NAVAL POSTGRADUATE SCHOOL · NAVAL POSTGRADUATE SCHOOL * Monterey, California (OF DTIC MELECTE APR 0 8 THESIS y E AN ANALYSIS OF THREE AVCAL INVENTORY MODELS USING THE TIGER SIMULATION

NAVAL POSTGRADUATE SCHOOL* Monterey, California

(OF

DTICMELECTE

APR 0 8

THESIS y E

AN ANALYSIS OF THREE AVCAL INVENTORY MODELSUSING THE TIGER SIMULATION MODEL

C> by

LLJ Mark David Sullivan._JcSeptember 1984

9 Thesis Advisor: F.R. Richards

Approved for public release; distribution unlimited.

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An Analysis of Three AVCAL Inventory Master's Thesis;September 1984

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Mark David Sullivan

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Naval Postgraduate SchoolMonterey, California 93943

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AVCAL inventory models

RIMAIR TIGER

ACIM operational availability

simulation

20 ABSTRACT (Continue on reverse ede If neceeeary and Identify by block number)

This thesis investigates the effectiveness of threeAViation Consolidated Allowance List (AVCAL) inventorymodels in achieving aircraft system operationalavailability. The three models studied are the Aviation

*• Supply Office (ASO) Model, the Repairables Integrated Model

for Aviation (RIM-AIR), and the Availability CenteredInventory Model (ACIM). TIGER, a simulation model developed

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by Naval Seas Systems command, is amended to accommodatesimulation of multiple aircraft sorties with a realisticparts pipeline operation. AVCAL model inventory levels

are compared over a ninety day period utilizing availabilitystatistics computed by TIGER.

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An Analysis of Three AVCAL Inventory Models Using the TIGERSimulation Model

by

Mark David SullivanLieutenant Commander, United States Navy

B.S., University of Louisville, 1974

Submitted in partial fulfillment of therequirements for the degree of

MASTER OF SCIENCE IN OPERATIONS RESEARCH

from the

NAVAL POSTGRADUATE SCHOOL

September 1984

Author: _ _ _ _ _ _ _ _ _ _ _

Mark D. Sullivan

Approved by: _ __ _ _ _ _F.R. Richards, Thesis Advisor

A.W. McMasters, Second Reader

A.R. Washburn V'Chairman, Department ,f Operations Research

K.T. Marshall-,Dean of Information and Pol~vy Sciences

3

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ABSTRACT

I%

This thesis investigates the effectiveness of three

AViation Consolidated Allowance List (AVCAL) inventory

models in achieving aircraft system operational availability.

The three models studied are the Aviation Supply Office (ASO)

Model, the Repairables Integrated Model for Aviation (RIM-AIR),

and the Availability Centered Inventory Model (ACIM). TIGER,

a simulation model developed by Naval Seas Systems Command,

is amended to accommodate simulation of multiple aircraft

sorties with a realistic parts pipeline operation. AVCAL

model inventory levels are compared over a ninety day period

utilizing availability statistics computed by TIGER.

/ I 'A' f

Accession For

NTIS GRA&IDTIC TAB 0Unannounced 0Justif icatio

ByDistribut ion/

Availability Codes

Avirtil and/orDist Special

- iOtis

4

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TABLE OF CONTENTS

I. INTRODUCTION----------------------------------------1

A. BACKGROUND--------------------------------------1

B. PURPOSE----------------------------------------- 12

C. AIRCRAFT DATA----------------------------------- 12

D. MAJOR TOPICS------------------------------------ 13

I. THE TIGER SIMULATION PROGRAM---------------------- 15

rA. INTRODUCTION------------------------------------ 15

B. MAIN FEATURES OF TIGER------------------------- 15

1. Simulation---------------------------------- 15

2. TIGER Statistics--------------------------- 17

3. TIGER Subroutines-------------------------- 22

C. TIGER CHANGES----------------------------------- 23

1. Aircraft Sortie Simulation---------------- 23

2. Equipment: Repair and Resupply----------24

3. New TIGER Subroutines-------------------- 25

4. TIGER Validation------------------------- 26

II. ASO MODEL-------------------------------------------- 31

A. MODEL DESCRIPTION------------------------------ 31

B. INVENTORY DETERMINATION----------------------- 33

1. Attrition Rules---------------------------- 35

2. Rotatable Pool Rules---------------------- 36

C. MODEL LIMITATIONS------------------------------ 37

5

.. . . . . . .

IV. RIMAIR MODEL ----------------------------------- 40

A. MODEL DESCRIPTION -------------------------- 40

B. INVENTORY DETERMINATION -------------------- 42

1. Steady-state Supply Effectiveness ------- 42

2. Optimization --------------------------- 45

3. External Constraints -------------------- 50

C. MODEL LIMITATIONS -------------------------- 51

V. ACIM MODEL ------------------------------------- 54

A. MODEL DESCRIPTION -------------------------- 54

B. INVENTORY DETERMINATION -------------------- 56

1. ACIM Solution Equations ---------------- 56

2. Objective Function --------------------- 58

3. Input Data ----------------------------- 62

C. MODEL LIMITATIONS -------------------------- 71

VI. TEST RESULTS ----------------------------------- 74

A. INTRODUCTION -- ----------------------------- 74

B. FIXED BUDGET ANALYSIS ---------------------- 77

C. VARIABLE BUDGET ANALYSIS ------------------- 81

D. VARIABLE MSRT ANALYSIS --------------------- 83

VII. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS ------- 87

A. SUMMARY AND CONCLUSIONS --------------------- 87

B. RECOMMENDATIONS - ---------------------------- 90

APPENDIX A: TIGER DATA CARD FORMATS ------------------ 92

APPENDIX B: TIGER INPUT DATA FOR SERIES SYSTEM ------- 103

APPENDIX C: TIGER INPUT DATA FOR PARALLEL SYSTEM ------ 106

APPENDIX D: TIGER PROGRAM LISTING----------------------- 109

6

LIST OF REFERENCES----------------------------------------- 155

INITIAL DISTRIBUTION LIST--------------------------------- 157

I7

LIST OF TABLES

I. Critical Equipment Computation----------------------- 20

Ii. TIGER Validation Results---------------------------- 30

III. Part Parameters------------------------------------- 75

-IV. Fixed Budget Summary-------------------------------- 79

IV. Critical Equipment Analysis of ASO Model------------ 80

VI. AVCAL Stock Levels for Variable Budget-------------- 83

VII. RIMAIR vs. ACIM Performance for Variable Budget----84

VIII. ACIM Performance for Variable MSRT------------------ 86

8

LIST OF FIGURES

2.1 Phase Sequence Configuration---------------------23

LI2.2 Part Pipelines------------------------------------ 24

3.1 ASO Repair/Resupply Model------------------------ 32

*3.2 TAT Elements-------------------------------------- 38

4.1 RIMAIR Stockage Level Options-------------------- 49

5.1 Format A Data Elements and Record Example ------- 63

5.2 Format L Data Elements and Record Example-------- 675.3 Format I Data Elements and Record Example-------- 69

6.1 System Configuration (mission Code D)------------76

99

ACKNOWLEDGEMENTS

I wish to thank Peter Evanovich and Barbara Measell,

from the Center for Naval Analyses, for their patient help

in data collection and model research. I also wish to thank

my thesis advisor, Professor Russell Richards, for his helpful

guidance through the entire evolution of this thesis. A

special thanks goes to my wife, Mary, and my children,

Christine, Timothy, and Sean. Only with their constant

support and understanding was I able to complete this work.

1

10

II. INTRODUCTION

A. BACKGROUND

Navy ships, Marine Air Groups (MAG) and shore activities

receive AViation Coordinated Allowance Lists (AVCAL) to

support assigned aircraft for a prescribed period of time

(usually ninety days for ship and MAGs). AVCALS for carrier

deployed squadrons are especially crucial because operational

commitments will often exceed projected flight time estimates

and because the repair/resupply pipeline can be extremely

* lengthy. These lists are produced by Aviation Supply Office(ASO) prior to the assignment of aviation elements to a ship

or MAG. AVCAL's consist of Allowance Requirements Registers

(ARR's), which contain the projection of the range (which

* parts?) and depth (how many?) of spare assemblies and parts

necessary to support the aircraft and associated support

equipment at the Organizational (0) and Intermediate (1)

levels.

One of the key measures of effectiveness of a squadron's

performance is the aircraft operational availability.

Operational availability has many definitions, but here

availability refers to the expected percentage of time that

a weapon system or individual equipment will be ready to

perform satisfactorily in an operating environment.

I 11

0 -•

The Organizational (squadron) level maintenance concept

is based on "remove and replace". Weapon Replaceable

Assemblies (WRAs) are designed for rapid removal from the

aircraft. Parts that can be repaired at the intermediate

level are inducted to the Aviation Intermediate Maintenance

Department (AIMD) on the carrier. If a spare part is

available, a replacement part is issued to the squadron.

Parts that cannot be repaired on-ship, are sent off-ship to

the depot level repair facility. A replacement part is

re-ordered for the part placed in the off-ship supply

pipeline.

B. PURPOSE

This study will examine three inventory models currently

used to determine AVCALs. Model effectiveness will be

compared using simulated aircraft systems, representing

systems found on Navy E-2C Hawke'e aircraft. These parts

are also items that are found on the E-2C Mission-Essential

Subsystem Matrices (MESM), OPNAV Instruction 5442.4H [Ref.

1]. After inventory levels are computed, operational

availability is estimated by simulation of aircraft flights

on the TIGER program.

C. AIRCRAFT DATA

This thesis will concentrate only on repairable parts,

although consumables are also normally included in AVCAL

computation. Parts included in this study are WRAs from

12

. *....

the avionics portion of the E-2C aircraft, coded for removal

at the squadron level and repairable at the intermediate

level. The majority of the parts are complicated, expensive

pieces that cannot be stocked indiscriminately at high levels.

Equipment data was taken from Center for Naval Analyses

computer tapes of Navy wide E-2C parts data for the year

1981. Item unit costs, failure rates, and BCM (beyond the

capability of maintenance) rates reflect 1981 levels. Only

a limited number of parts were considered due to the limita-

tions of the TIGER simulation program.

AVCAL budget levels are based on predicted quarterly

aircraft operating hours. However, a recent E-2C squadron

operating level exceeded 1500 total hours in a quarter of

high tempo operations on deployment, thus exceeding histo-

rical operating levels by almost 50%. This is not uncommon

and suggests that it is important to have inventory levels

designed to achieve maximum availability while meeting

imposed budget constraints.

D. MAJOR TOPICS

Chapter II discusses the TIGER simulation model used to

compare inventory level effectiveness. The TIGER model is

examined, along with major changes introduced to the model

for this study. TIGER is a flexible program that allows for

sensitivity analysis by easy modification of part parameters

and system configuration. Aircraft sorties are simulated

13

... , . . .. ..... . .. ......... . .. ..

over a period of ninety days and the resulting system

availability is calculated.

Chapter III outlines one of the major inventory models

presently used to compute AVCAL, the ASO Manual Model.

Chapter IV continues with an outline of the RIMAIR Model,

and Chapter V covers the ACIM Model. Chapter VI presents

test results for the three models studied and Chapter VII

presents a thesis summary, conclusions derived from the

analysis, and recommendations.

14

14

~".. . . . . . . . . . . . . . . . . . . . . . . .

II. THE TIGER SIMULATION PROGRAM - 4

A. INTRODUCTION

TIGER is the generic name for a family of computer -

programs developed for Naval Sea Systems Command in 1979

which can be used to evaluate, by simulation, a complex

system in order to estimate various reliability, readiness,

and availability measures. Originally designed for testing

ship and shipboard weapon systems, TIGER has been amended

several times at the Naval Postgraduate School. Major

changes were undertaken by J. Leather in 1980 [Ref. 2], and

P. O'Reilly in 1981 [Ref. 3].

During the course of this study several significant

changes were made to the TIGER program. Several subroutines

were changed and two subroutines were added. This chapter

will outline the general features of TIGER and then detail

the changes made in this study. The TIGER Manual [Ref. 4]

is the primary reference source for all input, output, and

optional features contained in the TIGER program. Only

those options pertinent to this study will be outlined here.

B. MAIN FEATURES OF TIGER

1. Simulation

TIGER uses Monte Carlo simulation techniques to

evaluate the system model under consideration. Random

15

...............................................

numbers drawn from Naval Postgraduate School's LLRANDOMII

[Ref. 5] were used to generate equipment failure times,

repair times and other random numbers used in the simulation.

Based on the system configuration of equipment, the system

up and down times were determined. Based on these times,

system measures of performance were calculated. The simula-

tion was repeated a specified number of times and the results

averaged.

The configuration of the system being modeled is defined

in a top-down breakdown of the system into subsystem(s),

groups and equipments. Each type of equipment is given a

unique identifying number and its characteristics (MTBF,

MITTR, BCM rate, unit cost) are stated.

Events are significant mission occurrences. TIGER

recognizes the following types of events:

Equipment Failure (UP to DOWN)Equipment Repair (DOWN to UP)End of Phase Period Within MissionBeginning of MissionEnd of Mission

These five types of events are stored in sequential order

according to time occurrence. The first event becomes the

next step at which computations within TIGER are done.

The concept of phases is essential to the operation of

TIGER. A phase is s specified length of time that is

characterized by a set of equipment operating rules. For

this study two phase types were utilized:

16

Phase Type (1) is the flight phase. Equipments were

subject to failure during this phase. Parts that failed

during the flight phase could not be repaired until the begin-

ning of the next ondeck phase. Parts being repaired ondeck

continued to be repaired. If one part in the aircraft system

failed during flight, other parts on the aircraft were still

subject to failure.

Phase type (2) is the ondeck phase. Equipments were

not subject to failure during the ondeck (repair) phase. Air-

craft parts that failed during the previous flight phase were

taken off the aircraft, replaced with a spare if available,

and the failed part was placed in the repair pipeline. If no

spare was available the aircraft system was considered to be

in a degraded mode; that is, flight was possible but system

capabilities were decreased depending on the essentiality of

the failed parts.

Parts in the repair pipeline continue to be ordered,

shipped, and repaired during all phases.

2. TIGER Statistics

The statistics calculated by TIGER are system

reliability, readiness, and availability. The reliability

estimator used in TIGER is the ratio of the number of

successful missions to the total number of attempted

missions. A successful mission occurs when no system

failure occurs during the course of the mission. For a

system composed of high failure rate parts such as those in

17

this study, there is no statistical chance of completing a

mission of ninety days without a system failure. For this

reason the reliability statistic was not used.

The average readiness estimator (RED (EST)) used in

TIGER is the ratio of readiness (RED) uptime during the

entire mission to total calendar time of the entire mission.

Red uptime = Calendar time - Red downtime

Red downtime = Downtime prior to mission abort +

time after mission abort

This statistic was not used because it provides no indication

of system availability after the first system failure.

The most informative statistic is the average availability,

AVA AVERAGE (EST), or simply AVA. The availability parameter

is the probability that the system will be in a satisfactory

operating condition. It is estimated in TIGER as:

AVA =Total Uptime for all phasesTotal Simulation Time

For the scenario used in this paper AVA would include

downtime for an aircraft system during both the flight phase

and the ondeck phase. Since this study is primarily concerned

with aircraft system availability airborne, and it is assumed

that the scheduled launches would continue even with degraded

systems (a more likely event than waiting on deck for 100%

system availability), a new statistic was introducted.

The new availability parameter, AVMUP, measures the

availability of the aircraft system only during flight phases.

18

............ ....................-.--..--.- . ...........- *,- --. ... -... .... ..... ....- ,.. ......-... . .. ... ... , , ,

Summation of all Fliqht Phase UptimeSummation of Total Flight Phase Time

Although AVMUP approximates the AVA value, the only time

the two statistics are equal is when the ratio, A; where

A = Flight Phase Uptime/Flight Phase Downtime -

is equal to the ratio, B; where

Repair (ondeck) Phase UptimeB = Repair (ondeck) Phase Downtime

There are many scenarios in which these two ratios will not

be equal. For example, a system with high failure rate parts

will tend to have a lower A ratio. But these same parts may

not decrease ratio B to the same degree if adequate spares are

available. AVMUP emphasizes part criticality and reliability

more than AVA. For this study, AVMUP was consistently several

percentage points less than AVA.

Another set of statistics used in this thesis was the < -

Critical Equipments Summary produced by TIGER. This is an

optional printout that points out parts that are "worst

offenders". Parts that caused the system to go to a down

status or parts that failed while the system was already in

a down status are listed in this output.

Table I provides an example of this summary. It depicts

the events in a 90 hour mission, using a three part system,

System Y. At time 8.96 hours, Part A fails, but since System

Y is still up, no system downtime is recorded. At time 34.04

hours, part B fails, causing System Y to fail. TIGER counts

19

TABLE I

Critical Equipments Computation

Part A Part B

MTBF=50 MTBF=50

SYSTEM Y

Part CMTBF=30

1. TIGER events occurring in 90 hour mission, System Y

Total System

Time Event System Status Downtime

0.00 Mission start UP 0.008.96 Part A fails UP 0.00

34.04 Part B fails DOWN 0.0061.02 Part C fails DOWN 26.9890.00 Mission end DOWN 55.96

2. Breakdown of total system downtime among CriticalEquipments contributing to system downtime.

Period of System Downtime DividedTotal System Number of Among Down PartsDowntime Parts Down A B C

34.04-61.02 2 (A,B) 13.49 13.49 0.00(26.98)

61.02-90.00 3 (A,B,C) 9.66 9.66 9.66(28.98)

Total Downtime 23.15 23.15 9.66

Percent of Total 41.37 41.37 17.26System Downtime

20

I•

both parts A and B as critical equipments because both

contribute to system downtime. At time 34.04, system down-

time begins and continues until the end of the mission at

time 90.0. Thus total system downtime is

90.0 - 34.04 = 55.96 hours

At time 61.02, Part C fails. Part C is also considered

to be a critical equipment for the period from 61.02 to 90.0

(28.98 hours) even though System Y is in a down status during

this period. As shown in Part 2 of Table I, TIGER divides

system downtime during the period 34.04 to 61.02 (26.98 hours)

between the two parts (A and B) that are in a down status.

Parts A and B are each credited with 1/2 of 26.98 hours, or

13.49 hours each during this period. TIGER then divides the

system downtime for the period 61.02 to 90.0 (28.98 hours)

between parts A, B and C because all three parts are in a

down status during this period. Parts A, B, and C are each

credited with 1/3 of 28.98 hours, or 9.66 hours each during

this period.Iq

Therefore, total system downtime is divided between the

three parts A, B, and C as follows: A: 23.15 hours, B:

23.15 hours, and C: 9.66 hours. These hourly total are also

converted to percentages of total system downtime by part.

Parts that are large contributors to system downtime can be

easily identified through the Critical Equipments Summary and

inventory models can then be analyzed to isolate possible

weaknesses. Explanations of the other TIGER statistics can

be found in the TIGER Manual [Ref. 4].

21

I

3. TIGER Subroutines

TIGER in its present form at the Naval Postgraduate

School is written in FORTRAN, utilizing subroutines as major

subdivisions of the program. A short summary of the purpose

of each subroutine is presented below.

MAIN Program: The majority of data is input.TIGER statistics are calculated once after eachmission completion and again after all missions arecompleted.

Subroutine PACK: Equipment configuration dataand phase operating rules are input. Inventorylevels are computed.

Subroutine RUN: TIGER next event calculationsare done. This subroutine is called at the start ofeach new phase within a mission.

Subroutine TTE: Random numbers are generatedto provide times for part failures or repairs.Inventory levels are monitored. Major changes tothis subroutine were made for this study.

Subroutine STATUS: .Equipment(s) are reviewedafter each event for status (up or down) of the mainsystem and all parts.

Subroutine STANDBY: TIGER program arrays areindexed.

Subroutine EVENT: Events (part failures,repair, etc.) are sorted to find earliest time.Major changes to this subroutine were made forthis study.

Subroutine APPLE: Statistics generated duringa mission are summarized.

Subroutine SPARES: This subroutine is used toinput inventory levels to the main program.

Subroutine ASPARE: ASO Manual inventory levelsare computed. This is a new Subroutine.

Subroutine RIMAIR: RIMAIR inventory levels arecomputed. This is a New Subroutine.

22

C. TIGER CHANGES

1. Aircraft Sortie Simulation

One of the major changes made to TIGER permitted

the simulation of multiple aircraft sorties over a period of

ninety days. Since TIGER was originally desicned to test

ship systems that underwent a few lengthy phases, variable

dimensions had to be changed to allow for the many more

phases that were required. With these new changes a 24-hour

period may be divided up into as many as four phases. Figure

2.1 shows a sample combination of phases that can be arranged.

This combination was then replicated once for each day in

the mission.

Phase 1 Phase 2 Phase 3 Phase 4

<-4 > 8 ><-- 3 > -- 9 ---

Fly Ondeck Fly Ondeck

Figure 2.1. Phase Sequence Combination.

During each phase a number of aircraft may be onerated.

Since this version of TIGER does not allow for separate

aircraft (systems) to be operated in different phase

sequences, aircraft were operated simultarneously. For this

study three aircraft were operated in 'series" operation.

That is, three identical aircraft systems were operated

23

with the requirement that all aircraft must be in an up

status for the combined trio system of aircraft to be in

up status.

2. Equipment: Repair and Resupply

TIGER was modified so that parts that failed and

were removed from the aircraft, known as carcasses, could be

tracked through the repair and resupply system. The inventory

algorithms studied assumed a one-for-one repair policy; for

each part turned in, another is issued. Figure 2.2 shows a

schematic of the overall repair and resupply pipeline. When

a part fails, it has two different pipelines it can follow.

P (BCM) - io Part Ordered Off Ship

Part Failure -- 0.

1-P (BCM) - Part Repaired on Ship

Figure 2.2. Part Pipelines.

With a probability = P (BCM), it will be considered

"beyond the capability of local maintenance". In this case

the part will be shipped to the depot level repair center

off-ship, and a replacement part will be ordered. The time

to receive a replacement part is known as the order and

shipping time, OST. This time can vary depending on the

stock level of the part at the depot, the location of the

ship, and whether or not resupply to the carrier is possible

(wartime scenario). Tiger will assign an exponentially

24

L. .

distributed CST, with mean equal to the SRTIM parameter of

the part. SRTIM is defined as the off-ship order and

shipping time of the specific part type. This time is

placed in a new event time queue, RFITIM. Each part type

has its own RFITIM queue that tracks all parts placed in

the pipeline.

The exact number of parts in the pipeline is limited to

the number of parts originally stocked. This computation is

done through the NOP (number of parts) array. Whenever the

NOP level equals the original inventory level, no more parts

are available until a part is resupplied or repaired. The

RFITIM queue is sorted to find the earliest repair time.

The failed part can also be placed in the repair pipeline,

with a probability of 1-P (BCM). This corresponds to the

part being repaired at the ship repair facility, the Aviation D

Intermediate Maintenance Department (AIMD). The part is

assigned an exponentially distributed repair time, with mean*

equal to the REPTIM parameter of the part. REPTIM is defined I

as the on-ship repair time for the specific part type. This

time is also placed in the RFITIM event queue. This queue

runs independently of the main TIGER event chain, known as I

ETIME; but RFITIM does follow phase type rules outlined

previously.

3. New TIGER Subroutines

Two new subroutines were introduced into TIGER. The

first, ASPARE, calculates inventory levels based on ASO

2

25

............................................... ,-•,-,. .- .,..

Manual instructions for AVCAL determination. The second

subroutine, RIMAIR, calculates inventory levels based on

RIMAIR policy instructions. Both algorithms were used by

Boatwright [Ref. 6]. Later chapters will examine these

inventory policies.

Major changes were also made to the TTE and EVENT

subroutines in order to include new repair algorithms

(discussed in II.C.2), and new phase sequence rules

(discussed in II.C.l). Input data cards were changed. A

full listing of input card formats used in this study can be

found in Appendix A. Appendices B and C contain example

input data sets which are read into TIGER from separate files.

A complete listing of TIGER as utilized in this study is

included in Appendix D.

4. TIGER Validation

The complexity of the TIGER program makes extensive

validation difficult. Two simple scenarios were chosen in

order to validate this version of TIGER. Scenario One

involved a single flight phase of 100 hours, with a mission

time of 100 hours. Two parts, each with a MTBF = 100 hours,

were arranged, first in a series configuration and then in a

parallel configuration. This short mission time allows for

the possibility of a successful (no failure) mission.

With this simple equipment configuration, derivation

of the mathematical expression for the theoretical system

availability is given in Ref. 7. The average availability

can be found from the expression:

26

o , , . . .. . . . . . . . . . . . .. . .

AVA : E(T)/MT, (1)

where MT is the mission time 1 100 hours. This

assumes that no repair is possible during the 100 hour

mission. E(T), the expected lifetime, is

E(T) = t f(t) dt. (2)

| 0

For component analysis,

f(t) = d(F(t))/dt = d(l - R(t))/dt, (3)

where R(t) is the survivor or reliability function. For a

series system the reliability is

R(t) = Rl (t) * R2(t), (4)

where Rl(t) and R2(t) are the reliability functions for

components 1 and 2. Assuming exponential failure times,

Eq. (4) becomes

R(t) : EXP(- X1 t) * EXP(- X2t),1! 2= EXP(-(X + X )t) = EXP(- X t); (5)1 2

where X X 11 + X 2 = 1/50.

Substituting (5) into (3), f(t) can be expressed as

f(t) = X EXP(- X t). (6)

Substituting (6) into (2) now gives

E(T) tA EXP(- A t) dt. (7)

0

27

The above expression assumes an infinite operating period.

In our problem, time is truncated at 100 hours. Therefore

if t is the system failure time, the mission lifetime is:

t if t < 100

T

100 if t > 100

Thus, for our case, equation (7) is modified as follows:

1 00 0J

E(T) = t* EXP (-X t) dt + 100 j EXP(- t) dt

0 100

= 29.78 + 13.53 = 43.31.

Finally,

AVA (series) = 1/100 (43.31) = 0.4331.

For a parallel configuration system, its reliability, R(t),

can be expressed as follows:

R(t) = Rl(t) + R2(t) - Rl(t) * R2(t). (8)

The last term in (8), Rl(t) * R2 (t), is the series

reliability term (43.31) computed above. Also note that for

this problem Rl(t) equals R2(t) because the two components

have identical MTBFs. Substituting 43.31 for the last term

in (8), E (t) is computed as in the series system above to be

= 2 [ t lEXP(-Xlt) dt + 100 X1 EXP(-X1 t) dt]- 43.310 10 0

= 2 * (63.21) - 43.31 = 83.11.

This gives:

AVA (parallel) (83.11)/100 = 0.8311.

28

.. .. . . . . . . . . . .. .. ... . . .

Scenario Two involved a single flight phase of 5000

hours, utilizing the same two systems. A phase of 5000

hours ensures the failure of the system and an estimate can

only be made of the expected lifetime of the system. For

the series system, the expected lifetime is

E(t) S tX EXP(-t) dt + 5000 flightpaset) dt.

Therefore,

E(t) = 50.0 + 0.0 = 50.0 hours.

For the parallel system, the expected lifetime is

E(t) t(2 1 EXP(-XI t) + A EXP (-E t) dt

0 5 0

00

=2 * (100.0) - 50.0 = 150.0 hours.

Results for validation runs are shown for both

scenarios in Table II. One thousand iterations were done

for each run.

29

0

TABLE II

TIGER Validation Results

Scenario 1 (100 Hours)

Run Seed AVA (series) AVA (parallel)

1 2222 0.4294 0.82692 1245 0.4360 0.84443 1357 0.4341 0.8453

Theoretical Value 0.4331 0.8331

Scenario 2 (5000 Hours)SJ

Run Seed E (Lifetime E (LifetimeSeries) Parallel)

4 2222 50.3 149.85 1245 50.7 153.46 1357 49.5 144.9

Theoretical Value 50.0 150.0

i.4

30

. .. ..... .. . .- .. , ...

III. ASO MODEL

A. MODEL DESCRIPTION

The Navy Aviation Supply Office Manual model for deter-

mining the AVCAL is based on the repair/resupply pipeline

displayed in Figure 3.1. Failure of parts in a ninety-day

period create a demand, QTRDEM. With a probability equal to

P, parts are beyond the capability of shipboard maintenance

(BCM), or with a probability 1-P are determined to be

repairable onboard ship.

The BCM'ed parts are sent off-ship, either to be disposed

of or to be repaired at the depot repair maintenance facility

ashore. In either case a replacement part is ordered through

the requisition pipeline. The order and shipping time (OST)

is the time from order until receipt of a new part. A part

repairable at the shipboard level experiences a delay in the

repair pipeline called the turn around time (TAT). The

average number of parts in this pipeline is the mean repair

pipeline (MRP). When parts are received from either pipeline

they are placed back into the local (retail) inventory.

The following assumptions are made in the model [Ref. 81:

Demand is a Poisson process.

Demand rates are stationary over time (no surge orcyclic demand rates).

OST and TAT are independent of demand.

31

rp

L~. ..-. " . . . . . ..'--". . . . --. -.-.. -... . % . -- ,. , ..- , -- ' . ._., -.-- -:.- ,

The repair pipeline is never saturated.

Items are requisitioned on a one-for-one basis(S-i, S ordering policy).

All demands are satisfied by either immediatereplacement from supply, shipboard repair, orrequisition (back order)

Part cannibalization does not occur.

> CARRIER AVCAL t

IS PARE T REPAIRABLE ON CARRIER?

YES NO (BCM)

PROB = 1-P PROB = P

SCARRIER AII D I DEPOT LEVEL 1

REPAIR REPAI R/RES UPP LY

REPAIR PIPELINE REQUISITION PIPELINE

DELAY = TAT DELAY = OST

Figure 3.1. ASO Repair/Resupply Model.

32

. . . .

S

These assumptions are very generous, but the net affect

is that this model is a fairly simple one. The first

assumption leads to demand over a given period t being

distributed as Poisson, with mean = (QTRDEM * t) . It can

be shown [Ref. 91 that the two "pipelines", ship repair

and off-ship requisition, are independent Poisson processes

with means (P * QTRDEM)* t and (1-P)*QTRDEM*t, respectively.

The number of items in the ship repair pipeline is also

Poisson, with mean RPQ.

B. INVENTORY DETERMINATION

The Navy Aviation Supply Office's (ASO) Provisioning

Manual [Ref. 10] furnishes policy and procedures for

determining AVCAL range and depth levels. Although the

process of generating a complete AVCAL is quite complex, the

basic guidelines used for repairables. are concise. Navy 3M

data, contractor usage data, and laboratory results are

combined to predict failure rates. The ASO Manual refers

to failure rate prediction as "the most important function of

provisioning" in the determination of the AVCAL.

The Outfitting Directive, issued by the Type Commander,

specifies the Type/Series/Model of aircraft to be supported,

the number of aircraft, and the number of flight hours per

month per aircraft. The Allowance Requirement Registers

(ARRs), which make up the AVCAL, are divided into three

major parts:

33

Part I Attrition Support

Part II Rotatable Pool Items

Part III Special Support Requirements

This study will deal only with the first two parts. The

following data elements are used to construct ARR's:

Maintenance Cycle (MC) : Normally 100 hours foraircraft and installed equipment.

Units per Component/Aircraft (UPA): Number of partsof type X installed on each aircraft. An individualUPA exists for each part type X.

Planned Operating Hours: Planned aircraft utilizationper month in hours.

Number of Aircraft: Number of aircraft supported bythis ARR.

Maintenance Replacement Factor (MRF) : For repairableitems, the number of times that an item will be BCM atorganizational (squadron) and Intermediate (AIMD)levels during one MC.

MRF = # BCM's/(MC * UPA)

Rotatable Pool Factor (RPF) : Predicted number ofremoval/IMA repair cycles in one MC.

RPF = (Predicted # of repairs)/(MC * UPA)

Turn Around Time (TAT) : Average number of days between . -

removal of a repairable item for processing at the AIMDand return to Ready For Issue (RFI) condition. Thisestimate includes time to schedule, fault isolate,disassemble, repair, assemble, and test a repairableassembly.

The candidates for inclusion in the AVCAL are chosen as

follows. The attrition quantity in any ninety day period is

determined as follows:

(1) Compute Flight Hour Factor (FHF) for aircraft:

FHF = (avg. # of Aircraft)* (Operating Hrs./Qtr.)

(2) Compute Expected number of Maintenance Cycles per

quarter:# of MC = FHF/100

34

"" '-I .J. .' " "••. -•_" " -".' " . '. _" , •." •- . -" ." " "_" . _" " : ' " .' ' .7 ' . b ' .. ' .•_,_,_ _._ • _. " ._

(3) Compute Attrition Quantity (D):

D = MRF * UPA * (# of MC)

1. Attrition Rules

Attrition items are stocked to replace those parts

that are BCM'ed at the organizational or intermediate level.

The range rules for attrition parts depend on whether the

part is also included in the rotatable pool quantity. If a

part is supported in the rotatable pool, it must have a

demand (D) greater than or equal to one per quarter to be

eligible for the attrition portion of the AVCAL.

If the part is not supported in the rotatable pool,

the range rules for attrition are different. These low

demand items may still qualify for the attrition allowance

under the following guidelines:

a. Items with a unit cost of $5000 or more will

qualify if the predicted demand is equal to or greater than Ione in a six month period. This equates to an attrition

quantity of at least 0.50 before any units will be carried

in the AVCAL.

b. Items with a unit cost of less than $5000 will

qualify if the predicted demand is equal to or greater than

one in a nine month period. This equates to an attrition

quantity of at least 0.34 before a quantity of one will be

carried in the AVCAL.

Attrition quantities are used to determine attrition

range candidates as noted above. Once a candidate has been

35

-...... .,:. % .. ;., .-... :. ..- ,.. ....... .... . ..... . .. . ., .. . . .. ,. .

selected, the depth or amount to be stocked is computed by

rounding the attrition quantity to the nearest integer. A

minimum of one is stocked for all range qualifying candidates.

2. Rotatable Pool Rules

The rotatable pool portion of the AVCAL allowance

was intended to support the fast moving, critical parts and

assemblies required to support the aircraft. These items

must be capable of repair at the intermediate level (AIMD).

The raw pool quantity (RPQ) is the average number of units

repaired by the AIMD in a 90 day period and is given by:

RPQ = (RPF * TAT * UPA * (# of MC/in 90 days))/90

It should be noted that the value for TAT is an

averaged value that is truncated to a maximum of twenty days.

This data element will be further discussed later in the

chapter. Using RPQ as the mean, the Poisson distribution is

used to find the depth which will provide 90% protection

against being short at least one unit in ninety days. This

depth, called the rotatable pool allowance (RPA), provides

90% protection for those parts which have carcasses tied up

in the repair pipeline. Therefore,

P( X < RPA) = 0.9

where X = # of units of a part being repaired in the shipboard

pipeline. Under the assumption that X is Poisson distributed,

P(X < RPA) = RPA EXP(-RPQ) * (RPQ)X

X=0 X!

36

_ _ 0 . . .. . . . . . . .• . . - . - . . - . , . - ,

Using these calculations, an RPQ of 0.11 is the minimum

value that will require an RPA of one. Below the 0.11

level a stock quantity of zero satisfies the 90% protection, 0

and no part is stocked for the pool.

C. MODEL LIMITATIONS

The ASO model is the oldest of the three models discussed

in this thesis. It is the only model developed before data

automation and powerful computers became widespread in the

Navy. This partially explains the model's simple approach

to the inventory problem. Procedures are simple enough that

inventory levels could be calculated by hand for each part,

one at a time, with the use of one short table from the ASO

Manual. One noteworthy weakness in the model is the omission

of the concept of budget. The only direct reference to dollar

amounts is in the use of $5000 as a cutoff amount for attri-

tion allowance. But even this figure has become completely

arbitrary because there is no provision for its change or

update and because it applies to inventories with parts

typically ranging in price from a few hundred dollars to over

several hundred thousand dollars.

Mitchell [Ref. 11] pointed out that limiting TAT to twenty

days is not a true reflection of the real repair pipeline

operation. A breakdown of the TAT elements is shown below in S

Figure 3.2. The limit values were developed at ASO in a study

conducted in 1977 [Ref. 121. The limit values tend to under-

state the problems encountered in the repair pipeline. The

37

: ..oi i -<. i . , -. . ., _.i.._ - ;. .. :,. .. :i;. - .i . . il . . ;i.i ... .. i.i . -_ i i ;. _ ,- . , _.-. - - . . .. ,i: ,.

values are applied across all parts, although the complex

equipments encounter longer times than the simple parts.

TAT element Limit (days)

IP: In-process time 1SKD: Scheduling time 3RPR: Repair time 8AWP: Awaiting parts time 20

TAT: Total time 20

Figure 3.2. TAT Elements.

The ASO model is tasked to achieve material availability

goals and stockage criteria promulgated in OPNAVINST 4441.12A

[Ref. 13]. For ships, the objective for overall AVCAL per-

formance is to fill 75% of all demands and to provide overall

availability of 85% for items stocked. But as noted in the

Navy Fleet Materials Support Office RIM-AIR Study [Ref. 14],

the ASO model has historically failed to do this. Fleet

aircraft availability is often achieved only through a

constant process of selective cannibalization of squadron

aircraft parts. For example, in an E-2C squadron with four

aircraft aboard a carrier, one aircraft is designated the

"parts locker" in order to overcome shortcomings in both the

repair and requisition pipelines.

38

There is a disadvantage in the ASO criteria that

attrition and repair demand be segregated. Separate range

criteria are applied to determine attrition and repair

pool support. This splitting of demand results in non-

stockage of items that would have been stocked had demand

been combined. This contributes to the overall conservative

approach that characterizes ASO Manual AVCAL levels.

3 9

S ' ' ' "- - - "i . i . . . . . . , l i _ . ' " " " "

IV. RIMAIR MODEL


During the Seventies all DOD budget policies came under

close scrutiny by civilian government leaders. The DOD

Retail Inventory Management and Stockage Policy (RIMSTOP)

Study was issued in 1976 to set guidelines for retail level

inventory support provided by the military services [Ref. 14].

Out of RIMSTOP originated DOD Directive 4140.44 (Supply

Management of the Intermediate and Consumer Levels of

Inventory), and DOD Instructions 4140.45 (consumable items),

4140.46 (repairable items) and 4140.47 (war reserves).

DODI 4140.46 [Ref. 151 dictates that:

"the following levels will be computed for eachrepairable item to be stocked at the intermediatelevel on a demand-supported basis:

(1) Repair Cycle Level (RCL). The RCL is a functionof the anticipated number of maintenance replacementsthat will be repaired locally and the item's repaircycle time.

(2) Order and Shipping Time Level (OSTL). The OSTLis a function of the anticipated number of maintenancereplacements that will require supply from externalsources and the item's order and shipping time.

(3) Safety Level (SL). The SL is a function of thecapabilities that the repair cycle time will be exceeded,the order and shipping time will be exceeded, the main-tenance replacement rate will be higher than forecasted,and a number of maintenance replacements, anticipatedfor repair at the activity, will require resupply fromexternal sources.

40

(4) Operating Level (OL). The OL is an EconomicOrder Quantity (EOQ) and is a function of the cost toorder and the cost to hold an item of inventory.

(5) Replenishment. Replenishment action will betaken when the asset position reaches the reorder point."

In addition, DODI 4140.47 (Secondary Item War Reserve

Requirements Development) authorizes increments to the order

and ship time, repair cycle and safety levels to satisfy

wartime recurring demands over and above the peacetime

demands. An additional Resupply Delay Time (RDT) level is

also authorized to provide material coverage of anticipated

delays in the wartime retail level supply pipeline.

Commander, Naval Supply Systems Command (COMNAVSUPSYSCOM)

proposed a pipeline model that would adhere to these DOD

policies while attaining Navy availability goals. This model

was designated Repairables Integrated Model for Aviation

(RIMAIR). In addition to the levels mentioned above, RIMAIR

added a level of stock that assures a self-supporting capa-

bility for a prescribed period of time, known as an "endurance

delta". The same assumptions stated for the ASO model apply

to this model.

RIMAIR produces a total depth of stock that equals:

OST + EDTOSp

OL + RCL + MAX{ + SL,

OST + RDT

41

0

"'-. - '-J : t • - -' - - - - " "- " , - -. . ," " - : - . -. ' '2 '.-:-' . *- ' -.. -- , .- , -'.'-,- . - * . .. ." ",

where

OL = operating level;

RCL = repair cycle level computed with a wartimew flying hour program;

OST = order and ship time level computed with aP peacetime flying hour program;

EDP = endurance period support level to assureself-supporting capability to satisfy wartimedemands for a prescribed period of ti'me;

OST = order and ship time level computed with awartime flying hour program;

RDT = resupply delay time level;

SL = total safety level based on the sum of RCL

and the MAX computation.

The peacetime operating stock (POS) levels may be separated

from the total depth:

POS = OL + RCL + OST + SLp p p

The endurance delta represents the difference between

OST + EDP and OST + RDT [Ref. 14].p w


1. Steady-state Supply Effectiveness

Appendices C and D of the FMSO RIM-AIR Study [Ref. 14]

provide the mathematical background for this model. Initially

assume no stock is carried. The repair and requisition

processes can be modeled mathematically as stochastic queuing

processes in which non-RFI (failed) units arrive, wait for a

RFI replacement then leave. The average number of items in a

queuing process is given by the following relationship:

42

• , " , "- " ." ...' j .. •L . . .L'.," .".

.. .. .[

L= W

where L = average number of units in process

A = averaae arrival rate

W = average waitina time in process

The number of requirements for a RFI replacement in

the requisition process is the requisition pipeline. The

number of non-RFI units in the repair process is called the

repair pipeline. Given the above relationship, the average

number of non-RFI units in the repair and requisition pipe-

lines may be expressed as follows:

LT= LREP + LREQ

X REP * WREP + XREQ * WREQ

RPF* MC 9 0 MRF*MC9 0 OST= * ~TAT +*OS-.90 90

where

L = total non-RFI units waiting for replacementT

L RE = non-RFI units in the repair process

L RQ= non-RFI units in the requisition process

X = arrival rate for repair procesREP

XRE Q = arrival rate for requisition processWREP = waiting time for repair process

WRE Q = waiting time for requisition process

MC90 = waiting cycle program for 90 days

The actual number of units in the repair and requisition

pipelines at some point in time is a random variable. The

following assumptions are made in order to postulate a

probability function for this random variable:

43

.... •. . . .. .. . . . ..... ••,. ,... .. . . .,. .. .

The arrival process in Poisson.

The repair times have a distribution which isindependent of the arrival process.

The arrival rates and services rates are stationaryover time.

Arrivals are always single units.

Every arrival enters either the repair orrequisition process and completes service beforedeparting.

Given these assumptions, the number of units N in the

repair and requisition pipelines will be Poisson distributed

with mean LTfor repairables. That is, the probability that

N = n, is found from the expression:

P(N=n) = EXP(-LT) (LT)n/(n!).

The probability that there are no backorders, called

the protection, is computed as follows:

SProtection = P(N=n)

n= 0

where S = stock quantity.

When the number of units in the repair or requisition

processes is strictly less than the stock quantity, there is

at least one RFI unit available in stock to satisfy a demand

should one occur. Since demands are assumed to always be

for one unit, only one unit needs to be in stock when a demand

occurs in order to satisfy that demand. The probability of

satisfying a demand Is called the fill rate (FR) and is

cowmputed as follows:

44

S-1

FR= P (n)n=O

The expected number of satisfied demands is found by

multiplying the fill rate by the expected number of demands.

The expected demands (D) for a 90 day period is computed as

follows:

D = (MRF + RPF) * MC 9 0

Thus, the expected gross supply effectiveness, which is the

percentage of demands satisfied immediately from stock, can

be computed as follows:

Expected Supply Effectiveness =

mFR *D.

i=l 1 (1)

Q D.j=l

where

m = number of stocked itemsQ = number of installed itemsi = index of stocked itemsj = index of installed items

Expected net supply effectiveness is obtained by summing

expected demand over stocked items in the denominator.

2. Optimization 5

The objective of the optimization of this model is

to find an inventory that gives the maximum possible effec-

tiveness for a given cost. The effectiveness measure used

is the expected aross supply effectiveness derived above.

Expected units demanded for installed items remain constant.

45

. .. . . . . . . . . . . . . .. . ,

The optimization maximizes expected supply effectiveness.

The problem may be stated as follows:

mMaximize I E. * D. * FRii=l1 1

msubject to C 1 S. B

i=l1 1

where

i = item index;E i = Item essentiality code7

D i = Expected demand;

FR i = Fill rate per item;

C i = Unit price;

Si = Stock Quantity;

B = Cost target.

RIMAIR uses the method of Lagrange multipliers to

solve this problem. Formulating the Lagrangian function

from the problem above gives:

mL(X,S) = E.* D,* FR. -

m* C. *. -B)

i=l1

Because of the discrete nature of the demand

distribution, the stockage levels are determined usina

finite differences. Observe that L(\,S) is separable in

the items. Thus the Lagrange function can be written as:

m

L(A,S) L LS(s. A) + B Ai=l.

-:'. 46 ,

.......................................................

where L.(S.; ) ( El * D, * FR (S 1 I

For a given value of the stockace level for item i is then

the largest integer S1 such that:

A Li(S - A) L i(S1 +1, ) - L1 (S; ) 0

This is found to be the largest intecer S such that

• C* (2 )

Pi (S i) >

(2)

where p (S) is the probability density function of the

Poisson pipeline distribution, civen earlier as P(N=n).

The "optimal' stockage level corresponds to the

solution to this equation when \ : " where A is that

value such that [ C. * S = B. (Due to the discrete

nature of the items the required budget may never exactly

equal B and consequently, the Lagrange solution may not be

optimal. It will produce, however, an undominated solution

for each budget amount actually consumed.)

The procedure outlined above for finding S can be

applied with any value of A. When used with A , it produces

the solution to the original problem. When used with any

other A, it produces an inventory that still maximizes the

Lagrangian function with respect to S but does not satisfy

the budget constraint. The process then becomes one of

finding the correct A, until the cost is close to the

target B.

The RIMAIR implementation of the solution procedure

as applied to the stockage level for the ith item is sunarized

47

below:

a. Select the Lagrange multiplier.

b. Find the largest integer which is less than or

equal to L as an initial value for S..T 2.

c. If

x * ci

p(Si) <E 1

do not stock the item. This situation is depicted in

Figure 4.1, Case A. The Poisson density function p(S i

is everywhere less than the value for X * Ci/E i * Di -

Therefore the optimal stockage level equals zero. Ifp(S i ) > X * Ci/E i * D.

go on to step d. The second situation is shown in Figure

4.1, Case B. S. is initially set equal to 2 (the largest1

integer less than or equal to the mean LT = 2.5).

d. Increment Si by one.

e. If

X * C.

P(S) IE.*D.

1 1

select Si as Si and stop; otherwise go to step d. In

Case B, Si=4 would be chosen as Si (Note that this*

implementation will select S. to be one larger than that1

which would be generated by Equation 2.)

f. Compare the optimal stockage level to external

constraints and adjust accordingly.

48

Case A: Zero Stockage Level

XCi/EiD i

P(si) T

I'b 'I

0 1 2 3 4 5 s -

L =

LT= 2.5

Case B: Positive Stockage Level

P (S-.

~C./ED1 -

C i /E IDi I

0 1 2 t 3 4 5 si_ ..

LT =2.5

Figure 4.1. RIMAIR Stockage Level Options.

49

.. . . .-I. _ . . ] . . . . - < - . - . . . . > - . : . , . . . .. - < , ' . . [ - . - . , - . , . . , - . . , - . - , - _ ,

g. Iterate through all items, and compare the final

total inventory cost with the budget target B. If the total

cost is not within preassigned limits return to step a. For

example, if total cost is not within plus or minus 1% of

target budget, begin at step a with a new lambda value and

try to get total cost within 1% limits.

This procedure simultaneously produces the range and

depth criteria. That is, if the optimal stockage level is

greater than zero, then the item is stocked.

3. External Constraints

Step (f) includes comparing stockage levels to

constraints external to the original Lagrange problem. The

maximum constraint is the sum of a ninety-nine percent

protection on the mean basic pipeline (BP) and the operating

level. BP is defined as:

BP = L + ENDURANCE LEVEL (3)T

Since the basic pipeline quantity is assumed to be Poisson

distributed with mean BP, the 0.99 protection level would be

the smallest quantity S such that:

SxZ EXP(-BP) * (BP) /X! > 0.99 (4)X=0

The operating level is computed as follows:

OL = V(2 * A * Y)/(IC) (5)

Where: Y= annual demandsC= unit price

2A/I= constant (approximately 559)

50

The maximum constraint is the sum of S from (4) and OL

from (5) above.

The minimum constraint is the sum of (3) and (5) above.


The RIMAIR model corrected several of the deficiencies

of the ASO model. It was recognized that the ASO model's

attrition allowance, which was theoretically provided to

support wartime mobilization operations with resupply

delayed or cut off, was in fact supporting the number of

items in the wholesale resupply pipeline during normal

operations. The RIMAIR model includes the addition of

stock to the attrition portion of the allowance to support

the expected order and shipping time experienced during

peacetime, and the addition of a wholesale resupply pipe-

line to the repair cycle pipeline for the purpose of

providing Poisson protection to the entire pipeline.

One of the potential strengths of the RIMAIR model is

the inclusion of the item essentiality code parameter E,.

This code was developed to reflect the relative importance

of parts to total system availability. Suggestions for use

of this parameter are addressed in Boatwright [Ref. 6]. An

ideal code would be influenced by the part's MTBF, by the

system configuration (whether or not the part had backups),

and by the role that the part played in contributlnq to

aircraft mission completion.

51

-. .-.-.. . .. ....-. .. •... -.. .<-< ..-.......... . ..-.... .:... ... ._ ... "'..... ..

Incorporation of these concepts into the essentiality code

is difficult. For this study an item essentiality code

equal to one was assumed for all parts. One reason for this

was because all parts were considered equally essential for

aircraft mission performance.

The Lagrange multiplier provided control for budget

levels as discussed above. By decreasino lambda the inven-

tory cost would increase, or by increasina lambda the

inventory cost would decrease. This budaet control function

was discrete. The actual inventory cost could vary from the

target budget by as much as the cost of a single part.

The RIMAIR algorithm was included within the TIGER

program as a separate subroutine. First, RIMAIR inventory

levels are computed in the subroutine and second, TIGER

simulates aircraft flights with these RIMAIR stocks as

input. Lambda values are included in the input data file,

external to the TIGER program. Lambda values are changed

and new budget levels are then examined to see if they meet

the target budget.

The RIMAIR and ASO models share some of the same weak-

nesses because they are based on the same underlying assump-

tions. The problem that the ASO model encountered with TAT,

discussed in III.C, is also present in RIMAIR. This points*Iout that there are problems in the inventory decision process

that exist above the model level. In this case, it is with

the Navy process of data collection of TAT.

52

Another comparison can be made between the two models

as far as workload required to support it. The RIMAIR model

j| increases the workload compared to the ASO model because

RIMAIR introduces two new parameters, the item essentiality

code and the lambda value. The problem with the essentiality

code, as mentioned above is how to assign it7 faulty coding

can result in unbalanced AVCALs. Time must be spent assigning

and updating these codes. Since the lambda value is assianed

external to the RIMAIR subroutine, time is spent checking

budget levels and resetting lambda values. One improvement

to the present algorithm would be to include a loop in the

* program that would change the lambda value depending on

proximity to target budget.

Both the ASO and RIMAIR models are retail level, single

echelon models. This means that they calculate AVCALs only

for the organizational level facility. Multi-echelon models

have been developed that spell out stock levels at organiza-

tional, intermediate and depot level facilities. The next

chapter will examine one of these multi-echelon models, ACIM,

that can also be used for the single-echelon case.

53

. °

V. ACIM MODEL


The Naval Sea Systems Command's Availability Inventory

Model (ACIM) was developed after the Chief of Naval

Operations directed that "a sophisticated availabil'ity-

based sparing technique be developed and applied on a

selected basis for equipments which require a level of

readiness above that which standard policies can provide

[Ref. 16]."

In response to this CNO direction, the Chief of Naval

Material issued NAVMATINST 3000.2. This instruction

established Operational Availability (A ) as the primary0

measure of material readiness for Navy weapons systems

and established policy for A analytical techniques.

Subsequently CHNAVMAT recommended, and CNO approved, a

standard availability centered optimization model for use

by all program managers in determining consumer level

stockage quantities for selected equipments. This ACIM

0model develops repair parts allowances to achieve a

specified A at the minimum possible inventory cost.

0

This thesis will investigate ACIM model version 2.0,

developed by CACI-Inc Federal and implemented by Henry J.

Watras for use on the NPS IBM 3033. This chapter will

describe the ACIM model as it applies to AVCAL determination

54

14

in this thesis. A more detailed analysis of this model can

be found in McDonnell [Ref. 17] and in the ACIM Handbook

*[Ref. 16].

The underlying assumptions of the ACIM model are

listed below.

1. Included parts are organized in terms of anequipment with topdown breakdown. Multiple units of apart within a given next higher assembly are representedonly once in the breakdown. However, if the same partappears in different locations in the structure, eachappearance is treated as a unique item in the operationof the model.

2. External demands upon supply are stationary andcompound-Poisson distributed.

3. All stockage locations use a continuous review,(S-l,S) ordering policy.

4. Mean times to repair are defined as constantswhich include all equipment repair related down timesthat are not supply related.

5. Component failures are independent.

6. No further demands for parts can occur when oneor more parts are in down status. That is, when a partfails the system does not operate again until the failedpart is replaced.

A top-down breakdown is one which starts with the

highest level unit, in this case the E-2C aircraft. The

next level down is the WRA level, which are the individual

parts discussed in this study. Below the WRA level is the

Shop Replaceable Assembly (SRA) level, the sub-SRA level,

and on down until the smallest diode or resistor has been

itemized. This multi-level approach is also called a

multi-identured approach. For this study only WRA level

55

. - - ,,

inventories will be computed although ACIM can compute

stocks down to the lowest level.

The ACIM definition of availability is the same as

that used in the TIGER simulation model; namely,

A UPTIMEo UPTIME + DOWNTIME

ACIM replaces uptime by MTBF and downtime by Mean

Time To Repair (MTTR) plus Mean Supply Response Time

(MSRT). So, A° can be reexpressed as:

A =MTBF

o MTBF + MTTR + MSRT

The MTTR and MTBF parameters are inputs to the ACIM

model. The MSRT factor depends on the stockage levels and

ACIM uses this dependency to achieve a target value of A0

ACIM actually attempts to minimize MSRT in order to

maximize A0


1. ACIM Solution Equations

The model is defined recursively by considering an

arbitrary item in the system and an arbitrary facility.

The system is the aircraft, and the items are the individual

parts (WRAs). The structure of the model is civen by the

following set of definitions and equations:

a. Let i be an arbitrary item in equipment e (whichmay be e itself). Let u 0 represent an arbitrary facilityin the support system.

56

b. M. = DEL + RiU IU iu'

M. = mean time to return a failed item i atM. location u to a serviceable condition7

DEL. = expected delay per demand for item i

at location u, experienced in the

repair and requisition pipelines-

R. = mean time to repair item i at userlU location u (for on-equipment repair)7

= 0 if location u does not operate theequipment.

1C. DEL. = (X-S i ) * p(X; Y * T iu)iu X> S .u

where S. = stock level of item i at location7S lU

Y. = expected number of demands upon inventorylU for item i at location u;

p(X; Y iu*T ) = probability of X units of stock reductionfor item i at location u; the distribution

may be Poisson, Normal or Negative Bino-mial, depending on the mean and varianceof the part;

T. = mean resupply time (time to replace aniu inventory loss) for item i at location u.

d. T = P iu(Liu + L' iu) + (1-P.u) * (Riu + R' iu),

where Piu = probability that a demand for item iupon inventory at location u results ina loss (discard or sent elsewhere forrepair) which must be replaced throughresupply;

Lu = average resupply lead time assuminq stockis available at the resupply source;

L'iu = additional resupply lead time due toexpected shortages at the resupplysource;

57

+ . , . , . .,.

R : average shop repair cycle time assumingiu availability of spares for items within

i at the next lower indenture level;

R'iu= additional shop repair cycle time due toexpected shortages of srares for itemswithin i at the next lower indenturelevel.

The values of Liu, R iu' T iu' and Yiu are inputs to the

model.

D iv for u = 0

e. L

D io for u = 1,2,...,U,

where v is the resupply source for location 0 and v=0 if

the location 0 has no resupply source.

f. R' . Y. M U/ Y YjjCi ]l j C U u

where j identifies items within i at the next lowerindenture level; j = 0 if i has no subordinate parts.

g. A =/(i + Y *M ) ,eu eu eu

where A fraction of time equipment e is available foreu

use at location u (defined only for locations u whichoperate the equipment).

2. Objective Function

The overall objective of ACIM is to determine

stockages levels for all items and all stockage facilities so

that the expected operational availability of the equipment

is maximized for a given inventory budget or, conversely, to

find levels which achieve a given operational availability

at least cost. This objective can be explicitly stated as

follows:

Find values for Sk for all items k and locations v in the

58

support system which minimize DEL = DELeu for all user

locations u subject to:

SckSk < B,

k,v

where ck = unit cost of item k7

B = given budget for spares procurement.

A similar statement can be written for the converse

objective of achieving a given value for A at least cost.eu

The ACIM solution to the problem defined above is S

found by a recursive procedure based upon equations b-g.

First, however, a subproblem is defined and a solution

procedure is given for the subproblem. A recursive appli- 0

cation of the subproblem is then used to solve the original

problem.

The subproblem is set up as follows. Substituting

equation d in c, the expected delay per demand is given by

DEL. i DEL (S iv L iv, R'iDiv ,v ,v i

where the stock level S iv, additional resupply time L'iv,

and additional repair cycle time, R' iv, are considered as

decision variables for an arbitrary item ice and arbitrary

location v in the support system. Suppose that values for

Si are given for all items and locations v. The subproblem

is to find a particular item and location such that a one

unit increase in its stock level will yield the laraest

decrease in DELeu per dollar investment for some user

location u.-0

59

. . . .. .• . ........................° .......... . x' ............. ...............'. ' . °. ..,° '. '. . " , /..'.,-.% '-o'° _ . . . . - . . .," ' ' . _ . . _ . .

II

The solution of this subproblem is based upon a

recognition that the family of functions D. are hierarchi-iv

cally related (by equations e and f), each is a function of

three decision variables, and functions at the bottom of

the hierarchy depend only upon the stock levels, S.

Therefore, a marginal analysis solution procedure

can be applied as follows:

Define

As Div = D(Siv, L', R'iv) - D(Siv + 1, L'iv, R'iv

AL iv' i S iv * I R' iv

A =D (S L' R )-D(S L'i RR iv iv' iv iv iv

where

L' iv* least value of L'iv obtainable by a unit increase

increase in stock of some part wEi at the supply

source for v;

R iv least value of R' iv obtainable by a unit increase

in stock of some part rei at location v.

Letting w* represent the part which satisfies L iv* and r iv

the part which satisfies R' *v, find the largest ofIV

(a) As D iv/c , (b) ALD iv/C , and (c) ARDiv/Cr

and let

Div* = D(Siv + 1, L' iv, R'iv

06

= D(Siv, L'. *, R'.)iv iv .

( Liv Riv

according to which of (a), (b), or (c) is largest,

respectively.

60

""' " " ' "'-"" ' -~~~.. .. .. .. .. . .. .. .. .. .. ...-{-, ,,, . . ...- '...: .. , . ... .-..-.....--.---..-.

With the above definitions and using equations b, e, and f,

a recursion is aiven by:

L'. * = D. * (z = supply source for v);iv iz

' Y M + Y. M* v Y,.Jviv* ji ]vjV ]v jv j i ]v [

KM. D* RJV jv jv

where j identifies parts within i at the next lower

identure, and j' = r* or contains r* as a lower level

part. The recursion is initiated for items i and the

location v where L'i and R' are both zero and hence

D i* D(Siv + 1).

Justification that this procedure solves the sub-

problem follows from convexity properties of the functions

D . The solution to the original problem is given by

repeated application of the subproblem.

If the solution to the subproblem results in the

availability target or budget target being met or exceeded,

the original problem is solved. Otherwise a new subproblem

is solved to find the next item which will result in the

largest decrease in DEL per dollar investment. This process

continues to build up the stockage levels until one of the

two targets has been achieved.

Unlike the RIMAIR and ASO models, which were sub-

routines of TIGER, ACIM was run as a separate program using

batch processing. The ACIM program is made up of three

61

>-~........-< . .-•................< -F>> . - ..- •....-• .. . " .•. .. .. . .•

subprograms that operate in sequence. The first program

(Preprocessor) calculates stockage levels according to

designated comparison policies. The second (Main) program

of the model calculates levels according to ACIM. Stockage

levels calculated by the first and second programs are

passed to the third program (Postprocessor) which produces

three output reports: a cost-effectiveness report, a levels

by items summary, and a statistical summary report.

3. Input Data

Input data for ACIM is organized in the following

three data sets:

Systems Factors

Format A - Options and Default ValuesFormat L - Site data

Item Data - Format I

One other data set can be used as an option, the

Additional Item Data set, which further defines individual

parts with respect to MSRT and repair cycle times, and also

provides for user inserted site provisioning stocks at up to

ten sites. Data elements for each of the three data sets

along with an example of each record are provided on the

following pages.

Format A - Options and Default Values. There is one record

in this format. Figure 5.1 shows the Format A data elements

along with a sample record. Data elements are defined as . - -

follows:

62

S

Format A - Option and Default Value Data Elements

COLS DATA ELEMENT UNITS

1 Format Identification (A)3-16 Run identification

18-27 Run options28-31 Equipment MTTR Days32-35 Availability target Fraction37-43 Investment target $000

C-E Report Controls45-47 Units48-51 Availability Fraction52-56 Investment58-59 Part number field size

User MSRT62-65 Navy Days66-69 DLA Days70-73 Depot procurement leadtime Days74-76 Depot repair cycle Days77-80 Scrap rate Fraction

Format A Record Example

1 A E2C .083.999 42000000000011111111112222222222333333333344441234567890123456789012345678901234567890123

1 17.517.5 360 83 .1044444455555555556666666666777777777784567890123456789012345678901234567890

Figure 5.1. Format A Data Elements and Record Example.

63

. . .....

Format Identification. An "A" is inserted in the

first column to identify this data as format A.

Run Identification. Text entered in this field is

printed at the top of all output reports to identify the

particular run of the model.

Options. Entries in these fields control various

features or operations of the model. Currently, the first

four of the ten option fields are defined as follows:

a. MEC input type.

b. MEC use.

c. Default MSRT.

d. Levels format.

Equipment MTTR. Enter MTTR in days. This is the time

required to -ccomplish the repair assuming all required

repair parts are immediately available.

A Target. Enter the operational availability target

as a fraction (including the decimal point). The model

will build up stockages until this target or the investment

target is reached. Enter .99 if reachina the investment

target first is desired.

Investment Target. Enter the investment target, in

thousands of dollars, in this field. Enter a larce number

(e.g., "9' in all columns) if reachina the A taroet first

is desired.

Cost Effectiveness. These fields are used to control

the production of the Cost-Effectiveness Report. As a unit

64

• -

.........................................................

is added to stock, a line of data may appear on the

Cost-Effectiveness Report if any one of the conditions

based upon the following data occurs:

a. Delta Units. A line of data is produced for

every nth unit added to stock, where n is specified in this

field. e

b. Delta A . A line of data is produced whenever

the achieved A exceeds an integral multiple of this value.

c. Delta $. A line of data is produced whenever S

the achieved investment first exceeds an integral multiple

of this value.

Part Number Field Size. In the Part Number/Nomenclature 6

field of the Item Data Records, the left-hand side is used

for Part Number and right-hand side is used for Nomenclature.

The number of positions used for the Part Number is speci-

fied in this field.

Response Times. The average length of time, in days,

required for a user of the equipment to obtain resupply from

a higher supply source. One entry is for Navy COG items and

one for DLA COG items. CNO current policy is to enter a

value of 17.5 days for both items.

Depot PLT. A default value for depot procurement lead

time (total time required to procure material from a

manufacturer) is entered here, in days. This value is used

whenever the PLT field in the Additional Item Data file is

left blank.

65

<.. < , . -... .< . .- ..%. o. o < <. ...> . < . . . < . ..< <.< %< <i. > < .L~ .i < .< < ..-S

Depot Repair Cycle. A default value for the depot

repair cycle, in days, is entered in this field. This

value is used whenever the depot repair cycle field in the

Additional Item Data file is left blank.

Scrap Rate. A standard scrap rate is entered in this

field as a fraction (e.g., 0.05). This is used as a

default whenever the corresponding field in the Additional

Item Data file is left blank.

Format L - Site Data. There is one record in the 'L" format

for each different kind of user or higher level maintenance/

supply activity in the support system for the equipment.

Figure 5.2 shows the Format L data elements along with a

sample record. In this study only one level is examined,I

and so only one Format L Record is entered.

Identification. An "L" is entered in column 1 to

identify this format.

Site Name. Enter any text that identifies the site.

Indenture Level. Enter 1 for a single echelon case.

Echelon Code. Enter 0 for organization site.

Stockage Facility. Enter any mark if the site maintains

inventory levels. For this study the carrier maintains

inventory.

Repair Facility. Enter any mark if the site performs

maintenance. For this study the carrier AIMD performs it.

66

Format L - Site Data Elements

COLS DATA ELEMENT UNITS

1 Format Identification (L)3-16 Site Name

18 Indenture Level20 Echelon Code22 Stockage facility24 Repair facility

26-29 Lead time Days31-34 Repair Cycle Days36-38 No. of locations40-42 No. of equipments44-45 Comparison policy47-48 ACIM Policy50-54 Availability target Fraction56-69 Operating factor Fraction

61 Levels output format

Format L Rcord Example

L CVN 1 0 X 100000000011111111112222222222333333333341234567890123456789012345678901234567890

1 2 044444444455555555556666666666777777777781234567890123456789012345678901234567890

Figure 5.2. Format L Data Elements and Record Example.

67

0_

Lead Time. The average length of time required, in

days, for this site to obtain resupply from a higher supply

source assuming that supplies are immediately available at

the supply source. Enter 17.5 days.

Repair Cycle. Enter the average repair cycle, in days,

for items that are normally repaired at this site.

Number of Locations. Enter the number of different users

at this site (one for this study).

Comparison Policy. Not Applicable.

ACIM Policy. Code '0" for Optimization (ACIM starts

all stocks at zero).

Operating Factor. Leave blank.

Levels Output Format. Leave blank.

Format I - Item Data. There is one record of this format

in the Item Data file for each item in the equipment parts

breakdown. The first record must always represent the

equipment as a whole. Figure 5.3 shows the Format I data

elements along with a sample record. The data elements are

defined as follows:

Identification. Enter an "I" to identify this format.

Reference Number. The entry in this field is used to

identify the item and its position in the parts breakdown

of the equipment. Optional entry.

Indenture. The first record, representing the equipment

as a whole, must have an Indenture Code of 1. All candidates

68

m ., .-..-. -.- , " -,' . . .... " , .. ..' . .. ....,. .'. ..... . .. .. , ' .... ... ..... ....-.. -.,.. , .-. .. ... ..

Format I - Item Data Elements

COLS DATA ELEMENTS UNITS

1 Format identification (I)2-11 Reference number

12 Indenture14-42 Part number/nomenclature43-44 Cognizance45-50 Number per next higher assy $/cents60-64 SMR&R codes65-71 Best Replacement factor per year

bE 72-75 Minimum Replacement unit76 Military essentiality code77 Override code78 Override amount

Format I Record Example

1 1072 HF POWER AMP000000000111111111122222222223333333333123456789012345678901234567890123456789

IR 6 3494000 OG 8.4050 114444444444555555555566666666667777777777801234567890123456789012345678901234567890

Figure 5.3. Format I Data Elements and Record Example.

69

0 "• • . .. . .. • ...

iI

after the first should be assigned a code of 2.

Part Number. Enter the NIIN/NICN or other part or

stock number for item identification purposes. Part

number field size is defined in Format A. The rest of the

field entries are for Nomenclature.

Nomenclature. Enter textual data that identifies or

describes the item.

Cognizance Code. Enter a code identifying the manage-

ment cognizance of the item.

Number Per Next Higher Assembly. Enter the number of

units of the item in the equipment.

Unit Cost. Enter the estimated unit procurement cost

of the item in dollars and cents. There is an implied

decimal point between columns 57 and 58 (cents occupy

columns 58-59).

SM&R Codes. The Source, Maintenance and Recoverability

codes are given. Entries for the maintenance codes are

mandatory, others are optional.

Application Replacement Factor. Enter the actual

anticipated number of times that the item will be replaced

during one year of operation. This value represents an

average over all items (of this type) in the system.

Minimum Replacement Unit (MRU). Enter a value for

the MRU if different than 1. For this study 1 was used.

Military Essentiality Code (MEC). Enter a 1.

70

o .- , . ° . .

Override Code. The only override code used was Y,

which was assigned to indenture level 1 equipment (total

system). This code includes the item in all model processes

but a zero stock level is assigned.

Override Quantity. Not applicable.


The ACIM model is the most flexible model of the three

inventory models discussed so far. ACIM's flexibility lies

in its ability to solve either of the following problems for

multi-echelon or single echelon supply systems:

1. Select a minimum cost collection of spares for a

system so that the system will achieve a given availability

target.

2. For a given budget select a'collection of spares

that will produce maximum availability for the system.

For this study ACIM was usually operated with a budget

constraint. This was primarily due to the fact that the

RIMAIR algorithm provided for control of the budget only.

Therefore, the two models were compared on a equal budget

basis. After running ACIM at a specific budget level the

resulting inventory levels are manually input into the

input data file for the TIGER simulation model.

ACIM, like the other two models, is a steady-state

model. This means that the model operates on the assump-

tion that all flows through the repair and requisition

71

pipelines have stabilized. The inventory system is

assumed to be operating at a constant rate over a long

period of time. This means that the model cannot be used

to investiaate surge demand periods.

This model does have a few computational approximations

that should be noted. The first concerns ACIM's approxima-

tion of availability. ACIM assumes that no failures can

occur after the first failure occurs. In actual aircraft

systems, a single part failure will usually only degrade

the system performance rather than cause the entire system

to shut down. Parts usually continue to operate and con-

tinue to experience failures after one part fails. In

addition, the process of minimizing MSRT does not yield the

same stockage decisions as maximizing availability. For

some systems the results may be similar, but for other

systems there may be large differences.

Another peculiarity of the model is that it assumes that

the yearly operating tempo input for a system represents

operating tempo per "available year". For example, if an

aircraft is scheduled for 1000 flight hours per year and 50%

availability target is assigned, ACIM tacitly assumes it

flies 500 hours per year.

When using the ACIM model to match a target budget (or

availability), the iterative process only approximates the

target goal. The ACIM algorithm will always exceed the

target because it adds an item to the inventory until the

72

target is reached. Due to the discrete nature of the

problem, the budget goal may be exceeded by an amount almost

equal to the least expensive part7 and that may be significant.

The ACIM model does present a sianificant increase in the

workload required for data input. The exact topdown break-

down of parts, parts parameters, and maintenance facility

information is required. Nevertheless, ACIM appears to be a

useful tool and can be expanded to encompass many repair

facilities at different levels, handling inventory problems

of very complex systems.

7373 .

.....................................................................

VI. TEST RESULTS

A. INTRODUCTION

This chapter presents TIGER simulation results evaluating

availability performance using inventory levels generated by

the three models. The parts used for this evaluation were

arranged in two systems which had identical part lists but

which had different configurations.

The three inventory models were examined in three

scenarios. The three topics to be covered are:

Fixed Budget. Achieved AVCAL availability is

compared among the three inventory models, using a fixed

budget constraint for each model.

Variable Budget. Availability is compared between

the RIMAIR and ACIM models, while varying the budget over a

range of values.

Variable MSRT. The ACIM model availability is

analyzed with a variable MSRT parameter.

For each of the three tests it was assumed that spares

decisions would be made for three identical aircraft

systems. Availability would be computed for a period of

ninety days, with each aircraft flyina a total of 540 hours

during the period. Each day was divided into the following

four phases: a 3 hour flight phase, a 9 hour repair phase,

a 3 hour flight phase, and a 9 hour repair phase. Aircraft

74 4

operated simultaneously during the flight phase, and were

repaired simultaneously during the repair phase. This was

considered an artificiality that was forced on the author

by the nature of the TIGER simulation program (more

realistic simulation would allow the aircraft to fly at

different times during the day). For each test run, 25

iterations were done.

The system was composed of eight different part types

with a total of fourteen individual parts. The size of the

system and the number of aircraft used were limited by the

TIGER program and by computer time limitations. Table III

lists the part parameters according to part type.

TABLE III

Part Parameters

Part Type Unit Cost 4 Per A/C BCM Rate MTBF

1 34940 2 0.103 2572 13670 2 0.180 3523 10550 1 0.105 6584 21930 1 0.247 6675 37500 3 0.112 2726 3520 1 0.238 6997 38850 1 0.118 1968 5060 3 0.258 1124

Note: BCM Rate is fraction of repairs that result inBCM action. MSRT in days.

75..................................................

Aircraft parts were arranged in two different

configurations, corresponding to system configurations

defined in OPNAVINST 5442.4H. The first configuration

places the parts in series, corresponding to aircraft

mission Code C, Full Fleet Defense. As defined in this

mission, all WRA's are required to be in an operational

(up) status for the aircraft to be capable of performing

its mission. The second configuration corresponds to

aircraft mission Code D, Expanded AAW Control. Here the

requirements for WRA operational availability are more

complex than the series layout. Basically there is some

redundancy built into the second system, referred to as

the parallel system, shown in Figure 6.1.

System Configuration (By Part Type) for Mission Code D

Figure 6.1. System Configuration (Mission Code D).

Aircraft parts were chosen from part candidates in the

E-2C aircraft under the following criteria:

76

.. .' . - -i i . . i .' 'il ' i . - i' ' - i- " -: . 2- " -. i . .. - , . .: .- - .- .i . i i- -~ i , 2 .i - . " -. - . , , . - .'.12 •2 .,.. .. ,- . " .. ' ." - . .. ' . . "• . ,

* Each part comprised an individual WRA.

* Each part was listed on the E-2C Mission Essential

Subsystem Matrices (MESM).

* Most parts had low MTBFs.

* Each part was coded for removal at the 0 level and

repair at the I level.

B. FIXED BUDGET ANALYSIS

The object of this portion of the study was to examine

the effectiveness of the individual inventory models when

all three models were constrained to the same budget level.

The variable inputs to the TIGER program were the different

AVCAL levels computed by each inventory model. Using TIGER

generated aircraft availability, the capabilities and

weaknesses of each model algorithm were examined. Both the

series and parallel system configurations were used with

each of the three inventory models.

A serious attempt was made to ensure that the three

models were compared on an equal basis. This proved to be

a difficult problem because of the differences among the

models. The major difficulty was trying to equate the part

parameters across the three models. The RIMAIR and ASO

models are very similar so the parameters were matched for

these two models first. Both models are subroutines of the

TIGER program, and both use the same data input file. The

ACIM model parameters were then matched to the ASO/RIMAIR

parameters.

77

.,. - .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .., " .: _ -" -- " -_ .'-'_.'- _''.%_-" " . - -" "". . '_ " '-',

Since the ACIM model recommended using a benchmark

value of 17.5 days for MSRT, this value was converted to

hours (420) and used for both the Order and Shipping Time

and the Repair Time in the RIMAIR/ASO models (SRTIM and

REPTIM variables in TIGER). ACIM does not utilize these

separate pipeline times, but only considers a single supply

delay time (MSRT). A Mean Time to Repair equal to 0.083

days was input for ACIM, and the equivalent (2.0 hours) was

input to TIGER. All other parameters were as listed in

Table III.

The next step was to generate AVCAL stock levels for all

three models at a fixed budget level. This was accomplished

by first using the ASO algorithm to arrive at a benchmark

budget level. Using the parameters discussed above, the

total ASO inventory cost was $673,280. Next the RIMAIR model

was run, varying the lambda value to arrive at a total inven-

tory cost that was close to the ASO budget. The total RIMAIR

inventory cost was $668,700 (within 1% of ASO budget). The

ACIM target budget was set to a value equal to that of the

ASO budget, and the ACIM model arrived at a total inventory

cost of $675,300.

The resulting availability figures for both system con-

figurations are summarized in Table IV. The effectiveness

of both the RIMAIR and ACIM models appears to be better than

that of the ASO model. ACIM seems to perform better in the

78

. ,*". --.. =

S

series system than RIMAIR, with both about equal in the

parallel system.

TABLE IV

Fixed Budget Summary

No. of Parts Stocked by Type

Model Budget 1 2 3 4 5 6 7 8

ASO $673,280 5 5 1 1 7 1 3 3 SRIMAIR $668,700 4 5 2 3 5 3 4 4ACIM $675,300 5 5 2 2 6 3 3 3

Model Availability 0

Series ParallelModel AVA AVMUP AVA AVMUP

ASO 0.5643 0.5304 0.6963" 0.6788RIMAIR 0.6358 0.5950 0.8562 0.8348ACIM 0.7611 0.7129 0.8312 0.8120

The poor performance of the ASO model in comparison to

the other two models can be explained by examining the

inventory decisions made by the ASO algorithm. First, the

critical parts of the series system are found by examining

the Critical Equipments list on the ASO model TIGER output.

The results of this list are summarized along with a part

budget breakdown in Table V. The two most obvious oversichts

are denoted by the starred rows. ASO spent only 2.09% of the

79

. . . . . . . . . .. . . . . . . . . . . . .

total budget on part types 43 and =6. Yet these two part

types together accounted for 37.08% of the total unavaila-

bility of the system. The ASO model failed to observe that

these two lower priced, high MTBF WRAs were availability

bargains compared to the more expensive, low MTBF WRAs,

such as part type 45.

TABLE V

Critical Equipments Analysis of the ASO Model

Part Part P Stocked/ Part Contribution ToType Cost % Total Budget System Unavailability

3 $10550 1 / 1.57% 21.48% *7 $38850 3 /17.31% 15.98%6 $ 3520 1 / 0.52% 15.60% *1 $34940 5 /25.95% 15.25%5 $37500 7 /38.99% 13.52%4 $21930 1 / 3.26% 11.39%2 $13670 5 /10.15% 5.76%8 $ 5060 3 / 2.25% 1.02%

Further analysis of the individual ASO stock levels

shows that part types #3, #4, and 46 were stocked to a level

of only one unit. These three parts qualified for a single

spare each under the rotatable pool criteria, but none of the

parts qualified for a spare under the attrition allowance

portion of the AVCAL. This minimum stock level for these

three parts was the major contributor to the poor performance

of the ASO model. The ASO model failed to include unit cost

80

or cost effectiveness tradeoff analysis in computing stock

levels, instead inventory levels were decided totally on the

basis of MTBF and TAT.

For each case studied, the computed measure of availa-

bility, AVA, was several percentage points higher than

AVMUP. As noted in Chapter II, AVMUP measures only the

availability of the system during flight hours. AVMUP does

not consider the operational status of the system during the

repair (ondeck) phase. For the next two topics, AVMUP will

be used as the primary measure of effectiveness.

C. VARIABLE BUDGET ANALYSIS

In the previous section each AVCAL model was studied at

a single specified budget level. A more important question

concerns the performance of these models over a range of

budget levels. With an increase or decrease in budget level,

the decision maker must adjust AVCAL levels accordingly. The

ASO model was not included in this analysis since it does not

lend itself easily to a variable budget analysis and because

the ASO Manual does not provide any guidance for adjusting

levels. It was also decided that the lack of any cost

effectiveness measures in the ASO algorithm would cause the

model to perform poorly at all budget levels.

With only the RIMAIR and ACIM models to compare, the test

was arranged as follows. Part parameters remained as depicted

in Table III, and mission times also remained the same.

81

0 - -,. - . '- - '- - - '' - ' T' ' °' -'i ' ' , '-' " '-". "] [ - • _ ". ' ' '' ' ' ' ' ' ' " " . . -

Budget levels were varied from the benchmark budget used

in VI.B above. Using the benchmark budget of $668,700 as

100%, test budgets were varied from a low of $521,810 (63%)

to a high of $797,370 (119%). As before, the RIMAIR model

was run first, varying the lambda value to arrive at an

appropriate budget level. Using the resulting RIMAIR budget

as a target budget, ACIM was then run. Inventory levels

computed at each budget level are summarized in Table VI.

Using these inventory levels, model effectiveness was

studied using both the series and parallel systems. Table

VII summarizes system availability (AVMUP) for both models

over the range of budgets. Budget percentages listed are

those from the RIMAIR case. The average difference between

the RIMAIR budget and the ACIM budget was 0.63%, with a

maximum difference of 1.11%.

The results of this test were that both inventory models

achieved similar operational availability. At lower level

budgets the RIMAIR model did somewhat better than the ACIM

model. Starting at about 80% of the benchmark budget level,

ACIM performed equally well, and sometimes better. ACIM

performed much better than RIMAIR at the 100% level for the

series system. Considering the variability of the TIGER

outputs, no model could be considered superior for all budget

levels.

82

•- . ' . . .. ....... . .. .. . ... ~ · .. ·;., ·." ...... ' ..... . .. . . ·. ' .... . . · ... ·.·~·.: ·:..:-:-:· . ., .

- . - . . . .

. ' . ''

. .. .. . . " ... •, .. . ' .. .. .. .. . . ..... . .. . "' ........ . .. .... ... ~ ..... ·~---~ ~ .. -.~.~-'111 .... . '· ... .. ~ ... '!. ~ " ·-

TABLE VI

AVCAL Stock Levels For Variable Budget

RIMAIR Model

Total Cost % Benchmark Stock Level By Part TypeAVCAL Budget 1 2 3 4 6 6 7 8

$423,210 63.29 % 3 3 2 2 3 2 2 3$521,810 78.03 % 3 4 2 2 4 3 3 4$578,680 86.54 % 4 4 2 3 4 3 3 4$629,850 94.19 % 4 5 2 3 5 3 3 4

$708,700 105.98 % 5 5 2 3 5 3 4 5$759,870 113.63 % 5 6 2 3 6 3 4 5

$797,370 119.24 % 5 6 2 3 7 3 4 5

ACIM Model

Total Cost % Benchmark Stock Level By Part Type

AVCAL Budget 1 2 3 4 5 6 7 8

$423,170 63.28 % 3 3 1 1 4 2 2 2$524,890 78.49 % 4 4 2 1 5 2 2 3$585,670 87.58% 4 4 2 2 5 2 3 3$626,690 93.72 % 4 4 2 *2 6 3 3 3$714,150 106.80 % 5 5 2 2 6 3 4 3$767,260 114.74 % 5 5 3 2 7 3 4 4$802,200 119.96 % 6 5 3 2 7 3 4 4

D. VARIABLE MSRT ANALYSIS

For this portion of the study, the MSRT input to the

ACIM model was varied in order to investigate the effect

* a variable resupply and repair time on the effectiveness

a fixed budget inventory model. This analysis did not

include the RIMAIR model because of the difficulties invo

83

TABLE VII

RIMAIR vs. ACIM Performance For Variable Budget

% Benchmark SERIES AVMUP PARALLEL AVMUPBUDGET RIMAIR ACIM RIMAIR ACIM

63.29 % 0.3657 0.2960 0.6334 0.515278.03 % 0.4519 0.4461 0.7678 0.569686.54 % 0.5391 0.5579 0.7591 C.794194.19 % 0.6089 0.6029 0.8378 0.7867

100.00 % 0.5950 0.7129 0.8348 0.8120105.98 % 0.6821 0.7552 0.8678 0.8824113.63 % 0.7122 0.7733 0.8343 0.8850119.24 % 0.7964 0.7764 0.8813 0.8741

with keeping RIMAIR's budget constant while the supply

times were being varied. Each time the supply time was

changed in the RIMAIR model, a new lambda value had to be

found to keep the inventory cost near the target budget.

This proved extremely difficult because of the sensitivity

of the lambda value to changes in supply time.

The methodology used for this test was as follows. The

MSRT input parameter in ACIM was varied from 12 to 41 days,

while maintaining a constant target budget of $544,000.

Inventory levels were computed and then run on the TIGER

program. TIGER parameters for repair and resupply times

were matched to the corresponding MSRTs used in the ACIM

program. Systemn availability was analyzed for the series

system only.

84

~~~~~.........................., .... ... ,• -.. . . ,•,.. .. . ...... .'

The ACIM Statistical Summary Report includes an achieved

operational availability figure that theoretically could be

achieved for a series system, given the inventory levels

selected. These availability predictions, along with

availabilities calculated from TIGER simulations, are - .

compared in Table VIII. Several items should be noted

regarding these results. ACIM projected availability is

overly optimistic for low MSRT values, and then under-

estimates availability for high MSRT values.

Nother noteworthy item was that the ACIM AVCAL stock

levels varied slightly depending on the MSRT. When MSRT

was increased, inventory levels for part types #4 and 47

decreased by one unit each, while part types #2 and 45

increased by 1 unit and 2 units respectively. The reason

for this change is not clear. Once again it was observed

that ACIM only approximates its target budget. As MSRT

increased, ACIM overshot its target by a greater margin.

Initially ACIM was within $4,000 of target, but this margin

jumped to $32,000 (6% over target) at the maximum MSRT value

of 41 days.

85

. . . .' .". .. . : .,. : ... -: . ... ' .. .. - ,. .- ., . . . . .. , . . . .\. . . .• . . .

TABLE VIII

ACIM Performance For Variable MSRT

MSRT ACIM Forecast TIGER AVCAL By Part Type(DAYS) Availability AVMUP 1 2 3 4 5 6" 7 8

12 0.7922 0.6821 4 4 2 2 4 2 3 317.5 0.607 0.5359 4 4 2 1 5 2 3 324 0.365 0.3422 4 4 2 1 5 2 3 330 0.224 0.2953 4 4 2 1 5 2 3 336 0.145 0.3086 4 4 2 1 6 2 2 341 0.112 0.2535 4 5 2 1 6 2 2 3

Note: ACIM Target Budget = $544,00012 Day MSRT Inventory Cost = $548,00041 Day MSRT Inventory Cost = $576,000

86

VII. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS

A. SUMMARY AND CONCLUSIONS

Three areas of study were covered in testing inventory

model effectiveness. The first area, fixed budget analysis,

showed dramatic differences in model effectiveness. Budget

allocation for the ASO model was much less efficient than

either the RIMAIR or ACIM models. The ASO model, unlike the

other two, made no attempt to determine optimum allocation of

monetary resources. The ASO model also has no provisions to

increase or decrease inventory levels according to budgetary

constraints, except by manual additions or deletions to

individual part stocks.

Examination of the Critical Equipments Summary of TIGER

was useful in discovering inventory model weaknesses. This

summary provides a list of parts that contribute to system

downtime. Parts are listed according to the percentage of

downtime that each part contributed. By matching these

downtime percentages against part budget allocation per-

centages, inventory decisions can be evaluated.

The second area of study examined the RIMAIR and ACIM

models in a variable budget analysis. Budget levels were

varied from 63% to 120% of a benchmark budget level. Results

of this test were inconclusive. Neither model showed complete

87

......................................................C :.. :.-. :: : ::: : ::: :: : :: ::::::::: t- -- -: . :-. :- .

superiority at all budget levels. Similarities were noted

in individual part stock levels of both models, resulting

in similar availability statistics.

The t:.ird area of study concentrated on what effects

varying MSRT had on ACIM effectiveness. Test results

generally agreed with inventory theory. Availability

decreased as MSRT was increased from 12 to 41 days. ACIM

calculated availability differed from that derived in the

TIGER simulation. Also noteworthy was the change in individual

part stock levels as MSRT was increased. With a fixed target

budget, ACIM had different part priorities depending on the

length of MSRT.

This thesis investigated inventory model effectiveness

as measured by aircraft system operational availability

(AVMUP). One advantage to the use of AVMUP was that it

allowed for simulated operation of aircraft systems in a

degraded mode. That is, if one WRA failed the rest of the

system WRAs continued to operate even if the system was in

a down status. For complex aircraft systems the assumption

of independent failures may not be a completely correct one,

but it allows for simpler calculations.

Some of the advantages and disadvantages of each of the

three inventory models are summarized below:

ASO Model.

Advantages.

88

- . . * . . * . . * . . . . - . . . .. . . .

1. Easy input data preparation.

2. Simple algorithm to determine stock levels (included

as subroutine in TIGER).

Disadvantages.

1. Does not optimize budget allocation.

2. No provision for increasing or decreasing inventory

levels to match budget constraints.

3. Separates pipeline demand into two parts. Low failure

rate items may not qualify under either separate criteria.

RIMAIR Model.

Advantages.

1. Inventory levels can be varied to match budget constraints.

2. Provides protection for more portions of the inventory

pipeline system than the ASO model.

3. Essentiality code allows for weighting of parts

according to their relative criticality.

Disadvantages.

1. Lengthy process involved in changing lambda values to

meet budget target when more than one model parameter is

varied.

2. Model inherits weaknesses of ASO model because of

identical model assumptions.

3. Without a comprehensive essentiality coding scheme, the

optimization process only maximizes gross supply effectiveness.

This process does not necessarily result in maximumI

availability.

89

-oI ."

S

ACIM Model.

Advantages.

1. Powerful model which has the capability to compute

multi-echelon inventories for multi-indentured systems.

2. Stock levels can be determined for an availability

target or a budget target. S

3. Attempts to conform to recent CNO directives concerning

inventory policies, especially maximizing availability.

Disadvantages.

1. Complicated algorithm is used to determine inventory

stock levels.

2. Does not differentiate between repair and requisition

pieplines.

3. Assumes that failure of one part results in shutdown of

all other parts in system.

4. Optimization process only approximates maximization of

availability by minimizing MSRT.

B. RECOMMENDATIONS

The TIGER model proved to be a capable evaluation tool,

although it did have several limitations. Aircraft systems

had to be simulated as if they were operated simultaneously.

A more realistic simulation would allow for the overlapping

of operating cycles. Sort routines in the TIGER TTE sub-

routine are not efficient and need to be improved. There

are many TIGER calculations repeated every mission which are

90

. - . . .... . . . . . *.*.*

not always applicable, but there is no easy method to

eliminate these unnecessary steps. Input data preparation

for TIGER can be tedious, especially for system configura-

tion cards of complex systems.

Integration of the ASO and RIMAIR AVCAL inventory models

into the TICER model allowed for automatic AVCAL determination

and simulation. Changes need to be included in the RIMAIR

program to permit automatic adjustment of inventory levels to

meet budget constraints. Manual adjustments of the lambda

value to control budget levels was a slow process that

prevented broader testing of the RIMAIR model.

Comparison of inventory model effectiveness must be done

with some reservations. All three models assume steady-state

inventory flows. The simulations were done in a manner to

accommodate these assumptions. Different results may occur

if surge demands or cyclic patterns are introduced into the

simulation.

Another reservation involves the limited number of system

configurations used in this study. None of the three inven-

tory models take into account the configuration of the

system. Additional research needs to be done to determine

what effects alternate system configurations have on model

inventory decisions. More study also needs to be done on

the utilization of the item essentiality code parameters of

the ACIM and RIMAIR models.

91

1.

APPENDIX A

TIGER DATA CARD FORMATS

The following card formats were utilized in this study.

Most card remain unchanged from the TIGER Manual, but some

new cards are presented. Sample input data files are

presented in appendices B and C. All data is entered in 80

column, card/card-image format. Data types are real, integer,

and alphanumeric. All integer data fields must be right

justified. Variable names listed are those that appear in

this version of TIGER.

92

" -" " "' . . . . ". . . i .. . . .

1. RIMAIR Parameter Card

New Card. Provides parameters for RIMAIR model algorithm.Budget parameter was not used. Essentiality code (ESS) was

set to 1.0. Resupply delay time (RET) set to 0.

Columns Format Variable Description

1-4 14 NTOTA Total no. of part types per A/C

5-8 F4.0 XFLAG Used to select inventory policy:0.0-Manual input of stock levels1.0-ASO MANUAL policy2.0-RIMAIR Policy

9-16 F8.0 BUDGET Maximum budget constraint

17-31 F15.12 EL Lagrange multiplier

32-36 F5.3 ESS Essentiality code

37-42 F6.0 RET Resupply delay time

2. Part Parameter Card.

New Card. One card is entered for each type equipment, I.


1-8 F8.2 COST(I) Equipment unit cost.

9-16 F8.0 SRTIM(I) Off-ship order & shipping time

17-21 I4 NPET(I) No. of parts of type I per A/C

22-30 F8.4 BCM(I) Fraction of parts BCM'ed

3. Flight Hours Data Card.

JTIME is the total time in a 90 day period that an A/C is

expected to fly.

Columns Format Variable Escription

1-8 18 JTIME Total flight times, summed overa 90 day period.

93

. .. .. .

"'""'--: - , - _ : - < "' "'' -' " . .-. . '"". ' = - -. ._ .. : ",- - . ,z = .°- - '_ " ' i i'. ... , . i-h f .

4. Timeline Iteration Card.


1-4 14 JCC No. of timeline iterationsto be run for the datadeck.

5-80 19A4 RUNID Alphanumeric run identifier.

5. Statistical Parameter Card.

To run a predetermined # of missions, set NOPT & NMAX equal

to the no. of missions, and PL = 1.0. A value of XK = 1.28

corresponds to 90% lower confidence limit.


1-4 14 NMAX Max no. of missions to be

* run (may not exceed 1000)

5-8 14 NOPT Optimal no. of missions tobe run (may not exceed MAX)

9-12 F4.0 PL Reliability spec. required

13-16 F4.0 XK Std.Dev. for lower conf.limit

17-20 14 ISEED Random number seed

21-24 14 NPH No. of phase types (max of6)

9

94

6. Phase Type and Duration Cards.

This card specifies the type of phase and duration of eachphase. A phase is time period with both a repair policy anda system operation policy. Two phase types were used: type1, flight phase; and type 2, ondeck repair phase. One cardcorresponds to a 24-hour period. Duration is in hours.System is presently configured for four phases per day.


1-2 F2.0 XXT(l) Phase type no. of first phase

3-8 F6.0 XXT(2) Duratioi. of first phase

9-10 F2.0 XXT(3) Phase type no. of secondphase

11-16 F6.0 XXT(4) Duration of second phase

17-18 F2.0 XXT(5) Phase type no. of third,* phase

19-24 F6.0 XXT(6) Duration of third phase

25-26 F2.0 XXT(7) Phase type no. of fourthphase

27-32 F6.0 XXT(8) Duration of fourth phase

*

*

95

-. - - -. a. -. - - ;" ... . . . . . . . -... -,_.____

7. Deployment Scenario Card.

This card determines the scenario under which a simulationcan be run. The default values will allow TIGER to simulatea mission under the same conditions under which theinventory models will calculate planned inventory levels.So if the ASO model, for example, plans for a 1000 flight-hour quarter with pipeline times equal to ten days, TIGERwill simulate a 90 day mission with these same parameters.By changing the default values on this card, inventorylevels will be calculated under parameters entered onprevious cards, but TIGER will simulate under conditionsdefined by this card. This permits investigation ofinventory policy during periods of abnormally high tempoflight operations or lengthened pipeline times. NDAYS canbe varied from 0-90 days. NWAR is a 2-state variable: 0means previous inventory parameters will be used, 1 meanswartime scenario and new parameters will be used. One ofthe new wartime parameters is BCMFAC, which increases theBCM rate for all parts. Another is REPFAC, which willincrease the on-ship repair time for all parts. NTIME willbe the higher system operational time for the war scenario,equal to the flight time expected for one A/C in 90 days.


1-4 14 NDAYS Length of scenario (0-90days)

5-8 14 NWAR Sets wartime scenario:0: original parameters

(no change)1: new values for SRTIM,

BCM & NTIME will becomputed

9-12 14 NOAC No. of A/C used in scenario

13-16 16 NTIME A/C flight hours in wartime

17-21 F5.1 BCMFAC Fractional change in BCMrate

22-26 F5.1 REPFAC Fractional change in on-shiprepair times during war

96

. " -° •. °. • •.° . • . .. .. . . . ..... . . . .... .. . .. . . ...... .... °o o D

r• • . ° .'.-.." °. . . . . . °. -•o°°,-. - . . - . o °. • - - .

VJ

8. Printout Option Card.


1-4 14 KOPT Printout option switch:1: management summary

printout2: engineering summary

printout3: complete details

printout (for debuggingonly)

4: disables input dataprintout

5: to specify printoutusing the KS variables(see below)

6: TIGER/MANNING completedetails printout

If KOPT=5, select from the following output options asneeded (otherwise leave the fields blank)

5-8 14 KS(l) = 1: Input data

9-12 14 KS(2) = 1: equip. downtime attime of missionfailure

13-16 14 KS(3) =1: downtime at end ofphase

17-20 14 KS(4) =1: abort messages

21-24 14 KS(5) =1: all events

25-28 14 KS(6) =1: ETIME matrix

29-32 I4 KS(7) =1: not used

33-36 14 KS(8) =1: not used

37-40 14 KS(9) =1: not used

41-44 14 KS(10) =1: system & subsystemstatus

45-48 14 KS(II) =1: TIGER/MANNINGdebugging

49-52 14 KS(12) =1: status of all groups

53-56 14 KS(13) =1: downtime messages

97

I . -

................................

9. Phase Repair Card.

This this study repair option 0 was used to simulate flightops and repair option 2 simulated A/C on deck under repair.


1-4 14 IFLAG(l) Repair option for each phasetype, up to 6:= 0 if onboard repair allowed

in the phase= 1 if no on-board repair

allowed in the phase= 2 on-board repair allowed

but failure inhibited

5-8 14 IFLAG(2)

9-12 14 IFLAG(3)

13-16 14 IFLAG(4)

17-20 14 IFLAG(5)

21-24 14 IFLAG(6)

10.. Repair Policy Card.

REPOL was set to 1.0. Normally it determines what fractionof repairs will be done on-ship. In this study thisfraction was determined by BCM(I) instead. TAD2 specifieshow long a system can operate in a down state before systemfailure. For this study mission allowable downtime = 0.XM and XT were set at their default values = 1.0.


1-4 F4.0 REPOL Decimal fraction of repairsto be performed aboard ship

5-12 F8.2 TAD2 Mission Allowable Downtime

13-16 F4.0 XM MTBF multiplier

17-20 F4.0 XT MTTR multiplier

98

"-: ". . . . .... ... " " . . . . ." " . . . . ...... ' ''..... i " I" "

..... " ' 1

11. Equipment Type Cards.

These cards define the parameters for each type equipment.X is the time to replace a WRA from the A/C if a spare ison hand, arbitrarily set = 2.0 hours. V is used in thisstudy to specify the onboard repair time at the AIMD level.


1-4 14 I Equipment type numbers, tobe assigned sequentially,from 1 to a maximum of 200

5-20 4A4 DUM(J) Equipment type description

21-28 F8.0 X Mean time between failure

29-32 F4.0 Y Mean time to repair/replace

33-36 F4.0 U Duty cycle utilization

37-40 F4.0 V AIMD part repair time

41-44 F4.0 W Admin delay time (depot/ship)

45-58 14 IDUM Not used

12. * Blank Card *** (Signals the end of equip. cards)

13. Equipment Cards.

These cards, one for each type equipment list individualparts by number, according to the equipment type. The firstnumber is equipment type, the numbers following it on thesame line are the individual parts for each type equipment.


1-4 14 NTYPE The type no. associated withthe part numbers following it

5-8 14 LOAD(l) Part numbers, 19 per linemax. Numbers begin at 1 and

9-12 14 LOAD(2) may not exceed 500. No gapsallowed in numbering parts.

77-80 14 LOAD(19)

99

.....................

14. *** Blank Card *** (Signals the end of equipment cards)

15. Spares Model Card.

The only option used on this card was "999." (columns 21-24)

Column Format Variable Description

21-24 F4.0 SX Used to call Spares sub-routine to determineallowance levels

16. ACIM Inventory Card.

This card will input ACIM allowance levels. If XFLAG=0.0 is

selected on card #i, TIGER will simulate with this input.Any arbitrary inventory levels may be input on this line.


1-2 12 ISPARE One allowance is entered foreach equipment type, up to a

3-4 12 ISPARE max of 31.

61-62 12 ISPARE

17. System Card.


1-4 A4 ID Any alphanumeric e.g. SYST,to identify the specificsystem

5-8 14 LL Phase Type number (sequen-tial) maximum value is 6

9-12 14 NSS No. of subsystems in thephase (varies only from 1to 31)

13-16 14 ISS System identification number,usually last group number onthe configuration matrixcards

17-24 F8.0 SSTIME System allowable downtime.100000 inhibits aborts.

100

° ~~~. ...................--............ .- . .-.. ... .• . . . ., .. .°. - .° .. .. -. .... . .. . . . . . . . . . . .-...... . . . . .. . .•. .. . .. - - - ° , .. • . . . °.°

18. Subsystem Cards.

One for each subsystem - up to 31. At least 1 subsystem

is required.


1-4 A4 ID Any alphanumeric, e.g., theliteral SSl, SS2, ... SS31

5-8 14 LL Phase type number

13-16 14 ISS Subsystem identification no.This is a group # for a groupdefined on a ConfigurationMatrix Card. Each designatedsubsystem group must be agroup that, upon its failure,causes the system to fail.

17-24 F8.0 SSTIME(2) Subsystem allowable sustaineddowntime. To inhibit abortsuse a value of 100000.

19. Configuration Matrix Card.

One card for each group, up to 300 cards.


1-4 14 NRO No. of members in the groupdefined on this card that arerequired to be operating andin an up status.

5-8 14 IB(l) The group no. assianed to thegroup of members defined onthis card. It may vary from501 to 1000 in any order.

101

Configuration cards cont'd.


9-12 14 IB(2) The numbers of the equipment &groups which make up the group

13-16 14 IB(3) defined on this card. Themax. no. of members in a group

17-20 14 IB(4) is unlimited; but if there aremore than 7, a continuation

21-24 14 IB(5) card is required of the sameformat. The no. required and

25-28 14 IB(6) master group must be identicalon all continuation cards.

29-32 14 IB(7)

33-36 14 IB(8)

20. * Blank Card *** (Signals the end of phaseconfiguration cards.)

NOTE: For each phase type, a set of the above System,Subsystem and Configuration Matrix Cards areentered, each set separated by a blank card.

21. Optional Output Card.


1-4 A4 SPRS Place any alphanumeric, e.g.,SPR, in this field if a tableof spares usage is desired.

5-8 A4 APPL Place any alphanumeric, e.c.,APL, in this field if a sum-mary table of equipment thatcaused mission failures(unreliability) and systemdown times (unavailability)is desired.

9-12 A4 GMMA Not used

13-16 A4 DEMO Not used

102

pq

APPENDIX B

TIGER INPUT DATA FOR SERIES SYSTEM

This appendix contains the input data file representing

the series system configuration. The TIGER program reads

this file and proceeds with the simulation as defined in the

data file. Part parameters for Appendix B are identical

with those for the parallel system listed in Appendix C.

Input data cards 17, 18, and 19 are the only data cards that

are different for the series and parllel system data files.

103

P

1 0 3 i -'

I

. . . -. . . . • . ° ° - . . .. . .. .. . . . .. .. • ".".".. .... .". .. ... .".. .-.. .""- "".. .".. ... ""-. .. " ." . ,", ," -" ". '. i ' .- '-:'" - - ' .. -2

8 0.0 3000. o.00007 5198(1.o 0.034940. 420. 2 0.10313671. 420. 2 0.1801o550. 420. 1 0.10521930. 420. 1 0.247375'10. 420. 3 0.1123520. 428. 1 8 .2 3 8

3885 .. 428.18.5060. 420. 3 0.258

540 11 ACIM 675K 17C CODE83A 14AUG84

25 25 1.01.281234 21. 3.C 2. 9.0 1. 3.0 2. 9.0

90 0 3 540 1 .0 1.010 2

1. i.00 1. 1.IHF POWER AMP 257. 2. 1. 420.2HF ANT COUPLER 352. 2. 1. 420.3HF RADIO CChTRL 658. 2. 1. 420.4HF ANT CIU 667. 2. 1. 420.5ARC158 R/T 272. 2. 1. 420.61FF R/T 699. 2. 1. 420.71FF COOR/DECODR 196. 2. 1. 420.8ARC158 FLT CONV 1124. 2. 1. 420.

1 1 2 15 16 29 302 3 4 17 18 31 323 5 19 334 6 20 345 7 8 S 21 22 23 35 36 376 10 24 387 11 25 3S8 12 13 14 26 27 28 40 41 42

999.j 55226333SYST 1 3 88E 100100.SS5 1 555 100000.SS6 1 666 100300.S 7 1 777 100000.

7 511 1 2 3 4 5 6 77 522 8 S 10 11 12 13 142 555 511 5227 611 15 16 17 18 19 20 217 622 22 23 24 25 26 27 282 666 611 6227 711 29 30 31 32 33 34 357 722 36 37 38 39 40 41 422 777 711 7223 999 555 666 7771 888 999

SYST 2 3 888 100000.SS5 2 555 100100.SS6 2 666 100300.SS7 2 777 100000.

7 511 1 2 3 4 5 6 77 522 8 S 10 11 12 13 142 555 511 5227 611 15 16 17 18 19 20 217 622 22 23 24 25 26 27 282 666 611 6227 711 29 30 31 32 33 34 357 722 36 37 38 39 40 41 422 777 711 7223 999 555 666 777

104

- . . . . .

S

1. 888 999

SPRSAP PL

S

0

S

S

S

S

0

S

S

105

S

S. . .

................

APPENDIX C

TIGER INPUT DATA FOR PARALLEL SYSTEM

This appendix contains the input data file representing

the parallel system configuration.

106

8 0.0 3000.0 0.010000001 1.0 0.034940. 420. 2 0 .10313670. 420. 2 0.18010550. 420. 1 0.10521930. 420. 1 0.24737500. 420. 3 0.1123520. 420. 1 0.23838850. 420. 1 0.1185060. 420. 3 0.258

540 11 ACIM 5675 FOR CODE83P 15AUG84

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0 2

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1 1 2 15 16 29 302 3 4 17 18 31 32

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999.i ~5 5 2 2 6 3 3 3 99

SYST 1 4 88E 100000.SS5 1 555 1000 00.SS6 1 666 100000.SS7 1 777 100000.SS9 1 9s9 100000.

2 511 1 32 512 2 41 522 511 5126 533 5 6 7 10 11 122 541 8 132 542 9 141 544 541 5423 555 522 533 5442 611 15 172 612 16 1E1 622 611 6126 633 19 2C 21 24 25 262 641 22 272 642 23 2E1 644 641 6423 666 622 633 6442 711 29 312 712 30 321 722 711 7126 733 33 34 35 38 39 402 741 36 412 742 37 421 744 741 7423 777 722 733 7443 999 555 666 777

107

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SYST 2 4 888 1003300.SS5 2 555 109001.SS6 2 666 100130.SS7 2 777 100009 0.SS9 2 99S 1003.0.

2 511 1 32 512 2 41 522 511 5126 533 5 6 7 10 11 122 541 8 132 542 9 141 544 541 5423 555 522 533 5442 611 15 172 612 16 1E1 622 611 6126 633 19 2C 21 24 25 262 641 22 272 642 23 2E1 644 641 6423 666 622 633 6442 711 29 312 712 30 321 722 711 7126 733 33 34 35 38 39 402 741 36 412 742 37 421 744 741 7423 777 722 733 7443 999 555 666 7771 888 999

SPRSAPPL

108

. -. " "

APPENDIX D

TIGER PROGRAM LISTING

This appendix contains a complete listing of the TIGER

program as amended for this study. Input data is contained

in a separate file as depicted in Appendix B. For an

explanation of the changes made to this program see Chapter

II. For a further explanation of the subroutines and

options available to TIGER, see the TIGER Manual.

109

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154

LIST OF REFERENCES

1. Chief of Naval Operations Instruction 5442.4H(OPNAVINST 5442.4H), "Aircraft and Training DevicesMaterial Condition Definitions, Mission-EssentialSubsystems Matrices, and Mission Descriptions",pp. 101-104, 20 May 1983.

2. Leather, J.E., An Evaluation of the Effect of SparesAllowance Policy Upon Ship Availability andReliability, M.S. Thesis, Naval Postgraduate School,Monterey, CA., September 1980.

3. O'Reilly, P.J., An Evaluation of AllowanceDetermination Using Operational Availability,M.S. Thesis, Naval Postgraduate School, Monterey, CA,June, 1982.

4. Naval Ship Engineering Center, Report No. 6112B-036-78,TIGER Manual, February, 1979.

5. Naval Postgraduate School Report NPS55-81-005, NavalPostgraduate School Random Number Package LLRANDOMII,Lewis, P.A.W., Uribe, L., February 1981.

6. Boatwright, B.O., RIMAIR VS. Current ASO Policy: AComparative Analysis of Two Methods For DeterminingAvcal Stockage Levels, pp. 76-84, M.S. Thesis, NavalPostgraduate School, Monterey, CA, September, 1983.

7. Naval Operations Analysis, 2nd ed., pp. 262-272, UnitedStates Naval Institute, 1979.

8. Fleet Material Support Office, ALRAND WorkingMemorandum 352, Aviation Supply Support ofOperating Forces, 14 March 1980.

9. Ross, S.M., Introduction to Probability Models,New York, Academic Press, 1980.

10. Naval Aviation Supply Office Instruction 4423.32 CH-l,ASO Provisioning Manual, pp. 111-3-1, 111-3-15,27 November 1978.

11. Mitchell, M.L., A Retail Level Inventory Model forNaval Aviation Repairable Items, M.S. Thesis, NavalPostgraduate School Thesis, Monterey, CA, March, 1983.

12. Aviation Supply Office letter to Naval Supply SystemsHeadquarters ACA-I: JPB: mec 4790, Subj: Turn AroundTime Constraints, 2 November 1977.

155

.° .0 -.

*-77 --

13. Chief of Naval Operations Instruction 441.12A, SupplySupport of the Operating Forces, Enclosure (5), pg. 6,9 August 1973.

14. Fleet Material Support Office Report 155, RIM-AIR Study,pg. 1, Operations Analysis Department, 30 June 1983.

15. Department of Defense Instruction 4140.46, StandardStockage Policy for Repairable Secondary Items at theIntermediate and Consumer Levels of Inventory, pp. 3-4,7 April 1978.

16. Naval Seas Systems Command, Availability CenteredInventory Model Consumer Level Allowance DevelopmentHandbook, May 1983.

17. McDonnell, J., LAMPS MK III Pack-Up Kit SparesSelection As Depicted By the Availability CenteredInventory Model (ACIM), M.S. Thesis, Naval PostgraduateSchool, Monterey, CA, March, 1984.

156

INITIAL DISTRIBUTION LIST

No. Copies

1. Defense Technical Information Center 2Cameron StationAlexandria, Virginia 22314

2. Library, Code 0142 2Naval Postgraduate SchoolMonterey, California 93943

3. Assoc. Professor F.R. Richards, Code 55Rh 2Naval Postgraduate SchoolMonterey, California 93943

4. Assoc. Professor A.W. McMasters, Code 55Mg 1Naval Postgraduate SchoolMonterey, California 93943

5. Mr. Peter Evanovich 1Center for Naval Analysis2000 North Beauregard St.Alexandria, Virginia 22311

6. LCDR Mark David Sullivan 24921 Whitewood LaneVirginia Beach, Virginia 23464

157

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Documents

NAVAL POSTGRADUATE SCHOOL · NAVAL POSTGRADUATE SCHOOL * Monterey, California (OF DTIC MELECTE APR 0 8 THESIS y E AN ANALYSIS OF THREE AVCAL INVENTORY MODELS USING THE TIGER SIMULATION