1 Y DDG 15 G N

DDG 16 G Y DDG 17 G 1 Y


DDG 20 G 1 N DDG 21 G 1 Y




DDG 34 G Y DE 1015 G 1 N

DE 1021 B 1 N DE 1022 G 1 N

DE 1033 B 1 Y DE 1035 B 1 Y

DE 1036 B 1 Y DE 1037 G 1 Y

DE 1038 G•

1 Y DE 1040 G 1 Y

55

TYPE HULL # RPC FC O/H TYPE

Cont'd

HULL # RPC FC O/H

DESTROYERS

DE 1041 G 1 Y DE 1043 G 1 N

DE 1044 G 1 Y DE 1045 G 1 N

DE 1047 G 1 Y DE 1048 G 1 Y

DE 1049 G 1 Y DE 1050 B 1 Y

DE 1051 G 1 Y DE 1052 G 1 Y

DE 1053 G Y DE 1054 G Y

DE 1055 G N DE 1056 G 1 Y

DE 1058 G 1 Y DE 1059 G 1 Y

DE 1060 G Y DE 1061 G 1 Y

DE 1062 G 1 Y DE 1068 G 1 Y

DE 1072 G 1 Y DEG 1 G 1 Y

DEG 2 G 1 Y DEG 3 G 1 Y

DEG 4 G 1 N DEG 5 G 1 Y

DEG 6 G 1 Y DLG 6 G 1 Y

DLG 8 G 1 Y DLG 10 G N

DLG 11 G 1 Y DLG 12 C 1 Y

DLG 13 G 1 N DLG 15 G 1 Y

DLG 16 G 1 N DLG 17 G 1 N

DLG 21 G Y DLG 26 G 1 Y

DLG 27 G 1 N DLG 28 - G 1 N

DLG 29 G 1 Y DLG 30 G 1 Y

DLG 31 G 1 Y DLG 32 G 1 N

DLG 33 G N DLG 34 G 1 Y

DLGN 25 G 1 N DLGN 35 G 1 N

AMPHIBIOUS

LPD 1 G 1 N LPD 2 G N

LPD 3 G 1 Y LPD 4 G 1 N

LPD 5 G 1 Y LPD 6 G N

LPD 7 G N LPD 8 G Y

LPD 9 B N LPD 10 D N

LPD 11 G 1 Y LPD 13 G 1 Y

LPH 3 G 1 N LPH 7 G 1 Y

LPH 9 G 1 N LSD 28 N Y

56


AMPHIBIOUS Cont'd

LSD 29 B Y LSD 30 G 1 Y

LSD 31 G Y LSD 32 G 1 N

LSD 33 B Y LSD 34 N 1 N

LSD 35 G Y LSD 36 G N

LST 1179 G 1 Y LST 1180 N 1 Y

LST 1181 B 1 Y LST 1182 G 1 Y

LST 1183 G 1 Y LST 1184 B 1 Y

SUBMARINES

SS 344 N 1 Y SS 346 B 1 Y

SS 351 N 1 Y SS 416 B 1 Y

SS 425 N 1 Y SS 490 N 1 Y

SS 563 B 1 Y SS 564 N 1 Y

SS 565 B 1 Y SS 566 N 1 N

SS 567 N 1 Y SS 572 B 1 Y

SS 576 N 1 Y SS 580 B 1 Y

SS 581 B 1 Y SS 582 B 1 Y

SSBN 598 B 1 Y SSBN 599 B 1 Y


SSBN 602 B 1 N SSBN 608 B 1 N

SSBN 609 G 1 N SSBN 610 B 1 N

SSBN 611 G 1 N SSBN 616 G 1 N

SSBN 617 G'

1 N SSBN 618 B 1 N

SSBN 619 B 1 N SSBN 627 B 1 Y





SSBN 636 B 1 Y SSBN 640 N 1 Y



SSBN 645 N 1 Y SSBN 654 B 1 Y

SSBN 658 B N SSBN 659 B 1 N

SSN 571 B N SSN 579 B 1 Y

SSN 585 B 1 Y SSN 587 B 1 Y

57


SSN 590 B 1 N SSN 592 B N

SSN 596 G Y SSN 597 B 1 N

SSN 607 B 1 N SSN 638 B N

SSN 639 G Y SSN 646 G 1 Y

SSN 648 B 1 Y SSN 649 G N

SSN 650 G Y SSN . 651 G Y

SSN 652 G Y SSN 653 G Y

SSN 661 G Y SSN 662 B N

SSN 663 B Y SSN 664 G N

SSN 667 B Y SSN 668 G N

SSN 669 G Y SSN 670 B Y

SSN 673 G Y SSN 674 G Y

MISCELLANEOUS

AD 26 N 1 Y AG 153 N 1 Y

AR 6 G Y AR 7 N N

ARC 2 D 1 N ARC 3 G 1 Y

ARC 4 N 1 Y ARS 8 D 1 N

ARS 23 D 1 N ARS 24 D 1 N

ARS 25 N 1 N ARS 38 D 1 Y

ARS 39 N 1 N ARS 40 N 1 Y

ARS 42 N 1 Y ARS 43 D 1 N

AS 18 D 1 N AS 32 B 1 N

AS 34 N 1 N ASR 8 N 1 N

ASR 9 N 1 N ASR 13 N 1 Y

ASR 14 N 1 N ASR 15 N 1 Y

ASR 16 N 1 N ATF 76 N 1 N

ATF 84 N 1 N ATF 86 N 1 N

ATF 92 N 1 Y ATF 100 N 1 Y

ATF 101 N 1 Y ATF 103 N 1 Y

ATF 105 N 1 Y ATF 106 N 1 Y

ATF 110 N 1 N ATF 113 N 1 N

ATF 149 N 1 Y ATF 156 N 1 Y

ATF 157 N 1 Y ATF 158 N 1 Y

ATF 159 N 1 Y ATF 160 G 1 Y

58


MISCELLANEOUS Cont''d

ATF 161 D 1 Y ATF 162 N 1 Y

MSO 433 B 1 Y MSO 446 N 1 Y

MSO 449 N 1 Y PG 85 N 1 Y

PG 86 N 1 Y PG 88 N 1 Y

PG 89 N 1 Y PG 92 N 1 Y

PG 93 N 1 Y PG 94 N 1 Y

PG 95 N 1 Y PG 97 N 1 Y

PG 101 N 1 Y

59

APPENDIX E

The following tables list information extracted from the

master tape by using the data compilation program with the

exception of the five categories of overhaul mandays (RMDY,

SMDY, TMDY, UNDY and VMDY) . It should be noted that although

twenty-four months of data are available, models were con-

structed on the basis of the first twenty-one months of in-

formation, allowing use of months 22, 23, and 24 for testing

the predictive powers of the models. The following explana-

tion of headings and the methods of calculating the respec-

tive entries is described below:

Month : Month 1-24 are the respective months over which the

data pertained beginning with July 1970 (Month 1) and ending

with June 1972 data (Month 24) . This period was selected as

the most current for which 3M data on repair part consumption

could be extracted. A new generation of 3M data collection

was initiated in January 1970. Prior RPC information was

difficult if not impossible to extract and if extracted would

have been incompatible with the new generation data. The

Maintenance Support Office advised extracting data after

approximately July 1970 to insure complete implementation of

the most recent 3M data collection process. It should be

observed that data concerning overhaul information, steaming

hours, and fuel consumption was available as far back as 1965

60

RPC-APA (NSA, OTHER) : This figure represents, in dollars,

the total of all repair part consumption data reported for

the ships in the model and the particular month indicated.

APA, NSA and Other designate the type of repair part consump-

tion summed as reported by the Maintenance Support Office.

In providing the repair part consumption data, the Mainten-

ance Support Office developed programs to extract the extended

dollar value of material the subject ships reported consumed

in the respective months. This was done by categories, sum-

ming all even cog (APA) , odd cog (NSA) , and part numbered

items (Other) separately for each ship by month.

RPC-total : This is the sum of RPC-APA, NSA and Other for

the report month.

AGE : This data element is obtained by adding the ages (in

months from commissioning date) of all ships in the particu-

lar model for the report month.

TSLOH: The sum of time (in months) since the completion of

the last overhaul for all ships in the model.

SHIN/SHUW : The sum for the report month of the modeled ships

steaming hours in port/steaming hours underway, in hours.

FCIN/FCUW : The sum for the report month of the modeled ships

fuel consumption in port/fuel consumption underway, in gallons

TOTMDY : The total mandays expended during the last overhaul,

summed for all ships modeled by report month.

61

# SHIPS ; The number of different ships used in the particu-

lar model. Note that this figure remains constant from

month to month for each model.

Data Sources : The Repair Part Consumption data was obtained

from the Maintenance Support Office as previously described.

This data is initially obtained from source documents origin-

ated monthly by each ship, key punched and finally converted

to tape storage in MSO.

The data elements of AGE, TSLOH and TOTMDY were obtained

from CNA. This information is collected by the Naval Ships

Systems Command (NAVSHIPS) from overhaul departure reports

and general historical files including information such as

home ports, type command, types of overhaul, etc. CNA had

previously obtained this data from NAVSHIPS.

The remaining data of SHIN, SHUW, FCIN and FCUW was also

obtained from CNA. This information is reported monthly by

ships, based on ships logs, to the Maintenance - Support Office.

CNA had previously obtained this information on tape from MSO.

It should be noted that nearly all of the information

used in this study originates with ship reports. It is often

handwritten and requires key punching and other processing

before final conversion to magnetic tape records. This entire

process is hardly infallible and it is likely to create some

differences between the actual factors and the data incor-

porated herein. This, however, represents the best available

information and this data was purified to the maximum extent

feasible to insure the most reliable information available

was used in this study.

62

COIX fN <N (M CM C\l fM CM CM (M CM CM CM CM CM CM CM CM CM CM CM CM CM CM CMMOO

00

a? <TJ co tO 00 CO 00 CO 00 CO to 00 CO to CO OO CO CO CO CO CO co CO

r- r- sr CO fM u> Is- co CM co l\J CM r-4 "X r— CO 0> O m -r CM rn <o

>o r- m r» rO O u> o —

<

CM o -^ CO Is- C^ r- r» s —

!

o CJ» CO CM coa*-* r*- co CM CO CM sO >o o CO 00 CO co r~4 —4 so rn >o CO co Nf r- co 00Z.O —

(

r~ -O m fM CO •V 00 CM (j ~4 oo Us Is- a> in Us co r— -T c_> CJ) r-

•— U> —

y

>u t-J su C) <o <o c» r— r- U1 p- o IM CM to ci CO co t-> sr —4 t—

•

or- >o (j —

»

co >T U> u> »T CM CM r-4 --

<

00 ci *-* to u> Is- m m in oo CO

f- CO —

1

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109

APPENDIX J

MATHEMATICS OF PREDICTION INTERVAL COMPUTATIONS

The mathematics involved in the computations of the

average monthly repair part consumption prediction intervals

is explained in this appendix.

The definitions of the mathematical terms in this appen-

dix are as follows:

1. Y, , Y_, Y_ The reported repair part consump-tion for months one, two f andthree, respectively, of the threemonth test period.

22. a The variance of a model.

23. S The unbiased estimate of the

variance of a model.

4. Y* The average monthly reported re-pair part consumption for thetest period, defined as Y,+Y

?+Y^.

3

5. wj, w», w' Vectors of observations of thedependent variables of the modelsfor months one, two, and three,respectively, of the three monthtest period.

6. b The matrix of coefficients of themodels

.

7. t The t-distribution.

The assumptions of this thesis included the assumption

of normal distributions of the data of the models. This

assumption is utilized in the computations of the prediction

intervals. Specifically, it is assumed that the reported

monthly repair part consumption for each of the months of

110

the test period are normally distributed. This assumption

implies that the average monthly reported repair part consump-

tion, being the sum of normal distributions, is also normally

distributed. Using this assumption and the procedures con-

tained in reference (3) for construction of predicted inter-

vals, the mathematical computation of the prediction inter-

vals was obtained.

The mathematical derivation of the prediction intervals

for the average monthly reported repair part consumption is

shown below.

1. Y, was assumed to be normally distributed with mean

2 -1w'b and variance a, (1+ w' (X'X) w, ) . Y

2was assumed to be

normally distributed with mean wXb and variance

2 -lCp(l + w^X'X) "w«) . Y-3 was assumed to be normally distri-

2 -1buted with mean w'b and variance o -. (1 + w'(X'X) w~) . It

2 2 2 2was assumed, in the models, that a, =Oy=o~=o .

2. The average monthly reported repair part consumption,

defined as Y, + Y2

+ Y^ , was therefore distributedY* = — -

3

normally with mean (w," + w~ + w')b and variance of

3

a2(3 + w^X'X)" 3^ + w^CX'X)"

3^ + w^ (X^X)"1w

3) .

9

3. Then, using probability theory, the ratio

(w£ -f w- + w-)

3 *

j /3 + wJ(X'X)~1w

1+ w'CX'X)" 3^ + wX(X'X)" w_

2follows a standarized normal distribution. But (n-k)

s

2

111

is distributed as chi-square with (n-k) degrees of freedom,

and is independent of the above ratio. Therefore,

(w:T + w' + w')b_ - y*

| /3 + w£(X"X)~ 1V71

+ w'(X'X) w2

+ w^(X"X)~ 1w3

is distributed as the t-distribution with (n-k) degrees of

freedom. By using the limits P (-t q,,,. < t(n-k) < tq 7t

-) =

0.95, the following 95% prediction interval for Y* is

obtained:

(w£ + w^ + w^)b t#9?5

s

/3 + w£(X"X)~ 1w1

+ w^CX'X)1w2

+ Wg(X'X) W-

< Y* <

(w£ + w- + wj)b t>975 s

A + S

/3 + w£(X'X)~ 1w1

+ w^X'X)"" 1*^ '+ wJoTX)

1w3

.

The 95% prediction intervals for the average monthly reported

repair part consumption were computed for all models of the

thesis utilizing the above derived mathematical formula.

112

BIBLIOGRAPHY

1. BMD Biomedical Computer Programs (BIMED02R) ,' Universityof California Publications in Automatic Computation,Publication Number 2, Second Edition, University ofCalifornia at Los Angeles (UCLA), 1970.

;

2. Dixon, W. J. and Massey, F. J., Introduction to Statis-tical Analysis , Third Edition, McGraw-Hill Book Company,1969.

3. Theil, H., Principles of Econometrics , John Wiley andSons, Inc. , 1971.

113

INITIAL DISTRIBUTION LIST

No. Copies

1. Defense Documentation Center 2

Cameron StationAlexandria, Virginia 22314

2. Library, Code 0212 2

Naval Postgraduate SchoolMonterey, California 93940

3. Chief of Naval Personnel 1

Pers libDepartment of the NavyWashington, D.C. 20370

4. Naval Postgraduate School 1

Department of Operations Researchand Administrative SciencesMonterey, California 93940

5. LT C. F. Snyder, USN 1

Center for Naval AnalysisArlington, Virginia

6. Mr. Ben Barrouk 1

Maintenance Support OfficeMechanicsburg, Pennsylvania

7. Asst. Professor J. K. Hartman 1

Department of Operations Researchand Administrative SciencesNaval Postgraduate SchoolMonterey, California 93940

8. Asst. Professor M. O. Sovereign 1

Department of Operations Researchand Administrative SciencesNaval Postgraduate SchoolMonterey, California 93940

9. LT Richard A. Lippert, SC , USN 1

1223 Spruance RoadMonterey, California 93940

10. LCDR William T. Lee 1

1007 Halsey DriveMonterey, California 93940

114

UNCLASSIFIEDSecuntv Classification

DOCUMENT CONTROL DATA -R&D(Security cl.ss.lic.t.on of till,, body ol abstract and indeiing annotation t»ust be entered when the overall report Is classilled)

Originating ACTIVITY (Corporate author)


Za. REPORT SECURITY CLASSIFICATION

UNCLASSIFIED26. GROUP

|. REPORT TITLE

Factors Influencing Ship Repair Part Consumption

i oescRiptive notes (Type ol report and.lnclusive dates)

I Master's Thesis; September 1973r autmoRiSI (First name, middle initial, laet name)

Richard A. LippertWilliam T. Lee

|REPOR T D A TE

September 197 3

M. CONTRACT OR GRANT NO.

J>. PROJEC T NO.

7«. TOTAL NO. OF PAGES

116

7l>. NO. OF REFS

3

6«. ORIGINATOR'S REPORT NUMBER(S)

9b. OTHER REPORT NO(S) (Any other numbera that may be ae»l£nedthle report)

10 DISTRIBUTION STATEMENT

Approved for public release; distribution unlimited.

R. SUPPLEMENTARY NOTES

13. ABSTRACT

12. SPONSORING MILITARY ACTIVITY


An investigation was made of possible linear relation-

ships between several specific factors concerning ships of

the Navy and the actual repair part consumption dollar fig-

ures for a two year period for the purpose of using such

relationships for planning and budgetary aids. Factors con-

sidered included steaming hours, fuel consumption, overhaul

schedules and overhaul mandays, and ship age. Overall Navy-

wide linear models were developed for NSA (odd cog) stock

numbered items, for APA (even cog) stock numbered items, for

Other (odd cog) manufacturer's part-numbered items (items

without a Federal Stock Number assigned) , and for a combined

overall repair part model. In addition, some of the same

models were developed for the Pacific and Atlantic fleets

and for certain ship types.

DD, F

r:..1473 ,PAGE "S/N 0101 -807-681 1

115UNCLASSIFIED

Security Cl«tmificotion 1-31408

[^CLASSIFIED'Security C)a»»ifirBtion

KEY KO"OI

Repair parts.

Consumptions

Navy Logistics

D ,

f

.T..1473 < SACK >

Ot 01 -807-682 I

ROLE WT

UNCLASSIFIED116 Security Clarification A- 31 409

145506

Thesis M55U6'L678 Lippertc.l Factors influencing

ship repai r part con-sumption.

»3 JUN74 ?2195

»3MAY 763 1

11 jun ee

2 U 3 3 82 6 40.2 8198305 17

Thesis

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c.l

14550$Lippert

Factors influencingship repair part con-sumption.

thesL678

Factors influencing sh

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Factors influencing ship repair part consumption

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