factors influencing ship repair part consumption
TRANSCRIPT
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)
PI as % of predicted consumption: 22.3%
Number of ships considered in the model: 251
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
Test quarter average reported consumption: $312.61 million
24
Predicted average monthly consumption: $321.61 million
95% Prediction Interval: ($306.32 million, $336.90 million)
PI as % of predicted consumption: 9.5%
Number of ships considered in the model: 182
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
Test quarter average reported consumption: $17.64 million
Predicted average monthly consumption: $14.87 million
95% Prediction Interval: ($12.06 million, $17.68 million)
PI as % of predicted consumption: 37.8%
Number of ships considered in the model: 134
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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—
•H ft •H •H£ O C rH VO *-* rH co en ^ 5 w ^ ^w -H CD .^ CO CO • 00 rH ^ m • ^r CO ft CO CO4J-H UI D in o co VO VO VO CO CM rH 0) rH CD rH CDrH trj U -H o -«-> CN CO v O ---. co en <D rH >H CD rH a ih0) -H -H (fl H O O CO CM CO O vo ^ i^« in 'd XI <: 'd & TJ X)"d >»h 0) 0Q •^ rH rH CNJ CO CM rH CT\ in rH fd § o rd fdo <u u-i x; H o co in — r> -w K£> KO CO —
'
e -h ft £ -HS 'd Q) -p ffi »H ^ -rH >H w Mft •H *-* + «* in —' + o id Q fd fd
S s > 2 > 2 >
o1
1
ft W Q W Q>i ft w ft wEh
Ehl-H* 2 >H
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
OTHER 3.44 0.76 Accept
ATLANTIC OCEAN MODELS
. .OVERALL COMBINED
NSA 3.79 0.42 Accept
APA 4.28 0.28 Accept
OTHER 3.44 0.15 Accept
SHIP TYPES - DESTROYEIIS
0.39 AcceptOVERALL COMBINED 3.44
NSA 3.44 0.51 Accept
APA 3.79 0.24 Accept
OTHER 3.44 0.98 Accept
SHIP TYPES - CRUISERS
3.79 0.74 AcceptOVERALL COMBINED
NSA 3.44 1.12 Accept
APA 3.44 0.62. Accept
OTHER - - -
46
F Critical TestModel Value Statistic Results
SHIP TYPES - SUBMARINES
0.79 AcceptOVERALL COMBINED 3.79
NSA 3.44 0.67 Accept
APA 4.28 0.85 Accept
OTHER - - -
SHIP TYPES - AMPHIBIOU S
0.77 AcceptOVERALL COMBINED 3.79
NSA 3.44 0.91 Accept
APA 3.79 0.67 Accept
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
OTHER 1.22 1.42 2.56 Accept
ATLANTIC OCEAN MODELS
OVERALL COMBINED -
NSA 1.13 1.54 2.46 Accept
APA 1.03 1.67 2.50 Accept
OTHER 1.22 1.42 1.58 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
OTHER 1.22 1.42 1.50 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 4 G 1 Y DDG 5 G 1 Y
DDG 6 G 1 N DDG 7 G Y
DDG 8 G 1 N DDG 9 G N
DDG 10 G 1 Y DDG 11 G 1 Y
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 18 G 1 Y DDG 19 G 1 Y
DDG 20 G 1 N DDG 21 G 1 Y
DDG 22 G 1 Y DDG 23 G 1 Y
DDG 24 G 1 Y DDG 31 G 1 Y
DDG 32 G 1 Y DDG 33 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
TYPE HULL # RPC FC O/H TYPE HULL # RPC FC O/H
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 600 B 1 Y SSBN 601 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 628 B 1 Y SSBN 629 B 1 Y
SSBN 630 B 1 Y SSBN 631 B 1 Y
SSBN 632 B 1 Y SSBN 633 B 1 Y
SSBN 634 B 1 Y SSBN 635 B 1 Y
SSBN 636 B 1 Y SSBN 640 N 1 Y
SSBN 641 B 1 Y SSBN 642 B 1 Y
SSBN 643 B 1 Y SSBN 644 B 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
TYPE HULL # RPC FC O/H TYPE HULL # RPC FC O/H
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
TYPE HULL # RPC FC O/H TYPE HULL # RPC FC O/H
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
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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)
Naval Postgraduate SchoolMonterey, California 93940
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
Naval Postgraduate SchoolMonterey, California 93940
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
L67«
c.l
14550$Lippert
Factors influencingship repair part con-sumption.
thesL678
Factors influencing sh
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