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ESTIMATION OF DESTROYER TYPE NAVAL SHIPPROCUREMENT COSTS
Donald Mearns Hernon
LIBRARYNAVAL POSTGRADUATE SCHOOLMONTEREY, CALIF. 93940
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THEEstimation of Destroyer
Type Naval Ship Procurement Costs
by
Donald Mearns Hernon
and
Ralph Ray McCumber, Ir.
Thesis Advisor
March 1973
N. K. Womer
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kppLo\j?^d Ion. public hqJLqjO&q.} cli&.PUbuuti.on unZimi£e.d.
Estimation of DestroyerType Naval Ship Procurement Costs
by
Donald Mearns HernonLieutenant Commander, United States NavyB. S. United States Naval Academy, 1959
and
Ralph Ray McCumber, Jr.
Lieutenant, United States NavyB. S., United States Naval Academy, 1966
Submitted in partial fulfillment of therequirements for the degree of
MASTER OF SCIENCE IN OPERATIONS RESEARCH
from the
NAVAL POSTGRADUATE SCHOOLMarch 1973
LIBRARY
'TE SCHOOL93940
ABSTRACT
This study presents three models by which the total procurement
cost of Destroyer and Destroyer Escorts may be estimated. One model
utilizes 9 subsystem costs estimating relationships (CERs) to obtain
a total cost estimate; the second model utilizes k subsystem CERs;
the final model is a single total cost equation. The CERs were
developed using the linear least squares regression technique on a
data base of ships built from 1954-66. The CERs utilize input
variables that may be determined long before actual ship construction
begins. This fact, and the precision of the model estimates, recommend
usage of these models in cost-effectiveness analysis. The Patrol
Frigate is utilized as a sample application, wherein model estimates
compare favorably with the current NAVSHIPS cost estimates. This study
uses the data base from Resource Management Corporation Report CR-058,
The Navships Cost Model, and critiques that report.
TABLE OF CONTENTS
I. INTRODUCTION 8/
A. NAVAL SHIP CONSTRUCTION COSTS 9
B. RMC REPORT CR-058 — 10
1. Basic Contract Cost • — 11
2. End Costs — 12
3. Cost Model 13
4. Ships' Characteristics as Independent Variables 13
C. THESIS OBJECTIVES . 15 V
II. CRITIQUE OF RMC STUDY i8
A. NUCLEAR DUMMY VARIABLE i8
B. INDEPENDENT VARIABLES 20
C. STATISTICAL INFORMATION - 22
III. DATA BASE 23
A. DATA ADJUSTMENTS ?-4
1. Bid Cost Data 24
2. End Cost Data 28
B. THESIS DATA BASE 29
C. DATA BASE STRATIFICATION AND COST GROUP MODELS 31
D. INDEPENDENT VARIABLES 31
IV. ANALYSIS 34
A. RESULTS - CERs AND STATISTICAL SUMMARIES 34
B. DEVELOPMENT OF CERs 43
1. Criteria for Selection of Independent Variables ^3
2. Methodology and Discussion of CER Development q4
a. Models B and C - 9 CERs 44
(1) Hull Cost —"—. 44
(2) Propulsion Cost 46
(3) Electrical Cost ——
*
47
(4) Communication and Control Cost PlusElectronics End Cost 47
(5) Auxiliary Cost 48
(6) Outfitting Cost 49
(7) Armament Cost Plus Weapons End Cost 49
(8) Design and Engineering Cost 50
(9) Construction Services Cost PlusMiscellaneous End Cost 50
b. Models D and C - 4 CERs 51
(1) Base Cost 51
(2) Engineering Cost » 53
(3) Payload Cost 53
(4) Services Cost « 54
c. Models F and G - 1 CER 54
V. ESTIMATES OF TOTAL COST VARIANCE 57
A. SUMMATION METHOD 57
1. Model 5 7
2. Results 59
B. MEAN SQUARE RESIDUAL METHOD 59
1. Model 59
2. Results 64
C. ANALYSIS OF RESULTS 64
1. The Coefficient of Variation 64
2. Conclusions 65
VI. APPLICATION - PATROL FRIGATE 68
A. MODEL ESTIMATES 68
1. Parametric Input Data -
—
"°
2. Total Cost Estimates 68
B. NAVSHIPS ESTIMATES ^-^-^-— «- 71
1. Basic Contract Cost — . 71
2. End Costs 71
3. Total Procurement Cost '^
C. COMPARISON OF ESTIMATES 72
1. Estimates > • 72
2. Discussion of Results 75
VII. CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER RESEARCH 77
A. MODELS B AND C 77
B. MODELS D, E, F, AND G 78
C. APPLICATION OF MODELS - PF 79
D. COMPARISON OF MODELS TO THE RMC MODEL 80
E. CERs REQUIRING FURTHER DEVELOPMENT 81
1. Communication and Control Cost PlusElectronics End Cost (B4/C4) 83
2. Armament Cost Plus Weapons End Cost (B7/C7) 83
3. Design and Engineering Cost (B8/C8) 83
4. Construction Services Cost PlusMiscellaneous End Cost (B9/C9) 8Z
>
5. Services Cost (D4/E4) 8Z>
F. DATA BASE DIFFERENCES 65
G. ADDITIONAL RECOMMENDATIONS 86
APPENDIX A RESIDUAL VERSUS FITTED COST PLOTS FOR CER MODELSREQUIRING LOGARITHMIC TRANSFORMATION 89
APPENDIX B CUMULATIVE DISTRIBUTION OF RESIDUALS PLOTS USEDIN OUTLIER IDENTIFICATION 95
APPENDIX C DESCRIPTION OF SHIPS' CHARACTERISTICS USEDAS EXPLANATORY VARIABLES IN RMC REPORT CR -058 109
APPENDIX D DESCRIPTION OF SHIPS' CHARACTERISTICS USEDAS EXPLANATORY VARIABLES IN THESIS 113
APPENDIX E DESCRIPTION OF COST CATEGORIES 116
APPENDIX F TOTAL COST RESIDUALS - GENERAL DATA BASE 117
APPENDIX G TOTAL COST RESIDUALS - ESCORT DATA BASE 119
APPENDIX H DATA BASE (U) (CONFIDENTIAL document;published separately) —
LIST OF REFERENCES 120
INITIAL DISTRIBUTION LIST 121
FORM DD 1473 122
LIST OF TABLES
I. RMC Method for Computation of Cost Elements — « 14
II. RMC 9-Group Basic Contract Cost EstimatingRelationships: Destroyers —— 19
III. Bid Data Learning Curve Slopes 26
IV. Thesis Data Base Ship 'Types — 29
V. Data Base Stratification Levels and Cost Group Models 32
VI. Model B CERs and Statistical Summary 36
VII. Model C CERs and Statistical Summary 38
VIII. Model D CERs and Statistical Summary 40
IX. Model E CERs and Statistical Summary 41
X. Model F CERs and Statistical Summary 42
XI. Model G CERs and Statistical Summary 42
XII. Variables Used in Models B and C 45
XIII. Variables Used in Models D and E 52
XIV. Variables Used in Models F and G 55
XV. Estimates of Total Cost Variance as a Sum of
CER Variances 60
XVI. Estimates of Total Cost Variance by Mean SquareResidual Method 63
XVII. Variance, Standard Deviation, and Coefficient of
Variation for Estimates of Total Cost Variance 66
XVIII. Patrol Frigate Input Data 69
XIX. Model Cost Estimates for the Patrol Frigate 70
XX. Patrol Frigate End Cost Items 73
XXI. Patrol Frigate Total Cost Estimates 74
XXII. CERs of Poor Statistical Quality 82
I . INTRODUCTION
The problem of estimating the procurement cost of major weapons
systems is particularly important at the present time. The adoption
and wide use of cost-effectiveness as a tool of systems analysis has
made necessary the development of cost estimating techniques that demand
input data of far less than detailed engineering design quality and
that produce estimates of relatively good quality. The major use of
this type estimate is in comparing the relative cost of various
weapons systems competing as alternatives in a specified mission area.
Once the decision has been made to continue into the advanced design
phase on a given weapons system, the use of cost estimates changes.
The major usage now becomes one of planning, programming and budgeting
money to the selected alternative weapons system for development and
construction. The cost estimates required at this state of procure-
ment must of necessity be more precise and thus require a refinement
of the input data.
The general objective of this paper is to present several models
by which destroyer procurement costs might be estimated with a
precision acceptable in cost-effectiveness studies. The input data
required by these estimating models could be supplied during the
concept definition stage of procurement, making the models useful as
estimating tools from the onset of the project. During ship develop-
ment, the input data is refined as the project takes shape. As the
input data is more accurately defined, the cost estimate becomes more
precise. However, due to the inherent statistical discrepancies of
the models developed , the cost estimate will always retain a degree
of uncertainty. Thus the estimate must always be associated with a
measure of precision — variance. Because of the techniques utilized
in the development of these models, it is not expected that model
precision will ever approach t hat required for fiscal planning. However,
the usefulness of certain input parameters as cost predictors could be
verified, thereby indicating logical directions for further effort.
Therefore, the usefulness of the models developed in this paper is
logically confined to the phases of procurement prior to detailed
engineering design. The models should support the concept development
phase as cost-effectiveness tools.
It should be noted that the methods, results and conclusions
presented in this thesis are unclassified. However, some of the
parameters listed for specific destroyer type ships in the Data Base,
Appendix H, are classified CONFIDENTIAL. Therefore, this Appendix
has been published as a separate document.
A. NAVAL SHIP CONSTRUCTION COSTS
Naval ships may be thought of as major weapons systems consisting
of numerous subsystems including:
hull structure
propulsion plant
crew support facilities
sensor systems
weapons and fire control systems.
One method utilized to predict construction costs involves the
estimation of construction costs for each subsystem which, when
aggregated, form the total system cost. The CODE SHIP MODEL [1]
developed by the Center for Naval Analyses (CNA) is essentially of
this type. Another type of cost model involves the estimation of
procurement cost as a function of the ship's operational characteristics,
i. e. , maximum speed, type of weapons and sensors, endurance range,
etc. CNA has adapted this technique to t heir ESCORT SHIP COST MODEL
(ESCOMO) [2] which is currently under development.
The NAVSHIPS COST MODEL developed by the Resource Management
Corporation (RMC) under contract to the Naval Ship Systems Command and
published in January of 1969 as RMC Report CR-058, The Navships Cost
Model (U), classified CONFIDENTIAL [3], is of the first type discussed.
Within this model, subsystem costs are based on linear cost-estimating
relationships (CERs)developed from past ship construction data.
B. RMC REPORT CR-058
This report details the work done by RMC in developing the NAV-
SHIPS COST MODEL for estimating the cost of new construction ships
in civilian shipyards (as opposed to government-owned shipyards)
.
The project entailed two distinct phases:
1. Collection and review of historical data on ship construction
costs for a 13-year period (1954-1966) which led to the
development of CERs to predict cost as a function of ships'
characteristics
.
2. Development of computer models to:
a. Update and adjust the data base.
b. Predict total cost as a function of the CERs developed.
10
RMC employed the linear least squares regression technique to develop
CERs from the historical data base for each ship subsystem. The total
cost of the ship was defined as the summation of these subsystem costs
(basic contract cost) plus the cost of electronics, weapons and mis-
cellaneous items, added after completion of basic ship construction
(end-cost items)
.
1 . Basic Contract Cost
Winning contractor bids, as amended by negotiation, were used
in the data base to compute basic contract CERs. RMC utilized two
different approaches in deriving CER S from the 13-year data base.
The first approach consisted of a stratification of the data into six
groups according to ship type, as follows:
a. aircraft carrier
b. destroyer
c. submarine
d. auxiliary
e. amphibious
f. patrol/minesweeping
The basic contract costs of each subsystem were then utilized
as dependent variables for which CERs were developed, one for each
of the following subsystems :
a. hull
b. propulsion
c. electrical
d. communication and control (C&C)
e. auxiliaries
f. outfitting
11
g . armament
h. design and engineering
i. construction services.
The summation of these nine cost categories plus profit and overhead
was defined as basic contract cost. Thus, nine CERs were developed
for each of the six ship types examined, for a total of 54 CERs. The
nine basic contract cost categories are described in more detail in
App endix B". C^
The second approach treated the data as an aggregate; i. e.,
unstratified according to ship type. In addition, RMC found it
necessary to condense the original 9-subsystem cost groups into
4-subsystem cost groups, due to significant differences between
contractors concerning which cost was included under a sub-system
heading. The four condensed sub-system cost categories included:
a. hull- group : hull, design and engineering,
construction services
b. propulsion group : propulsion, auxiliary
c. armament group : armament, electrical,
communication and control
d. outfitting : outfitting
Thus, within this approach, a single CER was developed in each of
the four areas listed above to apply to all nine naval ship-types, for
a total of 4 CERs.
2. End Costs
The source of end cost data employed by RMC was the NAVSHIPS
records of Shipbuilding and Conversion, Navy (SCN) fund. Navships
Hardcore Cost was subsequently defined as Basic Contract Cost plus
12
Miscellaneous End Costs and Electronics End Costs. The Total End Cost
then became Navships Hardcore Cost plus Weapons End Cost. CERs were
developed from the data base for predicting Total End Cost and Miscella-
neous End Cost. No CERs were developed for Electronics or Weapons End
Costs. Again, a separate CER was developed for each of the six different
ship types. The end cost categories are described in more detail in
Appendix E.
3. Cost Model
Table 1 summarizes the cost models employed within the RMC
study. These alternatives represent different methods of achieving a
total cost prediction.
A . Ships' Characteristics as Independ ent Variables
The development of CERs to predict ship construction costs
requires the use of numerous ships' characteristics to serve as
independent variables in t he regression analysis. The variables
utilized by RMC for this purpose were obtained from various sources,
including
:
a. Naval Vessel Register/Ships Data Book
b. Navy Materials Annex/Weapons Dictionary
c. Weight Control books
d. Contractor's accepted estimates
e. Navy contract design estimates.
These variables generally consisted of characteristics that could be
estimated long before ship construction began, such as:
13
TABLE I
RMC METHOD FOR COMPUTATION OF COST ELEMENTS
Cost Element Options
9 groups of
Basic Contract
No options. These cost elements are always estimated
with the CERs.
If Profit % is Supplied: If Profit % is notSupplied
:
Profit Profit = (Sum of gps 1-9) x % Profit = Sum gps (1-9)
x 6%
Basic Contract BC = Sum gps (1-9) + Profit BC = Sum gps (1-9) +Profit
Electronics
Miscellaneous
If Electronics Cost is
Supplied
:
If Electronics Cost is
not Supplied:
ELEC = Supplied Value
MISC = Predicted Value
ELEC = HC-BC-M1SC
MISC = Predicted Valueunless BC+MISOHC,then MISC = HC-BC
NAVSHIPSHardcore HC = BC + MISC + ELEC HC = Predicted Value
Weapons
Total End Cost
If Weapons Cost is
Supplied:If Weapons Cost is not
Supplied
:
WEAP = Supplied Value WEAP = Predicted TEC-HC
TEC = HC 4- WEAP TEC = HC + WEAP
In all cases
:
Basic Contract=Sum of Groups (1-9) + Profit
Total NAVSHIPS Hardcore = Basic Contract: + Miscellaneous+ Electronics
Total End Cost = Total NAVSHIPS Hardcore + Weapons
14
a. Subsystem weights: armament, electrical, propulsion,
C&C, auxiliary, outfitting, hull, light ship weight
(LSW), etc.
b. Performance specifications: maximum shaft horsepower
(SHP) , maximum speed, endurance range, total kilowatt (KW)
capacity, etc.
c. Payload specifications: number of m issile launchers,
number of generators, complement, etc.
A complete listing of all the characteristics included in the data base
by RMC may be found in Appendix C.
C. THESIS OBJECTIVES
The general objective was to develop a model for the prediction of
the total procurement cost of destroyer type naval ships that increases
in precision as input data is refined and attains a level of quality
acceptable in cost-effectiveness studies. The thesis was limited to
destroyer type ships in order to reduce the scope of the problem and
also because of the authors' familiarity with this type ship.
Specific objectives:
1. In analyzing the RMC study numerous deficiencies were noted
and are discussed in detail within Section II. The first objective
was to correct these deficiencies. In addition, certain convenient
alterations to the RMC model were made because the emphasis of this
paper is upon the prediction of total cost rather than the identification
of Basic Contract Cost and separate End Costs. For this reason the
End Cost data was aggregated with the Basic Contract Cost data as
follows
:
15
a. Electronics End Cost was added to Command and Control
Cost.
b. Weapons End Cost was added to Armament Cost
c. Miscellaneous End Cost was added to Construction Services
Cost
2. Another initial change to the RMC approach involved the
establishment of two data bases from the single destroyer data base
used by RMC. DLG type ships have often been associated with different
operational missions than DD, DE, DDG or DEG type ships, and obviously
have a larger displacement. To determine whether these factors proved
significant in the estimation of total cost for smaller destroyer type
ships, two data bases were utilized wherein:
a. The general data base includes all DD, DDG, DLG, DEG and
DE type ships.
b. The escort data includes all destroyer type ships with the
exception of DLG ship types.
Thus, as each alternative model for total cost estimation was developed,
it was developed using two data bases, one a subset of the other. This
provided a capability to examine statistical results and test the
hypothesis that DLG type ships are not strictly of the same class as
escort ships.
3. Three models were to be examined using each data base. The
first model was essentially the same as employed by RMC, but included
End Cost data in the nine subsystem costs. The second model was an
aggregation of these nine subsystem costs into four subsystem cost
categories, as defined in Section III. The last model was a single
cost estimation equation. The primary criteria for comparing the
16
predictive value of these models was the estimate of variance
associated with each model. This estimate of variance was to be
derived in two different ways, as discussed in Section IV. This
procedure was employed to permit a test of the hypothesis that the
models are not essentially different in their individual predictive
capabilities.
A. The final objective associated with this paper was the estima-
tion of total procurement cost of an escort or general destroyer type
ship currently under development, and a comparison of these model
predictions to the best estimate available within the Naval Ship
Systems Command.
17
II . CRITI QUE OF RMC STUDY
A. NUCLEAR DUMMY VARIABLE
The RMC study made use of two dummy variables, NUC and DE-DEG,
and one indicator variable, PROLSW. These variables are discontinuity
variables taking on the following values
:
1. NUC: value of 1 if ship is nuclear, if the ship is non-
nuclear.
2. DE-DEG: value of 1 if ship is DE or DEG, if the ship is
DD or DLG.
3. PROLSW: value of light ship weight (LSW) if ship is a proto-
type, of ship is not a prototype.
The technique of dummy and indicator variables can be very useful in
explaining additional costs associated with only a portion of the
ships in the data base.
However, the RMC study had only one nuclear powered ship,
DLGN-36 , in its destroyer data base while the dummy variable NUC was
found in five of the nine bid cost group CERs . Utilizing this
variable assured that for each of these five CERs, the predicted cost
of a nuclear powered ship fell precisely on the observed cost and
thereby tending to increase the value of the coefficient of determina-
tion, pv2 , for the CER in a questionable manner. Since there was only
one data point, it would have seemed more reasonable to disregard it
and to develop CERs for non-nuclear powered ships, rather than develop
a general equation for both nuclear and non-nuclear powered ships. As
more data on the costs of nuclear powered ships becomes available,
CERs can be developed separately.
18
TABLE II
RMC 9-GROUP BASIC CONTRACT COST-ESTIMATING RELATIONSHIPS: DESTROYERS(millions of dollars)
1. Hull Cost
CER: Y = -0.870 + 0.00144 HULWGT + 3.794 NUC -I- 22.652 AR/LSW
2 • Propulsion Cost
CER: Y = 2.090 + 0.00640 PROWGT + 17.461 NUC - 0.0790 SERIES
3. Electrical Cost
CER: Y = 0.134 + 0.283 GEN + 0.00350 ELEWGT + 2.310 NUC
4. Communication and Control Cost
CER: Y - 0.237 + 0.00361 C&CWGT + 1.513 NUC
5. Auxiliary Cost
CER: Y = 0.09582 + 0.00176 PROWGT + 0.00295 AUXWGT
6. Outfitting Cost
CER: Y - 0.150 + 0.00544 OUTWGT
7. Armament Cost
CER: Y = -1.453 + 0.0068 ARMWGT -I- 1.151 DEDEG
8. Design and Engineering Cost
CER: Y = -1.0520 + 0.00667 ARMWGT + 0.00156 PR0LSW
9
.
Construction Serv ices Cost
CER: Y = -0.0109 + .000241 LSW + 1.131 NUC
19
Therefore, it was decided to delete this one nuclear data point
from the data base_and to develop CERs for only non-nuclear powered
ships. Thus, it was necessary to develop new regression equations for
the five CERs which originally used the dummy variable NUC. A complete
listing of the nine RMC CERs appears in Table II. The precise defini-
tion of each independent variable employed by RMC can be found in
Appendix C.
B. INDEPENDENT VARIABLES
The selection of independent variables to be utilized as cost
predictors in various CERs should be based upon several standard
criteria. The statistical tool used in the CER analysis was multiple
linear regression. This technique produces more precise estimates in
situations where there is low intercorrelation among the explanatory
variables. High intercorrelation among the explanatory variables
yields large variances for their coefficients and therefore imprecise
estimates of them. This concept is explained in more detail in
(Ref. 4, p. 179], The RMC study generally considered correlation
coefficients of less than 0.6 to be acceptable.
Another valid requirement asserts that each independent variable
should exhibit, subjectively, a logical cause-effect relationship with
cost. For example, the use of the independent variable NO-GEN,
representing the number of main electrical generators, in the electrical
cost CER appears subjectively logical because the addition of another
generator to the electrical plant should increase the total electrical
cost.
20
In three of the CERs developed by RMC, these criteria seem to
have been disregarded. The auxiliary CER was developed with two
highly intercorrelated explanatory variables, PROWGT (propulsion
weight) and AUXWGT (auxiliary weight). The high intercorrelation
(correlation coefficient =.78) between these two variables is not
surprising since the auxiliary system provides support for the
propulsion plant as well as the rest of the ship. It would be concept-
ually possible to design a ship with a large propulsion plant and only
a minor auxiliary system, but empirically this is not the case. In
fact, empirical data suggests that it would be difficult to believe that
these two variables are not highly inter-dependent.
The variable, DE-DEG, was utilized within the RMC armament
CER to indicate, whether a ship was a DE or DEC If the ship was a
DE-DEG, then this variable took the value one, while all other ship
types assumed a DE-DEG value of zero. Used in this manner with a
positive coefficient, the inclusion of DE-DEG is extremely counter-
intuitive. Logically the cost of DE-DEG armament should be lower
than other ship types. Given a constant armament weight in the equation,
ARMAMENT COST = a + b (ARMWGT) + c (DE-DEG) , the implication is
made that it costs more to arm a DE or DEG than a DLG, with the same
armament weight. It is not obvious why this would be true and
no further discussion was offered within the RMC study to support this
concept.
Finally, the RMC study utilized SERIES as an explanatory variable
in the auxiliary CER. To construct the SERIES variable, RMC
separated the. destroyer observations into three groups: (1) DD and
DDG, (2) DE and DEG, and (3) DLG and DLGN . Within each of these
three groups, arbitrary numbers were assigned to each ship based
21
upon its relative completion date within the group. The logic of this
type ordering is not thoroughly documented in the study nor does it
appear reasonable to utilize such a variable, especially when the
explanatory variables are to be input oriented. It would be
impossible to create such an ordering until all ships were completed -
and then all predictive value of this CER is lost.
The criticisms presented above suggested the development of
three new CERs utilizing other variables.
C. STATISTICAL INFORMATION
A final criticism of this study arises in the exclusion of significant
statistical information from the published study. First, no reference
is made as to the relative independence of two or more explanatory
variables utilized in a given CER. Secondly, the exclusion of F-values
and t-values for each CER or independent variable, respectively,
detracts from the credibility of the study. However, it should be noted
that upon investigation, each variable was found statistically sig-
nificant utilizing a .05 confidence level and each equation was verified
using an F test at the same level of confidence. Finally, there was
no mention within this study of any analysis of residuals based on
scatter plots or normalized residual plots. The verification of the
normality assumptions of the linear least squares regression technique
and the identification of any significant outliers could have been
accomplished had these methods been used.
22
Ill . DATA BASE
One significant point should be addressed before proceeding
further. It is understood that the use of contractor bid data for
predictive purposes is not an optimal procedure. It would be much
more desirable to utilize ^actual ship construction costs if these costs
were available. However, this is not the case. During the period
from which this data was collected (1954-1966) , cost accounting
systems differed greatly among the various contractors and NAVSHIPS,
making it virtually impossible to obtain data on a uniform level of
aggregation and in a manner suitable for the objectives of this thesis.
In addition, bid costs are really prices in the shipbuilding industry
and are thus subject to price fluctuation. Some types of ships can
only be built by certain shipyards due to the required level of expertise
in electronics or weapons systems, for example. The bids on these
ships could reflect a "monopoly" effect. Some shipyards are fully
employed in the building of both naval and commercial ships. These
shipyards might have a lower overhead, and thus produce lower bid prices,
than shipyards that were not operating at full capacity. Thus, bid
costs can be affected by many variables, some of which are not
directly concerned with the construction costs of a specific, ship.
However, contractor bid data is the most meaningful data avail-
able for the period under study (1954-1966) . Using this data at
least allows a preliminary effort to be made in deciding which
ship's characteristics determine construction costs and within what
limits of accuracy these estimates might fall.
23
The cost data utilized in the RMC study consists of contractor
bid data and end cost data, the sources of which have been discussed
earlier. The study presents a. listing of this cost data in its raw form
and a similar listing wherein the raw data has been adjusted for tem-
poral and learning effects. The adjustments made to the raw data
are discussed below.
A. DATA ADJUSTMENTS
1. Bid Cost Data
Contractor raw bid data was adjusted in four specific
ways to remove cost variations due to other than ships' characteristics,
as follows
:
a. learning effect,
b. temporal effect,
c. installation of government furnished equipment, and
d. cost of plans from external sources.
The learning effect implies that the cost of ship construction
decreases progressively with each ship in a procurement lot. This
effect may be stated mathematically as follows:
y aX 1b
where y = average cost of X ships
a = unit cost of lead ship
X = total number of ships in procurement lot
b = learning coefficient
The information necessary to adjust for the learning effect, was
derived from NAVSHIPS FORM 4282.2, UNIT PRICE ANALYSIS - BASIC
CONSTRUCTION, which lists contractor estimates for the nine different
construction cost groups, subdivided into three categories: direct
24
labor, direct material, and overhead costs. Utilizing a data base
of 210 ships of all types (DD, AE, LSD, MSC, SSN, etc.), for which
19 bids were for 4 or more ship «r lots, 73 bids for 3 ship-lots, and
118 bids for 2 ship^lots, an overall average learning curve slope
was determined for all ship types to apply to labor hours and material
dollars for each of the 9 basic contract groups. The overall average
learning curve slopes are listed in Table III, and represent the
percentage change in average cost that results from a doubling of the
quantity produced. Thus, the relationship between the slope, s,
and the learning coefficient, b, is:
log s = b log 2
25
TABLE III
BID DATA LEARNING CURVE SLOPES
Labor Materiel Total Cost
Cost Groups 1-7, 9: mean 95.4 98.5 95.2
standard deviation 3.4 1.4 2.3
Cost Group 8: mean 64.9 65.9 63.1
standard deviation 15.3 18.9 13.6
Note that cost group 8, design and engineering, is listed separately
since its average slope was significantly different from those of the
other cost groups. Also, the values of standard deviation for the
cost groups merit examination. Even a 3% change in the cost of a $30
million ship results in about a $1 million difference. In cost group 8
the standard deviations are much larger, but the group cost is in the
range of $.1 to $1.9 million with the exception of three destroyer
type ships that have group 8 costs in the range of $8.5 to $11.5 million,
Thus, using average learning curve slopes to adjust bid data can
result in significant errors.
Temporal effect refers to the variation of prices, productivity
and wages over time. The RMC data base included construction data
from 1954 to 1966. To remove the temporal effects inherent in this
data, 1965 was chosen as the base year, and all data from other
years was adjusted to the base year by means of standard shipbuilding
industry indices for prices, productivity and wages.
The installation of government furnished equipment by the
contractor required significant adjustments, especially in the prop-
ulsion category. To achieve consistency, the cost to the government
26
of government furnished equipment (GFE) was added to the appropriate
cost group since the contractor's bid represented only the cost of
installation and not the cost of the GFE.
The cost of plans supplied to the builder from an external
source was added to cost group 8, design and engineering. Again,
this was done to achieve an accurate and consistent cost breakdown.
The order in which these adjustments were made to the data
was as follows:
1. application of the learning curves produced data
representing unit one costs;
2. adjustments, using 1965 indices, produced data
representing unit one costs in 1965 dollars; and
3. addition of the cost of GFE and plans, produced
data representing all basic contract costs, on a con-
sistent level, as unit one costs in 1965 dollars.
In most cases these adjustments involved relatively small
dollar differences between raw and adjusted data.' However, the
following adjustments superficially appear large and somewhat
inconsistent:
a. DLG-6. Propulsion cost was adjusted from $4.28
to $8.97 millions and Basic Contract Cost rose
from $17.7 to $25.8 millions.
b. DLG-16. Design and engineering was adjusted from
$1.18 to $11.56 millions and Basic Contract Cost
increased from $26.8 millions to $38.37 millions.
c. DLG-26. Design and engineering was adjusted
from $0.54 to $10.46 millions and Basic Contract
Cost increased from $19.66 to $29.56 millions.
27
Ho comment is made within the RMC study to indicate the
reasons for such large adjustments. These adjustments may well be
justified but, in each case noted above, these data points proved to be
extreme outliers when utilized in regression analysis. A brief des-
cription of these adjustments would have lent considerably more
validity to these values.
One further comment is necessary. The adjustment for
learning effects was carried out in terms of inflated dollars since the
temporal effects were treated after the learning adjustments. A
reversal of this order of treatment would produce different final
dollar values. An explanation concerning the order of treatment would
have been appropriate.
2. End Cost Data
End Cost Data was adjusted in much the same way that Contractor
Bid Data was adjusted. Three specific adjustments were made to the
raw End Cost Data, as follows:
a. Treatment for learning effect utilizing a slope of
96.8 percent.
b. An adjustment for temporal effect based on general
shipbuilding, electronics, and ordnance indices with
1965 as the base year.
c. An adjustment for nuclear technology with propulsion
costs. This adjustment applied to only one ship
(DLGN 36) and will not be discussed because that
data was ultimately deleted from the data base
for reasons that have been discussed earlier.
28
The three adjustments listed above provided small and con-
sistent changes between raw and adjusted data, and were therefore
accepted as reasonable.
B. THESIS DATA BASE
As indicated earlier, the adjusted values for Basic Bid and End
Cost Data were accepted as a point of departure for this analysis of
destroyer construction costs. However, one objective of this thesis
was to examine Basic Bid and End Costs simultaneously. This required
that each observation, or each ship, have complete information
in both cost categories. Within the KMC study, Basic Bid Cost
data was provided on 41 ships, and End Cost data on 90 ships. In
matching the two cost categories against one another, ship-by-ship,
4 ships were eliminated from the original 41 possible ships. The
exclusion of the one nuclear-powered ship, DLGN-36, reduced the
Thesis Data Base to 36 ships, as noted in Table IV.
TABLE IV
THESIS DATA BASE SHIP TYPES
TYPE - BASIC BID & END COST DATA AVAILABLE
DD 3
DDG 11
DE 11
DEG 2
DLG 9
TOTAL 36 ships
29
This breakdown of ship types in Lite data base cannot be considered as
a representation of the proportion of each type ship in either the
current or future Navy. The general purpose destroyer (DD) is
obviously underrepresented with only 3 ships in the data base. Thus,
the data base could be considered as being biased toward guided
missile ships (22 out of 36 ships) . There is no way to correct a
possible bias except by attempting to use weighted average values
(weight the average figures for each ship type by the proportion of that
type in the current or proposed Navy) or selectively dropping some
of the DDGs/DLGs to gain a more correct proportional representation.
However, there are relatively few ships (36) in the data base, and
average figures tend to eliminate possibly important differences
among ships of the same class. Also, there is no really objective
way to determine the proportional breakdown of ships in a future
Navy. For these reasons, it was decided to use the data base as
given, while recognizing a possible bias due to the number of ships
of each type that it contains. The data base is not truly homogeneous
since it contains five different types of ships. They are all bound
together under the general heading of surface combatant ships.
However, major differences exist, as follows;
1. DD - general purpose destroyer; good shore gunfire
support capability; ASW capability; poor AAW capability.
2. DDG — general purpose destroyer with good gunfire
support, ASW and AAW capabilities.
3. DE - ocean escort with good ASW capability only.
30
4. DEG - ocean escort with good ASW and close in AAW
capabilities.
5. DLG — major fleet escoi't ; extra communication and
control equipment; good ASW and best AAW capabilities.
It is obvious that a DE cannot perform all of the same missions that a
DLG can perform. Even so, each data point is given the same weight
in the data base.
C. DATA BASE STRATIFICATION AND COST GROUP MODELS
The RMC study considered destroyer type ships as a single group.
In reviewing the data, it was noted that some DLG type ships had
significantly higher costs in the following areas: hull, outfitting,
construction services, weapons end cost, and electronics end cost.
In addition, as described in Section III B, the DLG type ship can
be considered to have a different operational mission than the smaller,
less expensive destroyer type ships. Thus, two basic data base
stratification levels were examined:
1. General Data Base: DD/DDG/DE/DEG/DLG
2. Escort Data Base: DD/DDG/DE/DEG
Using both the data bases, CERs were developed using three
different methods of cost disaggregation schemes for each data base.
To maintain order within the analysis, a coding system was adopted
to label each CER. These codes appear in Table V.
D. INDEPENDENT VARIABLES
The RMC destroyer data base contains, in addition to cost
information, 41 physical characteristics for each ship in numerical
form. These characteristics are essentially design parameters such
as maximum speed, maximum draft, number of boilers, hull, armament,
31
TABLE V
DATA BASE STRATIFICATION LEVELS AND COST CROUP MODELS
MODELS B/C - 9 COST GROUP CERS
Hull Cost
Propulsion Cost
Electrical Cost
Communication & Control + Electronics End Costs
Auxiliary Cost
Outfitting Cost
Armament + Weapons End Costs
Design & Engineering Cost
Construction Services 4- Miscellaneous End Costs
CER CODEGeneral EscortLevel Level
B-l C-l
B-2 C-2
B-3 C-3
B-4 C-4
B-5 C-5
B-6 C-6
B-7 C-7
B-8 C-8
B-9 C-9
MODELS D/E- - 4 COST GROUP CER
Base Cost = Hull + Outfitting
Engineering Cost = Propulsion + Electrical + Auxiliary
Payload Cost = C & C + Armament + Electronics
End Cost + Weapons End Cost
Construction Cost = D & E + Construction Services +
Miscellaneous End Cost
MODELS F/G - TOTAL COST CER
Total Cost = Summation of 9 Cost Groups
D-l E-l
D-2 E-2
D-3 E-3
D-4 E~4
F-l G-l
32
outfitting weights, etc., and are listed in Appendix C. Almost
no information is available within the RMC data base that would
refer to mission capability or specific system capabilities. For
instance, the specific types of radars, sonars, guns, missiles, ECM,
NTDS or ASROC systems are not listed nor are the characteristics
of these systems included. Given sufficient time and resources, it
might have been possible to obtain mission capability data for the
ships in the data base. However, lack of time precluded this effort.
Thus, the study used the design parameters given in Appendix D, as
independent variables in the CERs developed. Values of these para-
meters for specific ships are contained in Appendix 11, Data Base (U) ,
classified CONFIDENTIAL, which has been published as a separate
document
.
33
IV. ANALYSIS
Part A is a listing of six sets of CERs (one set for each of the
three different models under each data base),plus a summary of
statistical information relevant to each CER. Within Part B, a general
discussion of independent variable selection criteria is followed by a
detailed discussion concerning the development of each CER.
A. RESULTS - CERs AND STATISTICAL SUMMARIES
The following tables present six different sets of CERs - one set
for each of the three models employing the general data base, and one
set for each of the same three models employing the reduced escort data
base. Following each set of CERs is a summary of statistical informa-
tion pertinent to that set of equations.
The statistical information provided in these summaries consists
of the following:
1. The computed t-value for each variable of each CER is utilized
to test the statistical significance of the coefficient of that
particular variable. The computed t-value should be greater than or
equal to t he tabled t-value to demonstrate the significance of the
coefficient statistically.
2. The tabled t-value is taken from standard Student-t tables,
with a significance level of .95 and degrees of freedom equal to
N-K-l, where N is the number of observations and K is the number of
independent variables utilized in the entire CER.
34
3. The computed F-value is utilized to test the statistical
significance of the entire CER and is merely the ratio of explained
variance to unexplained variance (S 2) . The F-value. should be greater
than or equal to the tabled F-value to demonstrate the significance of
the entire CER statistically.
4. The tabled F-value is taken from standard F tables, using a
.999 significance level and N-K-l versus K degrees of freedom (df).
5. R2, the coefficient of determination, is essentially a measure
of goodness-of-f it of the regression equation to the data. A perfect
fit with the data would be implied if R 2 equals 1.0. By definition,
R is the ratio of explained sums of squares to total sums of squares.
6. CV, the coefficient of variation, is a comparison between the
dispersion of data points about the regression line, and the average
or mean value of the dependent variable. The range of desired CV
values would be 0.2 or less.
7. df, degrees of freedom, represents. the number of observations
less the number of restrictions upon the observations. In this
section df will always be computed as N-K-l.
35
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42
B. DEVELOPMENT OP CERs
1 . Criteria for Selection of Indepen dent Vari ables
The choice of independent variables to be employed in each
CER was based upon several criteria:
a. Each independent variable should denote a subjectively
logical, causal relationship with cost.
b. Each explanatory variable should exhibit a high degree
of statistical independence (low intercorrelation) from all other
explanatory variables used in the same CER. Correlation coefficients
of less than 0.6 were considered acceptable in this stud)7, since this
value was used by RMC and appears reasonable.
c. Each variable should, in fact, vary in value, suggesting
that the use of indicator variables be minimized.
d. Each variable should be input oriented, implying that its
value could be obtained with a high degree of certainty before ship
construction began. For this reason, variables such as SERIES
(described on page U0) an<3 MOS (number of months between award date
and completion date) were not used in the study.
e. The t-statistic of each variable should prove significant
at the .95 confidence level under proper assumptions of normality.
f. Finally, the F-statistic of each CER should prove signi-
ficant at the .999 level.
These confidence levels were chosen since the RMC study
produced variables and equations which proved significant at these
levels
.
A3
2 . Methodo logy and Discussion of CER Developmen t
Within the framework of the preceding selection criteria,
numerous combinations of explanatory variables were regressed against,
both the general data base and the escort data base in order to develop
CERs for the 9-group, 4-group, and single equation models. The
resultant choices of explanatory variables will be presented separately
for each model with discussion applicable to the results for both data
bases unless otherwise noted. The primary regression technique
employed was Linear Least Squares performed on an IBM-360 computer,
using a program described in reference [5], LLSCF. Throughout the
iterative search for explanatory variables, statistical significance
was constantly balanced against the desire for a logical cause-effect
relationship between explanatory variables and cost,
a. Models B and C - 9 CERs
(1) Hull Cost . As may be noted in Table XII, the single
explanatory variable employed to predict hull cost was ENGPAY, the
summation of engineering and payload weights. In essence, the
variable ENGPAY represents the total light ship's weight (LSW) less
the weight of the hull (HULWGT) . Although numerous other combinations
of variables were tried - LSW, PAYWGT, ENGWGT - the most statistically
satisfactory variable, ENGPAY, was finally selected. The choice of
ENGPAY does have a significant basis in logic since the hull cost
should be directly related to the total weight of the ship's power-
plant (ENGWGT) and the total weight of ship's armament, C&C equipment
and outfitting (PAYLOAD) . These are the weights that the hull must
be designed to carry.
44
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45
(2) Propulsion Cost . Two explanatory variables, PWRLD and
RANGE, are used to predict propulsion cost under the general data base.
Under the escort data base, the significance of RANGE as an explanatory
variable was sufficiently reduced so as to require its deletion. The
use of these variables seems extremely logical. Both represent signi-
ficant characteristics of the required power-plant. PWRLD, the ratio
of maximum shaft horsepower to full displacement weight, is an indicator
of power. RANGE of course is an indicator of endurance capability.
Together, the required performance of a power plant is extremely well
defined and, hopefully, the cost too. At first, these variables were
utilized in a simple linear model:
COST a + b (PWRLD) + c (RANGE).
However, in analyzing the residual plots of this model, very definite
evidence of increasing variance was noted using data from both the
general and escort bases. (See Appendix A, pages 91 and 92 ) «
This indication of cost increase as a power function of PWRLD and
RANCE, predicated the following transformation:
LN (COST) = a + b (PWRLD) -1- c (RANGE) or
COST - e a + b (PWRLD) + c (RANGE).
This transformation withstands the test of logic. The phenomenon
of diminishing returns to scale has long been noted in the field of
power-plant design. Doubling a ship's shaft horsepower will not
double its speed. [6] As tbe power and endurance requirements of a
power-plant increase, there is ample evidence to suggest that cost
should rise at an increasingly steeper rate. It must be noted that
this data base contains predominantly steam power-plants. Therefore,
this equation, and especially this transformation, is assumed to apply
to only steam power-plants.
46
Since the cost became an exponential function of PV7RLD
and RANGE, the statistical data computed in the LLSCF program was not
strictly comparable to the statistical data of a pure linear model.
For this reason, the residual values for each observation
were manually transformed to dollar values after which the values
appearing in the statistical summary were manually computed.
(3) Electrical Cost . Two variables were employed to explain
the cost of the electrical power plant and associated equipment. The
use of the weight of electrical equipment, ELEWGT, has strong tradi-
tional justification. The inclusion of NO-GEN, an indicator variable
for the number of generators (1 to 4) , also has a logical causal
relationship with cost considering the positive coefficient of this
variable. Cost should increase with the addition of more electrical
equipment (weight) or an increase in the required number of generators.
The correlation between these two variables was sufficiently low
(.59) to allow the use of both in the same CER.
(4
)
Communication and Control Cost Plus Electr onic End Cost .
This CER proved once again the difficulty in estimating the cost of
electronic equipment. RMC cited numerous articles written on
precisely this subject and proceeded to form a less than perfect CER
in this area. The variables employed to explain these costs do have
a basis in logic. However, statistically, these variables are not
altogether satisfactory. Using the general data base, communication
and control weight (C & CWGT) and the binary indicator variable for
prototype ships (PROTO) , were employed. With the escort data
base, C & CWGT was again found significant, but PROTO was replaced
by MS-END, another indicator variable representing the number of
47
missile launchers to be included as armament. C & CWGT serves as
a traditional explanatory variable, representing the amount of com-
munication and control equipment as a bulk weight. The variable,
PROTO, indicates an increase in cost associated with prototype ships
and the introduction of new, more sophisticated electronic equipment.
MS-END also appears logical. The amount of electronic equipment
required for fire-control purposes, does in fact, increase considerably
with an increase in the number of missile launchers carried by a
given ship. Each launcher, to be independent of the other, requires
a dedicated acquisition and fire control system, and this obviously
increases the communication and control and electronics costs. The
inexplicably high communication and control and electronics cost noted for
DE-1047, made it an obvious outlier (see Appendix B, pages 98 and 99).
Since no further information cuuld be obtained to support this high
cost level, this ship was deleted from the data bases while developing
this CER.
(5) Auxiliary Cost . The CER for auxiliaries requires the
use of PRAXWT, a single variable consisting of the weight of auxiliary
equipment (AUXWGT) and the weight of the propulsion plant (PROWGT)
.
The RMC study utilized AUXUGT and PROWGT as separate explanatory
variables; however, the intercorrelation between the two was about
.78. This high correlation seems reasonable since the auxiliary and pro-
pulsion systems operate as a composite system in providing services
to the ship. The auxiliary system draws steam and power from the propulsion
plant and thus does not operate as a separate system. The combining of
these two weights thus eliminates the problem of intercorrelation and
logically explains an increase in cost as a function of both weights.
48
(6) Outfitting Cost. In developing the CER for outfitting
cost, it was noted that two highly intercorrelated explanatory variables
could be utilized separately to explain the cost. These variables,
LSW and outfitting weight (OUTWGT), produced approximately the
same statistical results utilizing the general data base. However,
neither was very effective within the escort data base. LSW was
chosen as the explanatory variable under the general data base due
to slightly better statistical results. In the escort data base, LSW
proved less useful than OUTWGT, although neither was statistically
strong. Both variables, when used separately, display logical cost
implications. The cost of outfitting a ship should, in essence, be
directly proportional to the weight of outfitting material, including
hull fittings, non-structural bulkheads, painting, workshop equipment,
and furnishings for quarters. The use of LSW as an explanatory
variable is likewise logically consistent.; As the LSW increases, it
follows that outfitting weight and therefore outfitting costs would
increase.
(7) Armament Cost Plus Weapons End Cost . This category
of cost is a combination of two cost items listed separately within the
RMC data base. Armament cost in all cases provided less than ten
percent of the total weapons costs, when Weapons End Cost was added.
The use of one CER to predict both costs, as an aggregate, appears
more reasonable. The explanatory variables developed from both
data bases were armament weight (ARMWGT) and MS-END. The use
of ARMWGT as an explanatory variable appears logical as does the use
of the indicator variable MS -END. It is reasonable to suppose that
armament costs would increase as a function of the weight of the
49
weapons systems and the number of missile systems installed. Within
the development of this CER, two ships exhibited extremely high, and
apparently unexplainable, weapons costs in comparison to the rest
of the data base. These ships, DDG-15 and DLG-16, were identified
as extreme outliers (see Appendix B, pages 100 & ]01)and deleted from the
data base while developing this CER.
(8) Design and Engineering Cost. The CER for design and
engineering makes use of the same explanatory variables as were
employed within the RMC study - ARMWGT and PROLSW. The significance
of PROLSW as an explanatory variable appears valid in explaining design
and engineering cost since this includes the cost of drawings, lofting,
technical manuals, mock-ups and models. These costs obviously would
be much higher for prototype ships and more expensive for larger
prototypes than smaller. The usage of ARMWGT is less obvious, unless
an association is developed between armament weight and weapons system
complexity, wherein increased armament weight could indicate a more
complex weapons system with higher design and engineering costs. While
developing the CEP, for this cost category under the escort data base,
the DDG-2 proved to be a significant outlier (see Appendix B, page 102).
Since no reason could be found to support this inordinately high design
and engineering cost, this ship was deleted from the data base while
developing this CER.
( 9
)
Construction Services Cost Plus Miscellaneous End Cost .
This category of costs includes a potpourri of odd costs attributable to
ship construction - staging and scaffolding costs ;> hull, mechanical
and electrical (HME) costs resulting from engineering changes;
launching costs ; trial costs; and drydocking costs. Three variables
50
were chosen to explain the cost of this "catch-all" category - PROLSW,
C&CWGT and AR/LSW, the ratio of armament weight to LSW. The inclusion
of PROLSW as an independent variable is directly associated with the
higher cost of lead ships as discussed before. The AR/LSW ratio
provides a measure of the relative armament weight of one ship as
compared to another , and is therefore a measure of relative complexity.
A ship with a higher AR/LSW ratio would require more HME change costs,
more staging and scaffolding, thereby increasing the construction
services cost. The same logic would apply to the use of C&CWGT since
this weight indicates relative electronic/electrical complexity
between ships, with the costs mentioned above increasing with
complexity, and, of course, with an increase in antenna arrays. The
cost for the DE-1047 under this category appeared very disproportionate
especially since the DE-1047 was not a prototype. For this reason
the DE-1047 was deleted from the general and escort data bases while
developing this CER. (See Appendix B, pages 103 and 104)
b. Models D and C - 4 CERS
The second model represents a condensation of the original
nine CERs of models B and C into four CERs . As may be observed in
Table XIII, the explanatory variables of models B and C to some extent,
carry over to the explanatory relationships developed in models D and E,
(1) Base Cost . The CER for base cost employs a single
explanatory variable, LSW, which is the sum of engineering weight,
payload weight, and hull weight. (ENGWGT + PAYWGT + HULWGT = LSW) ,
Since the base cost is a combination of hull and outfitting costs,
the logical explanatory variables would be those developed as a result
51
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52
of Models B and C. ENGPAY was used in the hull CER, while HULWGT was
the major variable used in predicting outfitting cost. The sum
of these two variables, LSW, does in fact represent a statistically
significant and logical explanatory variable,
(2) Engineering Cost . The engineering cost represents the
combined costs of the electrical, auxiliary, and propulsion sub-systems.
The major explanatory variable for propulsion cost in Models B and C
was PWRLD. Electrical cost was explained in part by ELEWGT while
auxiliary cost was a function of only PRAXWT. When ENGWGT is defined as
ENGWGT = PRAXWT + ELEWGT = PROWGT + AUXWGT + ELEWGT,
it represents the weight of the entire engineering system and as such
should explain the cost of the entire system. Utilized as explanatory
variables in the same logrithmic transformation model employed before,
both variables, PWRLD and ENGWGT, serve as extremely good indicators of
cost. The same logrithmic transformation was employed because within
both data bases, there were definite indications of increasing variance
using the linear model. (See Appendix A, pages 93 and 94 ) Note that
ENGWGT loses significance as an explanatory variable in the CER with
the escort data base, much as RANGE lost significance in the propulsion
CER for Models B and C.
(3) Payload Cost. The payload cost is a summation of
armament cost, weapons end costs, C&C cost and electronics end costs.
Thus the payload cost is merely the cost of the weapons, sensor, and
communication & control systems of the ship. One obvious explanatory
variable was MS-END, which was utilized in Models B and C to explain
armament cost and C&C cost. The other explanatory variable was LSW,
53
indicating a logical relationship between the LSW and the cost of its
payload, A ship exists in order to support a pay load of sensors and
weapons. It is natural to assume that LSW will not be any greater than
is necessary to support that payload. LSW should logically indicate
the relative size of the payload and, thus, the relative cost of the
payload. As was noted in the development of armament and C&C costs in
Models B and C, DE-1047, DDG-15, and DLG-16 again appeared as distinct
and obvious outliers (See Appendix B, pages 105 & 106) For this reason
they were deleted from the data base as this CER was developed.
(4) Services Cost . The category, services cost, includes
miscellaneous end costs, design and engineering cost, and construction
services cost. The variable, PROLSW, was again utilized to indicate
the higher costs of lead ships, weighted in effect by the LSW of the
prototype. Its use in Models B and C carries over well into this
aggregate cost. The other explanatory variable utilized was HULWGT.
The use of this variable is logical in that an increased hull weight
would generally indicate an increase in LSW, which tends to support
the idea of more services required in the construction of a large
ship than in the construction of a small ship.
c. Models F and G - 1 CER
The final model is an aggregation of all Basic Contract
and End Costs into a single Total Cost equation. The three variables
utilized in this single CER are listed in Table XIV. The explanatory
variable LSW is utilized twice in Models D and E, in the base and
payload CERs. In addition, propulsion cost is determined by ENGWGT
,
and construction cost by HULWGT in the CER's of Models D and E. A
logical aggregation of these weights would be in the form of LSW.
54
TABLE XIV
VARIABLES USED IN MODELS F AND C
MODEL D/ECOMPONENTS
VARIABLES IN
MODEL D/ERESULTANTVARIABLES
TOTAL COST
Base LSW
LSW
MS-END
PROLSW
Propulsion PWRLD
ENGWGT
Payload LSW
MS-END
Services HULWGT
PROLSW
Using this fact, the only variables left from Models D and E were
PWRLD, MS-END and PROLSW. Thus an initial attempt was made to utilize
these variables plus LSW, in a single CER for Total Cost. \ The
resultant regression was extremely surprising in its high statistical
significance. However, the variable PWRLD proved insignificant in
the linear form. A further attempt was made to add PWRLD in an
exponentiated form, but this again proved useless. Thus the three
variables, LSW, PROLSW and MS-END were selected as explanatory variables
in CER's for both data bases. The logic of including LSW as an
explanatory variable has its roots in its historical success in explaining
costs. Larger ships cost more. The inclusion of MS-END, attributing
an increase in cost to the addition of missile systems, is also logical.
The cost of armament, C&C equipment, auxiliary, and electrical equip-
ment must increase because all, to some extent, support a missile system.
55
The restively high cost of a missile system and associated fire-control
equipment is easily realized in comparing the cost of a missile ship
with the cost of a non-missile ship. The variable PROLSW accomplishes
two purposes. First it demonstrates that the cost of a prototype ship
is more than that of a non-prototype ship. Secondly, it indicates that
the cost of a larger prototype ship is more than that of a smaller
prototype. Both of these concepts are logical. The inability to prove
the utility of PV7RLD as an explanatory variable at this stage may be
in part due to the relatively small difference between power-plant
costs in the DLG-DD-DE data base.
The problem of outliers appeared again while this CER
was being developed (See Appendix B pages 107 & 108). Using the general
data base two extreme outliers, DE 1047 and DLG 6, displayed inexplicably
high total cost values and were subsequently deleted from the data
base. Utilizing the escort data base, an additional outlier, BBG 15,
was discovered. Therefore all three of these ships were deleted from
the data bases for this CER.
56
V . ESTIMATES OF TOTAL COST VARIANCE
Throughout this paper, emphasis has been continually placed upon
the development of models that determine estimates for total procure-
ment cost. An obvious measure of each model's effectiveness consists
of an estimation of the total cost variance associated with each model.
Two methods are outlined in Sections A and B from which two different
estimates for total cost variance are obtained for each model discussed
in this paper.
A. SUMMATION METHOD
1. Model
Associated with each CER is an estimate of CER variance based
on the summation of the squared residual values of each observation
divided by the degrees of freedom of the CER. Mathematically, for
each CER,
N
E (residual) 2
S? = i=l
N - K - 1
where S? = estimated variance of each CER
N = number of observations
K = number of independent variables
N-K-l = number of degrees of freedom.
Within this equation the term, residual, is defined as the difference
between the observed cost and the cost predicted as a result of the
CER. There is a residual value for each cost observation within the
data base.
57
Since each model predicts a total cost by summing the cost
estimates obtained from its unique set of CERs, it would be logical
to assume that an estimate of total cost variance would be the sum of
S 2 = I S 2
the individual CER variance estimates. That is
LI
i=l J
where S 2 = estimated total cost variance
S? = estimated variance of each CERJ
L = number of CERs in the model (1, 4 or 9).
Adoption of this technique requires the acceptance of one important
assumption; that each CER produces a cost estimate totally independent
of every other cost estimate within the model. This assumption is
obviously difficult to accept. Nevertheless, this method is still
quite useful because it allows the establishment of a lower bound on the
cost variance estimate; that is, a value of total cost variance which
represents the minimum total cost variance that my be attained utilizing
rthat particular set of model CERs. Should there exist any positive
level of dependence between the CERs of a model, the value of total
cost variance must be larger than this lower bound. The dependence of
one cost upon another may also be called covariance. Perfect inde-
pendence is exhibited when the covariance of all costs are zero with
respect to all other costs. For example, in Model B (using 9 CERs
and the general data base) , the hull cost must exhibit a zero
covariance with respect to all 8 of the other costs in order for the
total cost variance to be exactly S 2. Otherwise, if there exists any
positive covariance between hull cost and propulsion or armament cost,
58
then the correct estimate of total cost variance under these conditions
must be higher than indicated under the summation method. The
possibility that a negative covariance might exist between two cost
groups is remote. If this did exist, the summation method would, in
fact, over-state the total cost variance. However, a negative
covariance between cost group CERs x^ould imply that as one cost
increased, another decreased, and it is difficult to accept this type
of interaction between the cost groups of the models studied. Thus,
by stating that the summation method produces a lower bound on total
cost variance, the assumption is made that only positive covariance
exists between the various costs groups.
2. Results
An estimate for CER variance is automatically calculated
within the Linear Least Squares Curve Fitting computer program
utilized in developing each CER. Table XV lists these individual
CER variance estimates employing the same alpha-numeric coding system
as outlined in Section III. Note that the summation of each alphabetic
group represents the lower bound on the total cost variance estimate
as discussed earlier.
B. MEAN SQUARE RESIDUAL (MSR) METHOD
1. Model
The second method of total cost variance estimation involves
the calculation of a total cost mean square residual value (MSR) for
each model. The following equation represents the general method
utilized to calculate this value:
59
TABLE XV
ESTIMATES OF TOTAL COST VARIANCE AS A SUM OF CER VARIANCES
S 2
B-l .366
B-2 1.020
B-3 .086
B-4 3.308
B-5 .325
B-6 .102
B-7 8.564
B-8 1.708
B-9 2.218
17.697
S 2
C-l .157
C-2 .398
C-3 .048
C-4 1,100
C-5 .355
C-6 .064
C~7 1.789
C-8 .102
C-9 1.794
5.807
D-l .501
D-2 1.050
D-3 9.491
D-4 4.988
16.030 7.861
F-l 19.972 G-l 12.455
E--1 .207
E-2 .680
E-3 2.767.
E-4 4.207
60
N L
MSR Z fZ (RESIDUAL^) ]2
i-1 j=l J
N-M-L
where N = number of ships
M = number of variables utilized in all CERSof model
L = number of CERs utilized in model
For example, the total cost MSR for Model B (using 9 CERs and
the general data base), employs the following parameters:
N = 36
L = 9
M = 16
Thus the MSR for Model B is found by:
36 9
MSRR
=iZ1
[
jg1
(RESIDUAL. ) ]2
— -
Note that by summing t he residual values produced by each
CER for a given ship, the difference between observed and predicted
total cost is obtained for that ship as an aggregate of the individual
CER residual values. . When these total cost residuals are squared,
summed for all observations (ships) , and corrected for degrees of
freedom, an estimate of variance is produced for the given model.
Appendices F and G contain a listing, for each model, of
the total cost residual values of each observation (ship) used in
producing the CERs of that mode].
To accurately compare the MSR's of the three models developed
from the general data base (B, D and F) , the number of observations
was reduced to 33 to correct; for the outliers deleted in the development
61
of the various CERs . The same reasoning caused a reduction in the
number of observations to 25 for the escort data base models (C, E
and G)
.
The summation method may be thought of as a lower bound
on the total cost variance estimate. Analogously, the MSR method
may be thought of as an upper bound on the total cost variance estimate;
a value below which the estimate of total cost variance is expected
to lie. Implicit within the formulation of this method is the assumption
that each cost group observation is dependent upon every other cost
group observation. The degree of this dependence (covariance) is
assumed to be 1.0. It is highly unlikely that this degree of inter-
dependence will exist between all cost group observations. However,
this assumption allows the creation of an expected upper bound and is
therefore useful. Its usefulness is further strengthened by the enormous
difficulties involved in obtaining an actual estimate for the degree
of dependence that exists between the various sub-category costs in
a given model. If this covariance matrix were easily attainable and
accurate, the need for upper and lower bounds in the development of
total cost variance estimates would be eliminated. A thorough
discussion of this problem is presented in a recent RAND study [7].
Intuitively, the summation method rests upon the assumption
that each observation of sub-category cost (hull cost, payload cost,
propulsion cost, etc) is independent of all other sub-category costs
within the particular model. For example, if total cost had been
divided into 5 subcategories, then, for all N observations upon which
CERs for these 5 subcategories will be based, each of these five
costs must be independent. This implies 5 times N independent
observations of cost.
62
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The other extreme, the MSR method, requires that only the
N observations be independent, assuming that each sub-division of
total cost is entirely dependent on all other sub-divisions of cost.
Neither of these methods allow an exact determination of total cost
variance, since neither of the underlying assumptions is totally correct.
Thus, the best estimate of total cost variance should lie between these
two extremes.
2. Results
Table XVI summarizes the data used in calculating the MSR
value for each of the six models under discussion. The bottom line of
the table is the computed MSR value, and represents the expected
upper bound of total cost variance as discussed earlier.
C. ANALYSIS OF RESULTS
1. The Coefficient of Variation
Table XVII is a summary of the estimates for total cost
variance calculated using both the summation method and the MSR
method. Therefore, the left side of Table XVII contains data pertinent
to the lower bound (LB) on total cost variance, while the right contains
data on the upper bound (UB) . The square root of these variance
estimates (S^), is the standard error of estimate (s ) and is analogous
to the standard deviation. It represents a measurement of the dispersion
or spread that results from a less than perfect fit of the regression
line (CER) with the data. A common use of this measure of dispersion
is in the computation of the coefficient of variation (CV) . The CV is a
ratio comparison of the standard error of estimate (S), to the mean of
the dependent variable, in this case total cost. Thus, the CV rep-
resents a comparison between the expected dispersion of total cost
64
and the average total cost of the ships in the applicable data base.2
For instance, the estimate for variance (S ) of Mode3 B is 17.697,B
using the summation method. The expected dispersion or standard2
error of estimate for Model B is just the square root of S or 4.21,B
The coefficient of variation (CY) for Model B is the standard error
of estimate divided by the average total cost of all ships within
the general data base, 11.2%. Thus the standard error of Model B
(using the summation method) is only .112 of the average cost of ships
in the data base.
The summation method produces a LB on total cost variance
and the MSR method produces an UB. Therefore, the CV calculated
by using the total cost variance obtained through the summation
method produces a LB on the CV for the model. The CV calculated
by using the MSR method of variance estimation produces a UB on
the CV for the model. The ideal situation occurs when the UB and
LB for the CV are relatively small (.1 or .2) and extremely close
to one another. This would imply that the standard error of estimate
was small when compared to the average total cost regardless of the
method used to determine the estimate of variance.
2. Conclusions
On the. basis of the criteria presented in the previous section,
Models B and C produce discouraging CVs . The lower bounds on both
are acceptable values; however, the upper bounds imply that the ratio
of standard error of estimate to average cost could get as high as
a« 28.4% and 44.6% respectively. The major source of difficulty in
these models is the fact that the data base (with outliers deleted)
contained on] y 33 and 25 observations respectively.
65
TABLE XVII
VARIANCE, STANDARD DEVIATION, AND COEFFICIENT OF
VARIATION FOR ESTIMATES OF TOTAL COST VARIANCE
GENERAL DATA BASE
SUMMATION ESTIMATE MSR ESTIMATE
CV CV
MODEL B 17.697 4.21 11.2% 113.36 10.65 28. 4%
16.030 4.00 10.7%
19.972 4.47 11.9%
30.08
19.972
5.55
4.47
14.8%
11.9%
ESCORT DATA BASE
SUMMATION ESTIMATE MSR ESTIMATE
CV CV
MODEL C 5,807 2.42 8.7% 159.4 12.4 44.6%
E 7.861 2.80 10.1% 12.33 3.51 12.6%
G 12.455 3.63 12.7% 12.455 3.63 12.7%
NOTE: The average total cost for use in the calculation of
CV =TCAVG
37.42 million dollars for General Data Base V7ith 33 ships
27.82 million dollars for Escort Data Base with 25 ships
66
One degree of freedom is lost for each CER in the. model and
another is lost for each independent variable of each CER, thereby
reducing the remaining degrees of freedom to 8 and 1, respectively.
Since the sum of the total cost residuals squared is divided by these
values to obtain an estimate of variance in the MSR method, these
estimates remain relatively large when compared to the other models
where degrees of freedom were higher due to the use of fewer CER.S and
fewer independent variables.
Note that for Models F and G, the upper and lower bound on CV
are the same. This is because Models F and G utilize only one total
cost CER. Thus, the MSR method when applied to a model with only one
CER produces the same variance estimate as the summation method.
Models D and E produced fairly significant results with
relatively low values for CV and relatively close upper and lower bounds,
The use of Model E vice Model G is preferable since the upper and lower
bounds for Model E are less than the CV of Model G. The choice between
Model D and Model F is not so clear cut. The lower bound of Model D is
less than that of Model F, but the same is not true of the upper bound.
Here, the upper bound of Model D exceeds that of Model F by less than 3%
The choice here would involve a guess as to whether the CV of Model D
is nearer the upper or lower bound.
67
VI . APPLICATION - PATROL FRIGATE
The basic objective of this paper is to present procurement cost
estimating models that provide relatively precise total cost estimates
through which cost-effectiveness (or budgetary), decisions might be made.
Given a specific sot of input parameters for a current ship construction
project, a total procurement cost estimate can be generated using each of
the models discussed earlier. A comparison of these model estimates with
the currently accepted project estimate will provide a degree of validity
to the approach adopted. The current ship construction project selected as
a test case was the PATROL FRIGATE (PF) project. The Project Manager's
office provided both the parametric input data and the current cost
estimates necessary to make this comparison.
A. MODEL ESTIMATES
1. Parametric- Input Data
The necessary input data are listed in Table XVIII, with the
source of the data specified by each value. These data represent the
most current information available concerning weight allocation and ships'
characteristics for the PF.
2
.
Total Cost Estima tes
The parametric input data were substituted into the CERs of
each model and aggregated according to the model structure. Since the
PF is designed as an escort vessel and has the displacement necessary
to be included within this category, all six models were applicable
(3 models from the general destroyer data base, and 3 models from the
escort data base). Therefore, six total cost figures in FY 65 dollars
68
TABLE XVIII
PATROL FRIGATE INPUT DATA
CHARACTERISTIC VALUE UNITS SOURCE
Hull Weight 1235 Long Tons NAVSHIPS
Propulsion Weight 251 Long Tons NAVSHIPS
Electrical Weight 160 Long Tons NAVSHIPS
C&C Weight 87 Long Tons NAVSHIPS
Auxiliary Weight 358 Long Tons NAVSHIPS
Outfitting Weight 264 Long Tons NAVSHIPS
Armament Weight 96 Long Tons NAVSHIPS
LSW 2451 Long Tons NAVSHIPS
Full Displacement 3400 Long Tons NAVSHIPS
ENGPAY 1216 Long Tons CALCULATED
PRAXWT 609 Long Tons CALCULATED
ENGWGT 769 Long Tons CALCULATED
AR/LSW .0392 Leng Tons- CALCULATED
ENDURANCE RANGE * Naut:Leal Miles NAVSHIPS
MAXIMUM SHP * HP NAVSHIPS
MS-END 1 - NAVSHIPS
NO-GEN 3v
- NAVSHIPS
PROTO 1 - NAVSHIPS
PWRLD 11.75 SHP/]-.one Ton CALCULATED
*See Appendix H, Data Base (U) (CONFIDENTIAL document;published separately)
69
TABLE XIX
COST ESTIMATES OF PATROL FRIGATE - MODEL B THROUGH D
($ Millions FY 65)
Hull B-l 1.7309 C--1 1.7394Propulsion B-2 3.6700 C--2 3.6200Electrical B-3 1.5512 C--3 1.7290C&C + Electronics End B-4 2.0783 C--4 3.0062Auxiliary B-5 1.3916 C--5 1.3958Outfitting B-6 1.3814 C--6 1.4466Armament + Weapons End B-7 9.1113 C--7 9.1781Design and Engineering B-8 3.3342 C--8 1.2266Construction Services + Misc. End B-9 5.4649 c--9 5.3468Gas Turbine Adjustment 1.7000 1.7500Sub Total 31.4138 30.438510% Profit 3.1414 3.0439
TOTAL 34.5552 33.4824
Base D-l 3.3502 E--1 3.2916Engineering D-2 6.1000 E--2 6.4200Pay load D-3 13.1046 E--3 14.5630Services D-4 10.7775 E--4 10.2820Gas Turbine Adjustment 1.7000 1.7500Sub Total 35.0323 36.306610% Profit 3.5032 3.6307
TOTAL 38.5355 39.9373
CER F-l 39.1825 G--1 35.1828Gas Turbine Adjust:ment 1.7000 1.7500Sub Total _-
—-""40.8825 36.9328
10% Profit 4.088344.9708
3.693340.6261
TOTAL
70
were produced and are presented in Table XIX. Note that a contractor profit
figure of 10% of Loral cost has been added to each model result. This
was done to male the model estimates comparable to the estimate supplied by
NAVSHIPS wherein 10% profit has been figured. I As discussed earlier,
the models developed in this paper do not account for profit in any
way since the data base developed by RMC supposedly contained no profit
dollars in any category.
The PF is to be powered by gas turbine engines. The data base from
which these models were developed contains mainly steam powered ships
(two ships have diesel engines). For this reason, it was not expected that
the CERs for propulsion cost B-2 and C-2) or the CERs for engineering
cost (D-2 and E-2) would produce reliable estimates. The Naval Ship
Engineering Center (NAVSEC) estimates the cost of gas turbine propulsion
for the PF to be equivalent: to 5.37 million FY65 dollars. The estimate of
CER B-2 was 3.670 million FY"65 dollars and that of CER C-2 was 3.620 million
FY65 dollars. The difference between these two estimates and the NAVSEC
estimate for gas turbine cost was added to each model as a GAS TURBINE
ADJUSTMENT to compensate for the use of gas turbine engines.
B. NAVSHIPS ESTIMATES
1
.
Basic Contract Cost
The current NAVSHIPS estimate for the Patrol Frigate basic
contract cost is 35.1 million FY74 dollars.
2
.
End Costs
The data supplied by NAVSHIPS as end cost estimates in FY73
dollars represent lead ship end costs except for the NAVORD estimate.
for weapons cost. The NAVORD weapons cost estimate for the lead
ship included a phenomenal amount of research and development cost
71
associated with the proposed PF weapons suite. The data base upon
which the models were developed did not include any research and
development costs. To eliminate this problem, the figure for weapons
end cost is based on follow-on estimates of the weapons cost rather
than lead ship weapons cost. Table XX lists the end cost estimates
compiled by NAVSHIPS from cognizant project offices.
3. T otal Procurement Cost
The total procurement cost of the lead PF is merely the
summation of basic contract cost and end costs. Since basic contract
cost was given in FY74 dollars and end costs in FY73 dollars, the end
cost data was escalated by 4.0% to account for inflation during the
year 1973-1974. The 4.0% annual inflation rate represents the average
inflation rate for the years 1969-1972 as given in the Department of
Commerce5Survey of Current Business, and is applicable to government
purchases of durable goods.
Thus, the total procurement cost of the lead PF is:
BASIC CONTRACT COST 35.100
END COSTS 23.56 7
TOTAL COST 58.667 ($ millions, FY 74)
C. COMPARISON OF ESTIMATES
1. Estimates
Table XXI lists the total cost estimates of the PF based on
the models presented in this paper and also the estimate provided by
NAVSHIPS. Note that the estimates are listed in both FY65 dollars
and FY74 dollars. The deflator utilized in this transformation, 1.380,
was based on information from the Department of Commerce, Survey of Current
Business [8]. The deflator was extrapolated from 3972 to 1974 using a 4.0%
72
COST ITEM
Design Changes
Construction Changes
TABLE XX
PATROL FRIGATE END COST ITEMS
($ millions, FY 73)
COST BASIS
% of Lead Ship Construction Cost
% of Lead Ship Construction Cost
Govt. Engineering Support DD 963 Estimate
NAVSEC Electronics
NAVSHIPS Sonar
H/M/E Equipment
NAVORD Cost
NAVELEX Cost
SEC 6271 Estimate
PMS 378 Estimate
Preliminary Equipment List
NAVORD Estimate
NAVSEC 6179 Info
Increase by 4.0% inflation [8] for FY 74 dollars
COST
2.000
2.500
1.500
3.188
2.526
1.400
8.852
0.695
22.661
.906
"237567
73
TABLE XXI
PATROL FRIGATE TOTAL COST ESTIMATES
ESTIMATE SOURCE $FY 65 (Mi 1) $FY 74 (Mil)
NAVSHIPS (Adj usted forEnd Costs) 42.52 58.67
Model B 34.56 47.69
Model C 33.48 46.20
Model D 38.54 53.19
Model E 39.94 55.12
Model F 44.97 62.06
Model G 40.63 56.07
G^MC Model 35.54 49.04
^Discussed in Section VII, Conclusions
74
annual rate of inflation which represents the average annual inflation rate
for the years 1969 to 1971. It must be noted that the use of a 4.0% rate
is merely an estimate of future inflation based on historical data
and is therefore subject to uncertainty.
2. Discussion of Results
On the assumption that the NAVSHIPS estimate contained within
this paper represents the "best" estimate now available, the following
conclusions may be drawn concerning the results of Models B-G.
(a) The estimates produced by Madels B and C, are 11.0 and
12.5 million FY74 dollars low and therefore do not compare
at all with the NAVSHIPS estimate. This is not unexpected
since these models produced extremely high ranges of
expected variance as noted in detail within Section V.
A comparison between these estimates and those of Models B and
E indicates major differences in the area of payload
(communication & control, electronics, weapons) and in
the services category (design and engineering, construction
services, and miscellaneous end costs). The possible cause of
these differences are discussed in Section VII, Conclusions.
(b) The estimates of Models D, E, F, and G were all within
5.5 million FY 74 dollars of the NAVSHIPS estimate. Three of
these estimates were within 3.5 million FY74 dollars of the
NAVSHIPS estimate. This is obviously encouraging.
In summary, four of the six models developed within this study
produced estimates within 5.5 million FY 74 dollar:? of the NAVSHIPS
estimate and are therefore considered very comparable to the current
NAVSHIPS total cost estimate. The two 9-CER Models (B and C) are
75
not in any way comparable and therefore require further develop:
A direction for this development is suggested in Section VII.
76
VII . CONCLUSIONS AMD RECOMMENDATIONS TOR FURTHER RESEARCH
A. MODELS B AND C
Models 13 and C utilized 9 CERs to predict 9 cost group estimates.
Model B was developed from the general destroyer base of 36 ships, while
Model C was developed from the escort data base of 2 7 ships which
excluded DLG type ships. Both data bases included all end cost
categories as aggregates within one of the original 9 cost groups.
"Weapons end cost was added to armament cost, miscellaneous end cost was
added to the construction services cost, and electronics end cost was
added to communication and control cost. \ As noted in Section V, the
overall performance of these models in predicting total ship cost as
a summation of the 9 cost group estimates was discouraging due to the
extremely high upper bound on the total cost variance estimate (S 2)
for both models. The measure of effectiveness utilized was the coeffi-
cient of variation (CV) , wherein the standard error of estimate (S) was
compared to the average total cost of the ships within the model's
date base. Model B produced a CV that could range from 11.2% to 28.4%
of average total cost (37.42 millions). Model C exhibited a CV that
could be as low as 8.7% or as high as 44.6% of average total cost
(27.82 millions). As observed in Section V, this problem arose because
an attempt was made to develop too many CERs (with too many independent
variables), from a data base that was too small to retain sufficient
degrees of freedom to make the results statistically sound. Two
recommendations stem from this observation. First, the 9 CER model
should not be discounted. Further effort, with larger data bases,
77
could produce better results. Secondly, in enlarging the data base,
efforts should also be made to update the present data base, and recheck
the adjustments made by RMC to the present data base. The new data
base, as well as the old, should include final cost data vice the
contractor bid data utilized in this paper.
B. MODELS D, E, F, AND G
Models D and E both employed 4 CERs to predict 4 cost group estimates,
Models F and G utilized a single equation to predict total procurement
cost. Models D and F were developed from the general data base, while
Models E and G were developed from the escort data base. The 4 CERs
of Models D and E represented aggregates of 2 or more cost groups from
the 9 CER models. Models F and G were obviously the aggregates of 9 cost
groups.
Both models utilizing 4 CERs proved statistically significant as
estimators of total cost. Model D produced a CV of between 10.7% and
14.8%; Model E exhibited a CV that could vary between 10.1% and 12.6%.
Both of these ranges of CV values are considered acceptable.
The single CER models produced a single point estimate of CV as
discussed in Section V. The CV for Model F is 11.9% of average total
cost. A CV of 12.7% was found for Model G. These values are also
considered acceptable.
On this basis, the judgment was made that Models D, E, F, and G
produced estimates of total cost that should be very acceptable in
cost-effectiveness analysis. The nature of cost-effectiveness studies
does not require an extremely precise estimation of total cost. The
CV values above indicate that these models will produce reasonably
close estimates; i. e. , "ball park" estimates, that might be used to
78
compare alternative design options. The precision of these models
does not suggest their use as tools in any but the most rudimentary
budgetary process wherein crude estimates are. all that are available.
C. APPLICATION OF MODELS - PF
Within Section VI , these six models were utilized to predict total
ship cost based on current parametric input data for the Patrol Frigate.
A comparison of the six model estimates to the current NAVSHIPS cost
estimate produced the same general conclusions as noted in paragraphs
A and B. Models B and C produced estimates 11.0 and 12.5 million dollars
below the NAVSHIPS estimate, while the remaining four model estimates
were within 5.5 million dollars. Three of these four estimates were
within 3.5 million dollars of the NAVSHIPS estimate.
These facts alone prove only that four of the model estimates are
very comparable to the NAVSHIPS estimate. In light of the conclusions
drawn in paragraphs A and B, the apparently inferior estimates of
Models B and C are not surprising. However , it must be stressed that
these estimates are being compared to the NAVSHIPS estimate, not a
final cost. This comparison does not in any way represent a comparison
of model estimates to an actual observed total cost.
79
1). COMPARISON OF MODELS TO THE RMC MODEL
Using the nine CERs of the RMC model as presented in Sections
I and II, the basic contract cost ol the PF was estimated as 16.78
million FY65 dollars. This cost includes 5.37 million FY65 dollars*
the gas turbine propulsion cost estimate from NAVSEC, which replaces
CER B2. Applying a 10% profit factor and inflating to 1974 dollars,
this estimate becomes 25.47 million dollars. Summing basic contract
cost with the 23.567 million dollars end cost estimate of NAVSHIPS, the
RMC estimate becomes 49.04 million FY 74 dollars.
The RMC estimate is therefore more than 9.7 million dollars below
the NAVSHIPS estimate and 2.8 million above the Model C estimate
which was the furthest from the NAVSHIPS estimate. Although this
fact alone is not conclusive evidence that Models B through G are
better than the RMC model, they are at least, comparable to the RMC
model. In addition, Models B through G provide a means of estimating
basic contract cost and end costs simultaneously. The RMC model
placed little emphasis on the area of end cost prediction. Using these
models, the RMC concept has been extended to apply to total ship cost esti-
mation rather than maintaining emphasis on estimation of basic contract
cost. The results of this extension, Models B through G, produce
estimates which are at the very least comparable to the RMC estimate.
80
E. CERs REQUIRING FURTHER DEVELOPMENT
Table XXII lists CERS which, due to their poor statistical
quality, require further development. Each CER within this list,
except B-7 and C-7, exhibits either a relatively high CV value and/or
a low R2- value. A high CV value indicates a relatively large standard
error of estimate in comparison with the average observed cost of the
particular cost group. This means that the regression equation
(CER) developed for that cost group fails to explain a significant
amount of observed variance when compared to the cost group mean value
by means of the CV. R2 measures the proportion of variation in the
actual cost observations that is explained by the cost group CER. A
low value of R indicates that the CER has explained only a small portion
of the actual variation of the cost data. Normally this is due to the
use of an incorrect model form for the CER or an inappropriate selection
of independent variables for use in the CER.
Note that all of the cost group CERs listed, with the exception
of B-8 and C-8, contain an end cost group aggregated with a base cost
group. In the beginning of the study it was noted that the end costs
in the RMC data base exhibited extremely large ranges of values
(in million dollars):
HIGH LOW
MISCELLANEOUS END COST 13.81 1.09
WEAPONS END COST 39.20 0.18
ELECTRONICS END COST 21.36 0.21
81
TABLE XXII
CERs of Poor Statistical Quality
COST GROUP CV R2
B4 Communication & Control + Electronics End .45 .67
C4" .36 .63
''c B7 Armament + Weapons End .27 .90
* C7" .19 .95
B8 Design & Engineering .86 .78
C8 " .48 .45
B9 Construction Services + Miscellaneous End .24 .83
C9||
.29 .70
D4 Services = Design & Engineering + ConstructionServices + Miscellaneous End .29 .83
E4||
.35 .62
* These CERs were not included because of poor statistical quality
See the discussion in section E.2.
82
To reduce the effects of this large range of values, end costs were
added to the appropriate cost group of the nine basic cost categories.
Since the main thrust of the study is to develop models by which total
procurement cost may be estimated, this consolidation appeared quite
logical. As Table XXII indicates, this large range of end cost data
has not been fully accounted for by the CERs developed.
1. Communication and Control Cost Plus Electronics End Cost (B4/C4)
These CERs produced relatively high CV values, using C&C weight
and the number of missile launchers as independent variables. One
method by which a better CER might be developed requires the use of
performance/capability indices. For instance, one index might consist
of the number of missile fire control systems plus the number of air
and surface search radars carried by each ship. Using this type
index as an explanatory variable will obviously require more information
than was given in the RMC data base, but might prove worth the effort.
2
.
Armament Cost Plus Weapons End Cost (B7/C7)
As may be observed in Table XXII, the only difficulty with
these CERs occurs in the slightly high CV value of B7. These were
listed primarily to note the possible extension of the performance/
capability indices method in producing better CERs. In the area of
weapons, an index might be formed wherein a missile system was weighted
according to its maximum range and then used as an independent variable
in the development of a new CER.
3
.
Design and Engineering Cost (B8/C8)
These were probably the most difficult CERs to develop, and
are certainly by no means statistically perfect. Armament weight
and a weighted prototype variable were used within these CERs as
83
explanatory variables. Although numerous model forms and other
variables were tried, none were more significant than the results listed
in Table XXII. The extremely high CV values for both CERs and the
low R2 value for C8 testify to the poor degree of fit obtained by using
the variables now available in the data base. This is one area in which
more basic research must be accomplished before another approach
can be developed.
4
.
Construction Services Cost Plus Miscellaneous End Cost (B9/C9)
These CERs produced relatively high values for CV. The
explanatory variables utilized (AR/LSW and PROLSW) were not the
most logical choices available. However, considering the fact that
this cost group includes a potpourri of odd costs with cost components
varying from ship to ship, and exhibits a large range of cost observa-
tions, it is not odd that: explanatory variables were difficult to isolate
Like B8/C8, this area of cost requires a great deal more study before
better CERs can be developed.
5. Services Cost (D4/E4)
The cost groups related to these CERs consist of the summation
of B8/C8 and B9/C9 which were discussed above. The problems found
in developing the CERs D4/E4 were essentially those found in the
disaggregated CERs of B8/C8 and B9/C9. The aggregation of B8/C8
with B9/C9 did not reduce the difficulty significantly.
84
F. DATA BASE DIFFERENCES
The models presented in this study are of three types. One
utilizes 9 cost-group CEBs , the second employs 4 cost-group CERs
and the. third uses only one CER to estimate total procurement cost.
However, each of these models was developed using two different
data bases to determine if the exclusion of DLG type ships from the
escort data base proved significant in estimating the total cost for a
non-DLG type destroyer or escort.
The results are inconclusive. Using the total cost CV for each
model as discussed in Section V, no clear evidence exists to support
the hypothesis that DLG type ships should be exluded from the data
base, so that escort models might be utilized to predict the. total cost
of non-DLG type ships more accurately. The CV values for each model
are summarized, as follows:
DATA BASE
9 Cost Group B Generals Models C Escort
4 Cost Group D GeneralModels E Escort
Single Cost F GeneralGroup Model G Escort
Of the 9-cost group models, Model B seems to be the preferable model
due to the potentially high CV of Model C. In the 4-cost group models,
Model E has a smaller range of CV values than Model D, but only by
less than 2%. In the single-cost group models, wherein only a point
estimate of CV was computed, Model G produced the best CV value, but
only by about 17,. Therefore, this measure of effectiveness does not
support the hypothesis that the use of an escort data base will produce
better estimates of escort ship cost.
85
LOWER BOUND UPPER BOUNDON CV ON CV
11.2% 28.4%8.7% 44.6%
10.7% 14.8%10.1% 12.6%
11. 9%
12. 7%
G. ADDITIONAL RECOMMENDATIONS
As noted within Section V, the establishment of upper and lower
bounds on total cost variance estimates (and also CV values) was
necessary because no firm method was immediately available through
which a true determination of cost-group interdependence might be
gained. To arrive at a total cost estimate, 9 cost-group estimates
must be summed in Models B and C, and 4 cost group estimates must
be summed in Models D and E. The establishment of a lower bound on
total cost variance relied upon an assumption of total independence of
all cost-groups estimates. Conversely, the upper bound was set
under the assumption that each cost group was dependent upon every
other cost group at a covariance level of 1.0, implying complete depen-
dence. Neither extreme is true. However, the task of actually computing
the degree to which each cost-group varied with respect to every other
cost group involves the determination of an entire covariance matrix
by estimation techniques that require more data than is available in
the general or escort data bases. (See reference [7] for one method
of covariance matrix estimation). For this reason, no such technique
could be employed within this study. This is an area in which further
effort would prove profitable. The determination of an estimated
covariance matrix would ultimately allow a more precise estimation
of aggregated total cost variance and thus place a higher degree of
reliability upon the total cost estimate.
The problem of outliers arose a number of times during the develop-
ment of individual model CERs . When this problem occurred, the outlier
was merely deleted from the data base for that particular CER. A
86
better method of handling outliers would involve an investigation to
determined whether the large cost was due to an error in transcribing/
transforming the data or whether the cost figure was truly valid. If
the cost data was found to be correct, further research should be
attempted in order to reveal why the outlier exhibited a substantially
higher cost than similar ships. Unless a reason was found which indicated
the occurrence of an abnormal situation, the outlier should be retained
within the data base. Due to time constraints this was not a feasible
alternative for the treatment of outliers within this study. However,
any further effort in this area should include a thorough investigation
of the outliers found within this data base or in future data bases.
This investigation may reveal valuable insight into problems which to
this point have not been satisfactorily explained. Until the problem
of outliers can b e resolved, it is possible that actual cost of a
specific group of ships could greatly exceed the cost predicted by the
models.
One further recommendation is necessary. The ships found in the
data base of this study are predominantly constructed of steel and
powered by steam. For this reason, the models developed in this
study are applicable to only steam powered, steel-hulled ships. The
use of these models in predicting the propulsion, electrical, or
auxiliary costs of a ship to be powered by gas turbine engines is not
recommended. Nor would it be advisable to predict hull, design and
engineering, or construction services costs for ships which will
utilize aluminum hulls. The models developed in this study are not
meant to b e extrapolated in this manner. They were developed using
a technique which relies upon historical data and do not propose to
explain future procurement costs unless the future design is not a
87
radical departure from the past. This does not imply that the same
parameters might not explain the cost of future ships. It merely
cautions against the use of these models without a thorough under-
standing of their applicability.
88
APPENDIX A RESIDUAL VERSUS FITTED COST PLOTS FOR CER MODELSREQUIRING LOGARITHMIC TRANSFORMATION
Four CER models (B2/C2 - Propulsion Cost and D2/E2 - Engineering
Cost) demonstrated increasing variance as a function of increasing
cost as shown in the plots of residuals versus fitted cost in this
appendix. This problem was corrected by taking the natural logarithm
of cost as the dependent variable in the regression analysis as
suggested in Ref . [5]. The untransf ormed CERs are listed, and may be
compared with the appropriate transformed CER in Tables VI - IX.
89
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94
APPENDIX B: CUMULATIVE DISTRIBUTION OF RESIDUAL PLOTS USED IN
OUTL1 ER IDENT IFI CATI ON
Analysis of the cumulative distribution of residual plots served
to identify the following "outliers" (data points falling significantly
out of the range of the rest of the data base)
:
CERCODE COST CATEGORY OUTLIERS IDENTIFIED
B-4 Communication & Control DE-1047
C-4 Communication & Control DE-1047
B-7 Armament Plus Weapons End D'DG-15, DLG-16
C-7 Armament Plus Weapons End DDG-15
C-8 Design and Engineering DDG-2
B-9 Construction Services plusMiscellaneous End DE-1047, DLG-6
C-9 Construction Services plusMiscellaneous End DE-1047
D-3 Pay load DE-1047, DDG-15, DLG-16
E-3 Payload DE-1047, DDG-15
F-l Total Cost DE-1047, DDG-2, DDG-15
G-l Total Cost DE-1047, DDG-6, DDG-15
For comparison purposes, the CERs with outliers included are shown for
these categories. These values may be compared with the CERs without
the identified outliers, as listed in Tables VI - XI.
95
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108
APPENDIX C
DESCRIPTION OF SHIP'S CHARACTERISTICS USED AS
RMC REPORT CR-058
Characteristic Symbol Units
1. Light Ship Weight LSW Long tons
2. Full Displacement FLDISD long tons
3. Hull Weight
4. Propulsion Weight
5. Electrical Weight
6. Communication andand Control Weight
7. Auxiliary Weight
8. Outfitting Weight
9. Armament Weight
10. Length Overall
11. Length BetweenPerpendiculars
12. Beam
13. Depth
HULWGT long tons
PROWGT long tons
ELEWGT long tons
C&CWGT long tons
AUXWGT long tons
OUTWGT long tons
ARMWGT long tons
LOA feet
LBP feet
BEAM feet
DEPTH feet
14. Draft DRAFT feet
EXPLANATORY VARIABLES IN
Definition
Weight of ship completewith all items of outfit,equipment, and machinerybut excluding cargo,stores, crew, etc. Includeslead ballast for surface shipsbut not for submarines.
Light ship weight pluscargo, crew, ammunition,aircraft, fuel, etc.
These are tbe weights ofthe seven groups as des-cribed in the Bureau of
Ships Cons olidated Indexof Drawings , Materials
,
and Services Related to
Construction Conversion.
15. Complement COMP integer
Maximum width amidships.
Distance from bottom to
highest complete deck,
amidships
.
Maximum depth of keel.
For subs, this applies
to full-load surfaceoperation.
Allowance for all officers
and men on board.
109
Characteristic Symbol Units DefinitJ on
16. Combined Arma-ment Electric &
C+C Weights A+C+EW
17. Nuclear C NUC
18. Maximum Shaft MAXSHPHorsepower
20 . Range RANGE
Long torn
integer
19. Maximum Speed MAXSPD knots
nauticalmiles
Sum of three weight groups.
1 = nuclear; zero otherwise.
Total power that can be appliedcontinuously to the shaftsunder designed operatingconditions. For subs this
applies to surface operation.
Speed at full power shafthorsepower. For subs, sub-merged speed.
21
.
Number of
Missiles
22. Number of
Torpedoes
MI SSL
TORP
24. Maximum BoomCapacity
integer
integer
23. Cargo Capacity CARCAP tons
MXB00M long tons
25. Series Variable SERIES integer
Number of launchers or missilelaunching tubes.
Number of torpedo tubes.
Total cargo dead weight, fully
loaded.
Capacity of most powerfulequipment for lifting or
handling cargo.
A number that represents the
position of a ship in a seriesof similar ships. Forexample, DD 936 to DDG 30 havethe same basic design exceptfor missiles and constitutea series of 39 similar ships.DD 936 would be assignedseries number 1 and DDG 30
would be assigned seriesnumber 39 .
110
Characteristic Symbol Units
26. Sub Dummy SUB integer
27. DE or DEGDummy DEDEG interger
28. Prototype Dummy PROTO integer
29. Number of Screws SCREWS integer
30. Number of
Engines ENG integer
31. Number of GEN integerGenerators
32. Power Loading PWRLDFactor
33. Block BLOCKCoefficient
34. Cubic No. CUBIC
35. Length-to-BeamRatio L/B
36. Speed- to-Length S/LRatio
37. Propulsion Type PTYPE
38. Award Date AWARD
39. GeneratorCapacity
40. Propulsion and P+AWGTAux i .1 i ary We igh t
41. Communicationand ControlWeight Squared
CCWTSQ
integer
years
TKWCPY kilowatts
long tons
long tons
Def :i nition
1 = submarine; zero otherwise
1 = DE or DEG; zero otherwise
1 = prototype; zero otherwise
Number of screws or shafts.
Number of ship servicegenerators
.
Ratio of maximum shaft horse-
power to full displacement.
Ratio of volume of displace-ment to the product of LBP,BEAM, DRAFT; volume of
displacement = 35 x FULDIS
.
Product of LBP, maximumbeam and depth > divided by
100.
Ratio of LBP to BEAM.
Ratio of maximum speed to
square root of LBP.
1 = steam; 2 = diesel.
Last two digits of the yearin which the contract wasawarded.
Total maximum output of allgenerators
.
Propulsion weight plus
auxiliary weight.
Square of communication andcontrol weight.
Ill
Characteristic Symbol Units Definition
42. Prototype Times PROLSWLight ShipWe i gh t
For prototypes, this taken onthe value of LSW. For non-prototypes, it has the valuezero.
43. Missile End
Dummy
44. Nuclear TimesPropulsionWeight
MS-END integer
NUCPWT
0= no launchers; 1 = a
launcher at one end of the
ship; 2 = a launcher at eachend of the ship.
For nuclear ships, this hasthe value of propulsion weight,
For non-nuclear ships it has
the value zero.
45 . ArmamentWeight- to-
Light ShipWeight Ratio
46. Double Dummy
47. Communicationand ControlWeight- to- LSW
Ratio
AR/LSW
DOUBLE integer
CC/LSW
Ratio of armament weight to
light ship weight.
If missile end dummy equals 2,
DOUBLE equals 1; zero otherwise
Ratio of communication and
Control weight to light chipwe i gh t
.
48. AuxiliaryWeight- to- LSW
Ratio
AX /LSW Ratio of auxiliary weight to
light ship weight.
49. Hull Weight-to- HL/LSWLSW Ratio
50. BallisticMissileRepair Dummy
FBMREP
Ratio of hull weight to light
ship weight.
This has the value 1 if ship
has ballistic missile repaircapability; zero otherwise.
112
APPENDIX 1)
DESCRIPTION OF SHIP"S CHARACTERISTICS USED AS EXPLANATORYVARIABLES IN THES .! S
Characteristic Symbol Units Definition
1. Light ShipWeight
LSW long tons Weight of ship complete withall items of outfit, equip-ment, and machinery but
excluding cargo, stores,crew, etc. Includes leadballast for surface shipsbut not for submarines
.
2. Hull Weight HULWGT long tons
3. PropulsionWeight
PROWGT long tons
4. ElectricalWeight
ELEWGT long tons
5. Communicationand Control
C+CWGT long tons
6. AuxiliaryWeight
AUXWGT long tons
7. OutfittingWeight
OUTWGT long tons
8. ArmamentWeight
ARMWGT long tons
9. Complement COMP integer
These are the weights of theseven groups as described in
the Bureau of Ships Consoli-dated Index of Drawings
,
Materials , and ServicesRelated to ConstructionConversion
.
Allowance for all officersand men on board.
10. Maximum Shaft MAXSI1P
HorsepowerTotal power that can be appliedcontinuously to the shaftsunder designed operatingconditions. For subs this
applies to surface operation.
11. Range RANGE nauticalmiles
113
12
Characteristic Symbol Units
Series SERIES integer
13. DE or DEC DEDEG integer
14. Prototype Dummy PROTO integer
15. Number of
GeneratorsNO-GEN integer
16. Power LoadingFactor
PWRLD
17. Award Date
18. GeneratorCapacity
19. Propulsion andAuxiliaryWeight
20. PrototypeLigb t ShipWeight
21. Missile EndDummy
22. ArmamentWeight- to-
Light ShipWeight Ratio
AWARD years
TKWCPY kilowatts
PRAXWT long tons
PROLSW
MS-END integer
AR/LSW
Definition
A number that represents the
position of a ship in a seriesof similar ships. For example,DD 936 to DDG 30 have the samebasic design except for missilesand constitute a series of 39
similar ships . DD 936 wouldbe assigned series number 1
and DDG 30 would be assignedseries number 39.
1 = DE or DEG; zero otherwise.
1 = prototype; zero otherwise.
Number of ship servicegenerators
Ratio of maximum shaft horse-power to full displacement.
Last two digits of the yearin which the contract wasawarded.
Total maximum output of allgenerators
.
Propulsion weight plusauxiliary weight.
For prototypes, this takes on
the value o£ LSW. For non-prototypes, it has the valuezero.
= no launchers ; 1 = a
launcher at one end of the ship;
2 = a launcher at each endof the ship.
Ratio of armament weight to
light ship weight.
114
Characteristic Symbol Units Definition
23. Engineering ENGWGT long tons Total weight of all propulsion,Weight electrical, and auxiliary
equipment
.
24. Payload Weight PAYWGT long tons Total weight of all C+C,armament and outfittingequipment
.
25. Engine and ENGPAY long tons ENGWGT + PAYWGTPayloadWeight
115
APPENDIX E
BASIC CONTRACT COST CATEGORIES
CategoryNo. Category Name
1 Hull Structure
Propulsion
5
Electric Plant
Communicationand Control
Auxiliary
Outfit andFurnishing
Armament
Design andEngineeringServices
Construction
Includes
Shell plating and planking, logitudinaland transverse frames, decks, super-
structure, armor, etc.
Boilers and energy converters, propulsionunits, uptakes, propulsion controlequipment, feedwater and condensatesystem, etc.
Electric power generators, powerdistribution switchboards and cables,lighting systems, etc.
Navigation equipment, interior communicationequipment, fire control systems, radarsystems, radio communications systems,sonar systems, etc.
Heating, ventilating, air conditioning,plumbing, elevators, arresting gears,rudders, etc.
Hull fittings, nonstructural bulkheads,painting, equipment for work shops,furnishings for quarters, etc.
Guns and gun mount, ammunition handlingand storage systems, other weapon systemshandling and storage systems, etc.
Contract drawings, working drawings,technical manuals, lofting, mock-up andmodels, etc.
Staging, scaffolding and cribbing,launching, trials, cleaning ship,drydockixig, etc.
END COST CATEGORIES
Mis cell aneousEnd Cost
WeaponsEnd Cost
ElectronicsEnd Cost
Disaster costs; cost of hull, mechanical andelectrical changes; post-delivery costs; etc,
Weapons costs after contractor delivery;missile, ASROC systems; etc.
Electronics costs after contractor delivery;radar, NTDS, fire control systems; etc.
116
APPENDIX F
TOTAL COST RESIDUALS - GENERAL DATA BASE(Trillions FY 65 dollars)
Hull Number Model B Model D Model F
DD 945 -13.366 -8.415 -6.169
948 -4.565 -1.174 5.011
950 -5.602 -1.917 5.021
DDG 2 1.853 4.980 3.165
4 -1.499 .879 2.058
7 -1.596 - .125 1.246
9 2.039 -3.809 3.860
10 -2.236 .765 .296
12 -7.373 -5.817 -3.769
14 -3.876 -2.405 -1.994
18 -2.996 -1.525 - .564
20 -3.638 -2.511 -1.377
23 -6.389 -5.046 -4.833
DE 1021 - .817 - .794 -1.525
1023 • 3.087 1.856 3.233
1025 3.787 2.556 3.803
1027 4.82 7 3.686 4.213
1033 -2.536 -2.915 -5.067
1035 5.694 3.994 3.977
117
ull Number Model B Model D Model F
1037 1.104 .088 -1.483
1040 - .389 -2.331 -5.925
1043 3.550 .724 2.746
1048 - .756 -3.178 - .752
DEG 1 .981 2.147 -4.105
4 -3.214 -3.390 -6.238
DLG 14 -3.128 -2.700 - .757
19 6.695 7.962 -7.900
DLG 21 -4.968 -6.775 -7.159
22 .512 -1.295 -3.559
26 11.902 5.338 - .529
32 1.117 -5.010 -1.623
33 4.517 -1.585 .998
118
APPENDIX G
TOTAL COST RESIDUALS - ESCORT DATA B
(millions FY 65 dollars)
Hull Number Model C Model E Model F
DD 945 -4.462 -4 . 811 -3.281
948 - .652 1.136 3.387
950 -1.576 - .191 3.397
DDG 4 1.595 1.269 2.323
7 1.075 .665 1.509
9 4.631 3.701 4.110
10 .465 .025 .559
12 -4.251 -4.318 -3.498
14 -1.175 -1.615 -1.731
18 - .295 - .735 - .301
20 - .599 - .920 -1.099
23 -3.331 -3.808 -4.558
DE 1021 -1.532 -2.508 -1.360
1023 - .476 - .511 1.349
1025 .224 .189 1.919
1027 1.264 1.219 2.329
1033 -3.367 -3.148 -4.780
1035 1.909 3.149 2.105
1037 1.397 2.294 - .376
1040 3.614 .53 4 -3.357
1043 2.780 1.978 1.085
1048 -1.224 1.655 -2.417
DEG 1 4.626 2.397 .346
4 -3.927 -4.197 -6.050
119
LIST OF REFERENCES
1. Deleted
2. Wilson, R. V., Escort Ship Cost Model (ESCOMO) , under developmentat Center for Naval Analyses, Arlington, Va.
3. Deleted
*i. Thei 1 , H. , Prin ciples o f Econometric s, Wiley, 1971.
5.) Daniel, C. and Wood, F. S., F itt ing Eq uations to Data , Wiley,
1971.
6. Gillmer, T. C. , Fundamentals of Construction and Stabilityof Naval Ships, U. S. Naval Institute, 195b.
7. Rend Report R-903-PR, Confidence in E stimated Airframe Costs:
Uncertainty s s
m
e n
t
in A
g
g r e q a f c P r c. di ction s, by F. S.
Timson and D. P. Tihansky, October 1972.
8. 0. S. Department of Commerce, Surv ey of Current ['us? ness t"\
v. ^6-52, July issues.
120
INITIAL DISTRIBUTION LIST
(Except Appendix II, Data Base (U) CONFIDENTIAL document published separately)
No. Copies
1. Defense Documentation Center 2
Cameron StationAlexandria, Virginia 22314
2. Library, Code 0212 2
Naval Postgraduate SchoolMonterey, California 93940
3. Asst. Professor N. K. Womer, Code 55 Wr 1
Department of Operations Research and AdministrativeSciencesNaval Postgraduate SchoolMonterey, California 93940
4. Assoc. Professor M. G. Sovereign, Code 55 Zo 1
Department of Operations Research and AdministrativeSciencesNaval Postgraduate SchoolMonterey, California 93940
_> . ijoijiv u . rj . iieiuon. , U.J1N i
583 D Michelson RoadMonterey, California 93940
6. LT R. R. Mc Cumber, USN 2
7 28 Willivee DriveDecatur, Georgia 30030
7. Chief of Naval Personnel 1
Pers lib
Department of the NavyWashington, D.C. 20370
8. Naval Postgraduate School 1
Department of Operations Research andAdministrative SciencesMonterey, California 93940
9. Naval Ship Systems Command 2
Ship Cost Estimating Branch (NAVSIIIPS 0161)Washington, D.C. 02360
121
UNCLASSIFIEDS I 1 1 ;
*t < I
rw.**-i- MDM i~-^
ICUMENT CC -TA-R&DtSecurity classilication of title, body ol abstract and ind( notation ir-.n.t lie- onterr-rl whin the overall report I- elatalfled)
OR i o in a tino ACTIVITY (Corporato author)
Naval Postgraduate SchoolMonterey, California 939 40
it. REPORT SECURITY C L*i!inc» HON
UNCLASRIFIKD2b. CROUP
REPORT TITLE
Estimation of Destroyer Type Naval Ship Procurement Costs
I. DESCRIPTIVE NOTES (Type of report and, inclusive dates)
' or's Thesis: March 1973i. au THOR(S) (First name, middle initial, laat name)
Donald Mearns Hernon and Ralph Ray McCumber, Jr,
..REPORT DATE
i March 1973.t. CONTRACT OR GRANT NO.
6. PROJEC T NO.
la. TOTAL NO. OF PACES
123
lb. NO. OF REFS
P*. ORIGINATOR'S REPORT NUMBER19)
vb. OTHIR HEPORT NO(S) (Any other numbers that may be aaolftiadthfa report)
0. DISTRIBUTION STATEMENT
Approved for public release; distribution unlimited,
I. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY
Naval Postgraduate SchoolMonterey, California 93940
3. AOS1 R AC T
This study presents three models by which the total procurement cost of Destroyer
and Destroyer Escorts may be estimated. One model utilizes 9 subsystem cost
estimating relationships (CERs) to obtain a total cost estimate; the second model
utilizes 4 subsystem CERs; the final model is a single total cost equation. The
CERs were developed using the linear least squares regression technique on a data
base of ships built from 1954-66. The CERs utilize input variables that may be
determined long before actual ship construction begins. This fact, and the precision
of the model estimates, recommend usage of these models in cost-effectiveness
analysis. The Patrol Frigate Project is utilized as a sample application, wherein
model estimates compare favorably with the current NAVSHIPS cost estimates. This
Study uses the data base from Resource Management Corporation Report CR-058, The
Nav ships Cost Model, and critiques that report
FORM \AT\ (PAGE 1 )
I NOV 8 S n" / **J>
/N 01 01 -607-681
1
122 UNCLASSIFIEDSecurity CleacilicHtion
&-Sl«09
IiNf I
' [SIFTED
KEY WO R O*
Costing
Ship Construction Costs
DD Procurement Costs
Cost Estimating
Cost Effectiveness
CERs
PF Cost Estimates
NAV SHIPS Cost Model
DD Parameters and Costs
pkna -.-. -. • - hmh5F0RMfc*1 ' I NOV 6 8
/N 01 01 - A07- 6821
1473 (BACK)
L ( f4 K A .INK F3
123 LSJ-ELEILSecurity Classification
tt496
143514ThesisHH965 Hernon
c# l Estimation of destroy-
er type naval ship pro-
curement costs.2 1 H V 2
13 AUG 73 §2292?3 JUL 74 2 2 112I60CT74
1
I 6 NOV 77 *7 <o7(6 NOV 77 1JAA/
29 JUL 83 27918
H4965 He rnon 4. H O J x *c.l Estimation of destroy-
er type naval ship pro-
curement costs.
thesH4965
E
2«?.!i°n ° f destr°Ver ^Pe naval ship
3 2768 001 91893 1DUDLEY KNOX LIBRARY
*
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