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AD-A093 584 NAVAL POSTGRADUATE SCHOOL MONTEREY CA F/6 15/5AN EVALUATION OF THE EFFECT OF SPARES ALLOWANCE POLICY UPON SHI--ETC(U)
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S :. THESIS,AN EVALUATION OF THE .9FFECT OF-SPARES ALLOWANCE _?OLrCY UPON
SHIP AVAILABILITY AND .kELIABILITY0
by
'. John Edward/Leather ;
Jjept~abov 1-98,0
Thesis Advisor: F. Russell Richards
Approved for public release; distribution unlimited.
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An Evaluation of the Effect of Spares Master's Thesis;Allowance Policy Upon Ship Availability caltmhall 1Qafand Reliability G. P"om em~m 01600TW101111
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John Edward Leather
iPEUtronuawG ORGANIZATION NAME AMC A00016111 If. PROGRM aawaxMS. POjECT. T ASKNaval Postgraduate School AREA A30K KuMITNIsSMRS
Monterey, CA 93940
IC004T3LLING OPPICS N AME AMC ADDRESS 12. REPORT DATE
Naval Postgraduate School September 1980Is. Munson OF PAGES
Monterey, CA 93940 115s1.MONITORING AGENCY NAMIL 6 AOUESSO 40101issiin = CotWm 013 0 6 Ofle L SEUI T 7 CLAVIL (of M@ viloset
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Is. SUPPLgmENTARY NOTES
19. NET WORDS (CmEnfl An rawwo side Of .nsee i ss It~m"I OF 6000 amos)
Cosal AvailabilityProvisioningTigerRe iability
20. ASIACT (Conflonse m ,,wse side It in....mip -ws OdafI, Or al inmb
U.S. ships are provided onboard spare parts for equipment theship's force is capable of repairing while at sea. The range anddepth of spares provided has a pronounced effect on the availabil-ity of both ship and weapon systems. The spares suite for aparticular ship is the Coordinated Shipboard Allowance List pro-duced by the Ship's Parts Control Center. A mathematical model isused to produce this list, aiming to achieve stocking goals setby the Navy. This thesis examines the relationship between these_.
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goals and the model in use. A simulation model developed by theNaval Sea Systems Command has been modifed so that it is compati-ble with the Naval Postgraduate School computer system, and thissimulation model is used to evaluate the provisioning models.This simulation model is capable of being used for a variety ofother projects at the Naval Postgraduate School._,-
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Approved for public release; distribution unlimited.
An Evaluation of the Effect ofSpares Allowance Policy Upon
Ship Availability and Reliability
by
John Edward Leather
Lieutenant, Supply Corps, United States NavyB.S., Case Western Reserve University, 1971
Submitted in partial fulfillment of therequirements for the degree of
MASTER OF SCIENCE IN OPERATIONS RESEARCH
from the
NAVAL POSTGRADUATE SCHOOLSeptember 1980
Author
Approved by: _ __ _ _ __
Thiesis Advisor'
Second Reader
Chairman, bepartment oOperati Research
Dean of Information and Policy Sciences
3
ABSTRACT
U.S. ships are provided onboard spare parts for equip-
ment the ship's force is capable of repairing while at sea.
The range and depth of spares provided has a pronounced
effect on the availability of both ship and weapon systems.
The spares suite for a particular ship is the Coordinated
Shipboard Allowance List produced by the Ship's Parts Control
Center. A mathematical model 's used to produce this list,
aiming to achieve stocking goals set by the Navy. This
thesis examines the relationship between these goals and the
model in use. A simulation model developed by the Naval Sea
Systems Command has been modified so that it is compatible
with the Naval Postgraduate School computer system, and this
simulation model is used to evaluate the provisioning models.
This simulation model is capable of being used for a variety
of other projects at the Naval Postgraduate School.
4
I.L .-
TABLE OF CONTENTS
I. INTRODUCTION -.-.-.-.--------------- 7
II. THE COORDINATED SHIPBOARD ALLOWANCE LIST (COSAL) - 10
A. NAVY POLICY FOR PROVIDING SUPPLY SUPPORT OFOPERATING FORCES - - - - ----------- 10
B. CURRENT COSAL MATHEMATICAL MODELS - -i- - --- 11
1. FLSIP Model - --------------- 12
2. TRIDENT Model - -------------- 14
3. Maintenance Criticality Oriented (MCO)Model - - - - --------------- 15
III. THE NAVAL SEA SYSTEMS COMMAND (NAVSEA) TIGERSIMULATION PROGRAM - --------------- 16
A. INTRODUCTION - ---------------- 16
B. PRESENT NAVSEA TIGER UTILIZATION - ------ 18
C. PROPOSED TIGER UTILIZATION FOR COSALPREPARATION - ----------------- 21
IV. BEST REPLACEMENT FACTOR (BRF) - ---------- 24
A. BRF - WHAT IS IT?--------------- 24
B. MEAN TIME BETWEEN FAILURE (MTBF) - - - - --- 25
C. DIFFERENCES BETWEEN BRF AND MTBF ------- 25a D. BRF AS AN INPUT TO TIGER - ---------- 27
* V. TIGER USED TO EVALUATE THE EFFECT OF SPARESALLOWANCE POLICY UPON RELIABILITY AND AVAILABILITY 29
J1 A. INTRODUCTION - - - ------------- -- z9
B. RELIABILITY (REL) - -------------- 29
C. AVAILABILITY (AVA) --- ------------- 30
..
D. READINESS (RED) - -------------- 30
E. RELIABILITY VS AVAILABILITY AS A MEASURE OFEFFECTIVENESS - ---------------- 31
F. ALLOWANCE POLICY EFFECT - ----------- 32
1. Reliability Block Diagram of System- - - 32
2. Proposed Allowance Policy Input ------ 33
3. Figure of Merit Results ---------- 33
VI. EXAMPLE OF TIGER ANALYSIS ..-..-.-.-.------- 3S
A. EQUIPMENT CONFIGURATION AND FAILURE RATES- - 35
1. Block Diagram and Operating Rules--- -- 35
2. Equipment Failure Rates - --------- 36
B. LOGISTIC SUPPORT (COSAL) MODELS USED ----- 36
C. RESULTS OF ANALYSIS - ------------- 37
1. Results of TIGER Simulation- - ------ 37
2. Interpretation of Results- -------- 38
VII. SUMMARY AND CONCLUSIONS - ------------- 39
APPENDIX A ACRONYMS - ----------------- 42
APPENDIX B TIGER PROGRAM VARIABLE LIST-- ---- - - 44
APPENDIX C SPARES SUBROUTINE VARIABLE LIST --------- 55
APPENDIX D MODIFICATIONS TO TIGER PROGRAM INPUT - - 56
TIGER COMPUTER OUTPUT (SAMPLE) ------------- 72
TIGER IBM/360 FORTRAN IV COMPUTER PROGRAM- ------- 78
LIST OF REFERENCES - ------------------ 114
INITIAL DISTRIBUTION LIST - --------------- 11S
6 -2
I. INTRODUCTION
The capability of a modern warship to be combat ready
and maintain this readiness over a deployment period depends
on logistics support. While this support includes such
necessities as food, fuel, medical supplies etc., a crucial
element in maintaining the sophisticated shipboard systems
is the availability of repair parts. More important, of
course, is the necessity of having a skilled technician
capable of diagnosing any problems and effecting the re-
quired repairs. This thesis will focus entirely upon the
'part' side of this two-way problem, knowing full well that
the desired technical expertise is not always available on
all ships.
To provide for the capability of repairing equipment
while away from port or support ships, each ship is provided
a quantity of spares designed to enable it to be self suf-
ficient for a period of 90 days. Budget and storage con-
straints prohibit stockpiling spares to cover all possible
requirements, therefore a choice must be made as to the
method to allocate the range and depth of spares to be
provided.
Chapter II discusses the way the Navy is currently
making this allocation. The method has been successful for
a number of years, but less so recently due to changes in
7
provisioning model parameters. These changes were dictated
by the 'high cost' of the allowance list generated by
previous parameters.
Chapters III, IV, and V describe the use of a reliabil-
ity block diagram simulation program to evaluate the effect
of changing the spares suite upon the reliability/availability
of a shipboard system over a 90 day period with no external
spares replenishment. To obtain an upper bound on the
spares effectiveness, the 90 day period was simulated with
all repairs being instantaneous; thereby placing the entire
burden of making the system available on the spares suite
and not upon the speed of the repair. From this technique a
measure of effectiveness of each given spares suite can be
derived.
As an example, a particular reliability block diagram is
analyzed in chapter VI using the simulation technique. The
nature/configuration of this block diagram has a large
effect on the figure of merit results. For example, three
different items connected in series would be less reliable
than the same three connected in parallel where only two are
required to be functioning at once and the third was in cold
standby. It is for this type of reason that a provisioning
process based on parts counting rather than reliability may
provide satisfactory results for one system and unsatisfac-
tory results for another when both systems possibly consist
of the same piece parts or perform the same function.
8
ILA
The simulation (called TIGER) is a general reliability
simulation model and is capable of many other uses besides
the one chosen for this thesis. With the help of the
appendices, the program listing, and the TIGER manual (Ref.
1) further use of this program on the Naval Postgraduate
School (NPS) computer system or any other FORTRAN IV com-
patible system with random number generation capability
should be feasible.
9
- /
II. THE COORDINATED SHIPBOARD ALLOWANCE LIST (COSAL)
A. NAVY POLICY FOR PROVIDING SUPPLY SUPPORT OF THE
OPERATING FORCES
The amount of logistic support required to support the
desired levels of fleet readiness are delineated in Ref. 2.
Of concern here are the sections on Shipboard Stock Levels
and Criteria for Shipboard Allowances.
All non-Fleet Ballistic Missile (FBM) self-sustaining
ships have a stockage objective of 90 days, which is equated
to the endurance for the ship. This objective is applicable
to repair parts, spares, and equipment related consumables.
The specific criterion for developing a COSAL from a list
of those items capable of being repaired by shipboard person-
nel is the subject of the next section of this thesis.
The measures of effectiveness for COSAL performance as
stated in Ref. 2, are to 'fill from onboard stocks 65% (gross
effectiveness) of all demands and to provide an overall
availability for items allowed to be carried of 85% (net
effectiveness)'. It is essential to note that no mention is
made of such terms as reliability, availability, or readiness
in the context of the supported ship as a measure of COSAL
effectiveness.
Net effectiveness is often called 'system' effectivenss,
in that it is the effectiveness of the entire logistics
10
I -'
system in replenishin, shipboard spares once they are used
and reordered. As this is not specifically related to the
COSAL provisioning document, but is a function of such
diverse items as order and shipping times, specific examina-
tion of this measure will not be attempted. Rather, certain
stated assumptions will be made regarding the percentage of
spares onboard when it is necessary to do so.
The objective of 65% gross effectiveness is the central
issue which this thesis will focus upon. As will be shown
in the next section, the COSAL mathematical model in no way
can be substantiated as a '65% gross effectiveness model'.
More important is the question of '65% gross effectiveness'
as a measure of effectiveness for shipboard support. One
could conceive of ways to fill 75% of the requisitions
received in 90 days from shipboard stock and never be able
to get underway. Alternatively, a low fill rate could
result in a highly successful deployment. The key, obvious-
ly, is to stock those items which are important to the ships
mission, and not to stock simply to maximize stock turn.
B. CURRENT COSAL MATHEMATICAL MODELS
Several mathematical models are currently being used to
generate COSALs. The Fleet Logistic Support Improvement
VT Program (FLSIP) model is used for surface ships and Fast
Attack Submarines (SSN) and is the most extensively used
technique. The TRIDENT model is used on Fleet Ballistic
/1
A II I II m i I I ml i i i I I - -- J ,w ... .. . : a m I m, • I J] . . ....
Missile Submarines (FBM) and is similar to the Maintenance
Criticality Oriented (MCO) COSAL being implemented on the
FFG-7 Lo-Mix class of ships.
1. FLSIP Model
The FLSIP model has been in use for many years and
has proven to be a rapid, workable, and understandable method
of generating the large quantity of COSALS that must be run
(approximately 50 per month). This model simply processes a
list of all repair parts applicable to the particular ship
and capable of being replaced by the ship's force. Each part
is individually totaled for its' entire installed shipwide
population and then is multiplied by its' Best Replacement
Factor (BRF) (explained in chapter IV). The resultant value
is called the 'mean', and this mean is used with the essenti-
ality of the parent equipment to determine the final allowance
quantity. A FLSIP logic diagram is shown in figure 1.
The attempt to incorporate essentiality into this
model has been negated by the migration of over 90 percent
of the parts on file into the 'vital' category. Technical
Overides (TORS) have been frozen by the Chief of Naval
Operations (CNO) as a cost reduction measure.
The currently used model is called a .25 FLSIP model
since the insurance cut point is .25 (one expected demand in
four years). As over 90 percent of the items stocked on-
board a ship are stocked at a depth of one, this cut point
is critical to the ability of the model to provide sufficient/"
wii 12
T /
FLSIP COSAL LOGIC
p=Item PopxBRF/ Pi l.0 Tr Stock this itemDetermine MRU to a depth ofDetermine PMR F max(s,MRU, PMR, TOR)Determine TOR (Demand based)
Item coded Stock this itemvital-vital to a depth of
max(MRU,PMR,TOR)(Insurance item)
PMR/TOR LT Stock this itemrequirement T to a depth of
F max(PMR,TOR)(Deep insurance item)
-ontstocid
Definitions:
Item Pop - Consolidated population of the item throughoutthe ship's systems
BRF - Best replacement factor
- minimum stocking depth such thatPr (Actual 90-day demand s)=.90(Assuming P6isson distribution)
MRU -Minimum replacement 'unit'quantity, if any
PMR -Required preventative maintenancequantity for planned maintenance
TOR - Technical override quantity, if any;determined by engineers/designersduring equipment provisioning review
Vital-Vital code - Item vital to its parentcomponent, and its component vitalto a primary mission
Figure I
13
,.
support. This cut point was changed from a previous value
of .15 due to various budgetary pressures.
Aside from the arbitrary nature of the value chosen
as the cut point the main problems which continue to exist
are the effectiveness criteria established in Ref. 2 and the
fact that the FLSIP model (Figure 1) has no mathematical
relationship to these criteria. If the FLSIP is to be
continued in use, and indications are that it will (Ref. 3),
meaningful effectiveness criteria must be established and a
means developed to justify the use of the FLSIP model to
meet these criteria.
2. TRIDENT Model
The TRIDENT model incorporates military essentiality
codes (MEG) assigned to the parent equipment into the stock-
age allowance decision. The more essential the equipment,
the better it will be supported. The following equation is
used to calculate the allowance quantity:
Allowance quantity = u +(Zxp)
Where V is the mean of the assumed Poisson distribu-
tion of repair part requirements in 90 days).
The multiplier Z is a function of essentiality and
to a lesser degree the unit price cf the part. As in the
FLSIP model each candidate part is processed individually and
is not subject to budget constraints (although the levels may
be adjusted through the manipulation of the various factors
which comprise Z).
14
This model is currently in use; takes essentiality of
equipment into account; and provides excellent support. But
as could be expected, the resulting COSAL provides generous
allocation of spare parts and its cost would be hard to
justify outside of the FBM arena.
3. Maintenance Criticality Oriented (MCO) Model
The MCO model is an allowance list to be implemented
on an increment of the new FFG-7 Lo-Mix class of ships. The
mathematical technique is very similar to the TRIDENT model,
the main difference being that essentiality is carried all
of the way to the part level. The documentation required to
achieve this is extensive and costly and must be maintained
throughout the life of the ship. The documentation required
to backfit the MCO model to older classes of ships does not
exist.
I
15
U . d •'
III. THE NAVAL SEA SYSTEMS COMMAND TIGER SIMULATION PROGRAM
A. INTRODUCTION
TIGER is the generic name for a family of computer
simulation programs which can be used to evaluate a complex
system in order to estimate various reliability, readiness,
and availability measures. This program was developed by
the Naval Sea Systems Command (NAVSEA) reliability branch.
The reliability block diagram of the system/component under
study is the foundation from which a TIGER simulation run is
constructed. This block diagram may be for a large system
(ship) with each block representing a component of the system;
or it may be for a single component with each block repre-
senting a lowest replacement unit part; or the block diagram
may be any type of combination of both. As an input for each
block the Mean Time Between Failures (MTBF) and Mean Time to
Repair (MTTR) must also be known.
The unique feature about TIGER is the flexibility in-
corporated into the program. Scenarios with block diagram
configurations which change duting the time period being
simulated are evaluated through a series of different time-
line 'phases' in the input. A phase is a specific reliabili-
ty configuration for the ship being studied. The simulation
will accept up to six different phases, and they may be
sequenced in any order and be of any interval of time. The
16
phases may be strung together until the simulation capacity
of 95 total phases is reached. MTBF, MTTR, and spares
multiplier factors may be entered to perform sensitivity
analyses on the system under study.
TIGER uses Monte Carlo random number methods to evaluate
the input block diagram. The random numbers are generated
through the use of the NPS LLRANDOM routine (Ref.4).
The TIGER simulation is a discrete event step simulation.
Exponential failure and repair times are generated using the
MTBF and MTTR input data. As equipments fail spares are
used; repairs effected (if allowed in the phase); standby
equipment turned on/off if required; and different block
diagrams initiated as the different phases are encountered
during the timeline. Statistics are collected as a result
of each event and change of configuration.
The TIGER output includes estimates of reliability,
readiness, availability, and critical components which caused
the most severe degredation of reliability and availability.
The user may change the random number seed and replicate a
timeline as many as 1000 times in a single TIGER run. TIGER
will calculate and provide a lower confidence limit for the
point estimate of reliability.
The inherent limitations to the use of this type of simu-
lation include both the problem of providing accurate input
data (MTBF, MTTR) and the exponential failure/repair rate
assumption used in the program. Under many scenarios and for
many types of equipment this exponential assumption is valid$ 17
but certainly many types of equipment exhibit wearout and
not all repair times are exponentially distributed.
In addition to the output mentioned above, spares usage
may also be displayed as well as several standard and
optional outputs of the progress of the simulation. The
detail can vary from every event being shown to a much
simpler management summary.
Two subroutines of TIGER were omitted in this thesis
research but may be useful in different types of analysis.
One of these, the GAMMA option, assumes that the system
being evaluated has a gamma failure distribution and calcu-
lates the two parameters (shape and scale) for the gamma
distribution which would exhibit the same mean and variance
of mission failure times as the system being modeled. The
DEMO option of TIGER provides the capability of generating
a sequential probability test ratio plan for the system as
prescribed in MIL-STD-781. Detailed information about TIGER
including GAMMA; DEMO; and a TIGER/MANNING personnel
requirements type program is found in Ref. 1.
B. PRESENT NAVSEA TIGER UTILIZATION
The TIGER program is being used by NAVSEA to evaluate
Reliability, Maintainability, Availability (RMA) performance
characteristics of new ship classes (Ref. 5). This analysis
is performed only on the major mission-essential systems:
Navigation, Auxiliary, Electrical, Ship Control, Propulsion,
18
IL
Exterior Communications, and Combat. Only these systems and
equipment which impact the operational readiness of the ship
and the ship's ability to perform its assigned primary
combatant mission are included in the analysis.
All surface ships constructed since 1970 have reliabil-
ity block diagrams available (in computer readable form).
This eliminates the major undertaking of having to construct
the reliability block diagrams prior to using TIGER. The
necessary MTBF and MTTR data for existing equipment is found
in the Reliability/Maintainability/Availability Design Data
Bank (Ref. 6), which is acompilation of data from both
engineering design and fleet feedback. Engineering estimates
must be used for the many new systems found on a new class of
ship, where no feedback data yet exists.
Along with the various reliability block diagram con-
figurations (steaming, in-port, ASW, etc.) and MTBF/MTTR
data, the operating rules for the equipment must also be
provided. These rules include allowable downtime, spares,
mission timelines, and maintenance policy.
A sample RMA timeline (Ref. 5) is shown in figure 2.
Timelines are tailored to the class of ship and its designed
usage in a period of combat.
Allowable downtime is the time that the system or equip-
ment can be down for maintenance without causing a mission
abort. During simulated combat periods this time is
usually zero for most mission essential systems.
19
P/
a, a Ia, a,~a, ~ c.~j.i.
U. ~ a, a C C - ~E~4
- B4.4 a - -4., - -a4.4 a4.4 - z~J
~ -4.4 ~
a,- a
U. fl.fl~- - :.ft =
C- a,
U.r..g
~' :a, ~0.
- 4.,
- H a,
ft ~ -K~a ai
.. 8 ~= U ~
-~ m -. -, a- a, -
- afta a
- 4.4 -=
4.4 ~ -. 4..- 4.4 ft a,
ft-4fta,
8 8a
i ~ ~
*1' 20
/
Maintenance policy limits certain equipment to being
capable of repair only during certain phases. For example,
repair of the main engine would not be permitted while
hunting a submarine, but would be permitted while in-port.
Spares are assumed to be available as needed for initial
TIGER analysis. Supportability tradeoff studies are con-
ducted separately to evaluate the effect of different spares
efficiency percentages and off-ship logistic delay times.
The results of the TIGER simulation are compared with
design specifications to see if any inherent (non-spares
related) reliability problems exist. Critical equipments
are then identified and closely monitored during the final
phases of design and construction.
C. PROPOSED TIGER UTILIZATION FOR COSAL PREPARATION
Reference 7 describes a methodology of using the TIGER
program to evaluate a COSAL with respect to reliability.
The inputs to the TIGER program would be the same as those
in the last section with the exception of the spares input
and the indenture level of the reliability block diagram.
The diagram must not stop at the equipment level, but be
carried out to the repair part level. MTBF/MTTR data must
also be provided at the repair part level.
As may be readily apparent, the block design for just
the essentail equipment of an entire ship would be very
cumbersome and unworkable. This type of TIGER analysis must
3 21
. . ..7I- ,. ... . . I I I | I I I~ i l l II I. . . .
be done on a system or equipment basis. The spares input
would be that generated by the COSAL model under evaluation,
usually FLSIP.
A deployment timeline is simulated and the resulting
reliability/availability figures are compared to the design
goals. If the goals are not achieved the 'bad apples' list
of repair parts indicates the particular parts which caused
the most degredation. Additional quantities of these parts
are added to the spares suite and the process is repeated
until the goal is attained. This method may also be used in
reverse, removing spares and observing the resulting changes
to reliability/availability.
While this methodology is feasible and would certainly
provide better support than an unaugmented FLSIP COSAL, it
has several drawbacks. One is the lack of reliability block
diagrams down to the repair part level. Although new equip-
ment procurement contracts may specify that this documenta-
tion must be provided, the task of assembling it for just
one ship's essential equipment would be awesome.
Another problem is the lack of MTBF/MTTR data for each
part. Reference 8 may be used to estimate the required
parameters, but again this is a large undertaking. As was
mentioned earlier in this thesis, current provisioning
i processes use a BRF vice MTBF to determine logistic support.
A further clarification of the differences between these two
and a proposed solution will follow in a later section.
22
A final problem results from the fact that repeated
computer runs on a vast network of reliability block dia-
grams are required to produce a single COSAL. The computer
system at the Ships Parts Control Center (SPCC) is saturated
and could not begin to process the large quantity of simula-
tion runs necessary to use this proposed method on all
COSALs. In addition, a significant number of manhours would
be required to review each run and decide which parts to
augment and in what quantity. Though this process would
undoubtedly produce a COSAL superior to the FSLIP model,
practicality prevents its adaption at the present time.
2
23
1.-."
IV. BEST REPLACEMENT FACTOR (BRF)
A. BRF - WHAT IS IT?
The BRF is the projected annual replacement rate for one
installed unit of a repair part. Only one BRF exists for
each part even if it is used in numerous applications
throughout a given ship or the fleet or ashore. The BRF is
found by dividing the annual reported usage in the fleet by
the total installed population. This yields annual failures
per installation. Before any calculations are made the in-
put data are adjusted for inaccuracies caused by bad
reporters and inactive ships in overhaul. The BRF is calcu-
lated annually for each item in the SPCC files. To prevent
rapid fluctuations from occurring the previous value on file
is updated with the new value by the use of exponential
smoothing.
To illustrate this process suppose that 105 ships in the
fleet were each recorded as having two of part 'A' installed.
Five ships were in overhaul for this particular year so
)their data is not used for BRF update. The remaining 100
ships reported a total of 400 failures for item 'A'. Since
there are 200 of 'A' installed and 400 were used, the un-
smoothed BRF is 400/200 = 2.0. If the BRF currently on
file is 2.4 and exponential smoothing with smoothing constant
.25 is used, the updated BRF would be 2.4k.75 + 2.0x.25 =2.3.
24
This BRF would be put on file for use in all COSALS which
contain part 'A'.
B. MEAN TIME BETWEEN FAILURE (MTBF)
MTBF is the expected value of the operating time between
failures of an item. It is estimated by dividing the total
time in service by the number of failures:
MTBF = total time in service/number of failures
Sometimes the expression Mean Time to Failure (MTTF) is used
for the expected value. Another related measure is the
failure (hazard) rate which is the conditional probability
that an item surviving to age t will fail in the interval
(t, t+dt). A constant failure rate is equivalent to having
a failure distribution which is exponential; and for an
exponential distribution the failure rate is the reciprocal
of MTBF.
C. DIFFERENCES BETWEEN MTBF AND BRF
A MTBF provides an expected value of the length of time
an item will operate until failure. It is based on operating
time; and failures are not possible while the equipment is
) not in use or turned on. A BRF is the average number of
times an item will fail in an average year in an average
installation. Since these differences and similarities are
crucial to the analysis in section VI of this thesis, the
following example taken from Ref. 9 provides an insight intothe MTBF/BRF relationship.
25
----- -
A piece of equipment (lamp) has four repair parts (bulb,
socket/switch, cord, plug). It is operated for 1000 hours
per year. An arbitrary MTBF and corresponding Failure Rate
(expressed in failures per year) are shown below:
ITEM MTBF FAILURE RATEE1g t Bulb -=U HRS 1.333Socket/Switch 10,000 HRS 0.100Electric Cord 15,000 HRS 0.066Plug 10,000 HRS 0.100TOTAL 7TS-
As shown, the lamp is expected to fail 1.599 times per year.
This would be a BRF for the lamp if the maintenance policy
were to replace the whole lamp no matter what the cause of
the failure. The following table shows how maintenance
philosophy can have a pronounced effect on the five BRFs.
The 'Replace Failed Part' column represents the way repairs
are usually accomplished at the shipboard level. Only
catastrophic failure would lead to the attempted replacement
of the entire item, usually unsuccessful because the entire
assembly would not likely be stocked due to the low BRF.
MAINTENANCE PHILOSOPHYFAILURE REPLACE REPLACE FAILEDRATE FAILED REPLACE BULB, OTHERWISE
ITEM PER YEAR PART LAMP REPLACE LAMP
LAMP 1.599 BRF=0. BRF=I.599 BRF= .266BULB 1.333 BRF=I.333 BRF=0 BRF=I.333
V CORD 0.066 BRF=0.066 BRF=0 BRF=0S/SWITCH 0.100 BRF-O.100 BRF=0 BRF=0PLUG 0.100 BRF=0.100 BRF=0 BRF=0
/i 26
D. BRF AS AN INPUT TO TIGER
When MTBF is used as an input to TIGER, various time-
lines are used to provide scenarios in which the equipment
configurations and usage rates are required. When equipment
is on, it fails exponentially with the given MTBF, unless
the duty cycle is less than 100 percent, in which case the
MTBF is divided by the duty cycle. The BRF has incorporated
the various reasons the timeline approach must be used with
the MTBF; equipment being turned off and on, duty cycles for
equipment with cycles of less than one; and the various
configuration dependent usage rates for an average instal-
lation in an average year.
Consider, for example, an equipment with a duty cycle of
one-half (operating 50 percent of the time) exhibiting five
failures in a ten year period. The MTBF is calculated as
before; total time in-service/failures = (10x.5)/5 = 1 year.
Since the duty cycle is one-half, we would expect to see a
failure every other year, or .5 per year. The BRF calcula-
tion yields the same result; 5 failures/10 years = .5
failures/year.
To use a BRF in TIGER requires that the entire block
diagram, in a typical configuration, be used and equipment/
parts be allowed to fail at an annual rate (BRF) which takes
the numerous operating scenarios into account. While the
results from this type of analysis would be very difficult
to defend as providing entirely accurate reliability/
27
availability measures; they should be suitable for deriving
a 'figure of merit' evaluation for the support provided by
different COSAL models.
28I
r1
'p
1 28
!/
V. TIGER USED TO EVALUATE THE EFFECT OF SPARES ALLOWANCEPOLICY UPON RELIABILITY AND AVAILABILITY
A. INTRODUCTION
The current utilization of gross effectiveness as a
measure of COSAL effectiveness has been studied in previous
sections. An alternative measure will now be proposed. The
TIGER program calculates reliability, availability, and
readiness figures for each simulation run. The definitions
for these three measures, as found in Ref. I, are summarized
below.
B. RELIABILITY (REL)
For a given timeline the reliability (REL), as estimated
by TIGER, is the probability that the ship will successfully
complete the entire timeline. For example, if the timeline
previously shown in figure 2 were used, REL would be the
probability of the ship completing all of the different
missions assigned during the 60 day period, in the sequence
shown.
Reliability is calculated by TIGER as follows:
REL (EST) = 1 - Number of mission failures (aborts)*Total number ot simulated missions
Note that this calculation incorporates logistics support
considerations.
29
.4.
C. AVAILABILITY (AVA)
TIGER calculates two AVA parameters: Instantaneous and
average. Instantaneous availability is the probability that
the system will be 'up' at a specific point in time. Average
availability is the probability that the system will be up
at a random point in time. Because of the way TIGER is used,
average availability is the relevant measure.
Average AVA is estimated as the ratio of total system
'uptime' to the total time simulated. These times are
totaled for the entire number of missions simulated (up to
1000). The calculation is made as follows:
AVA (EST) = Summation of uptime for allmissions simulatedSummation of total mission calendar timefor all missions simulated
= UptimeCalendar time
D. READINESS (RED)
RED, like AVA can be measured as instantaneous or
average readiness. It is a measure of the probability that
there is neither a mission abort nor a system down. The
* forthcoming methodology for the use of TIGER results in RED
r equaling AVA, so RED will not be considered any further as
an alternative measure of effectiveness.
30
.9
E. RELIABILITY VS AVAILABILITY AS A MEASURE OF EFFECTIVENESS
A very common measure of effectiveness in use by the Navy
today is 'Operational Availability' (Ao). Ao is defined as
the probability that an equipment is ready when you need it.
MIL-HDBK-217C (Ref. 8) dictates that it be calculated by:
Ao - MTBF
An alternative form of this equation results from
breaking the MTTR up into the repair time (MTTR) plus the
Mean Supply Response Time (MSRT); the time necessary to
provide the required repair part(s). This yields:
Ao - MTBFMTBF + MTTR + MSRT
There are problems with the use of this formula for
estimating system operational availability (Ref. 10). From
a mathematical point of view the formula yields the correct
result for the limiting value of operational availability
when one considers a single component that transitions
between up and down states as an alternating renewal process.
If one is interested in the operational availability after a
fixed period of time for a system whose components have
limited spares support, the formula does not yield correct
results. In fact, the formula makes little sense. A
simulation like TIGER is precisely what is needed to esti-
mate Ao for a complex system with limited spares support.
Since AVA implicitly considers component reliability,
maintenance, spare parts support, system configuration and
31
operational scenario, it is used in this thesis to evaluate
COSAL models.
F. ALLOWANCE POLICY EFFECT
1. Reliability Block Diagram of System
The effect of a parts-counting type allowance policy
upon reliability/availability is dependent on the configura-
tion of the system being supported. Parts counting is a
method of allocating spares in proportion to the number of
each specific repair part in the equipment. In an environ-
ment of limited budgets and storage space, a more 'critical'
spare (in terms of reliability/availability) may be sacri-
ficed to provide unwarranted depth for another spare.
Figure 3 shows a simple reliability block diagram with two
Figure 3
of part A in parallel with each other and then in series
with part B. Both A and B have a BRF of 1. If A cost the
same as B, and only one spare could be provided, provisioning
by parts counting would provide one spare of type A, since
there are twice as many A as B. However, the availability of
this system would be much greater (all other things consid-ered the same) if the one spare purchased were of type B, due
to the parallel redundancy.
32
.5WWW W.
2. Proposed Allowance Policy Input
There are two methods of entering the quantity of
spares for each part type into the TIGER simulation. One is
to input that quantity as part of the input data. For small
systems this may be the most efficient method. For larger
systems or for those systems requiring a complicated mathe-
matical model, a subroutine has been added to TIGER to
calculate the COSAL.
For the FLSIP COSAL, the cut point is input with the
other system data and the spares subroutine is used to
generate the COSAL for the system. The MTBF is derived from
the BRF in the following manner:
MTBF=(l/BRF)x8766 (yr/fail)x(hr/year) = hr/fail
This MTBF is used as the exponential failure rate input for
the simulation, and converted back to BRF when. necessary to
determine COSAL support.
3. Figure of Merit Results
Several simplifying assumptions are made by using
TIGER to obtain the output availability measure. The most
important are exponential failures; BRF converted to MTBF;
zero repair times; a full allowance of spares onboard at the
beginning of the mission; and the use of a 'typical' relia-U bility block diagram configuration for the duration of a
single mission. Because of these assumptions, the availabil-
ity figure provided by TIGER should not be considered as the
true value for system availability. However, this figure
I
should be useful as a 'Figure of Merit' for comparisons with
the figure derived for the same system using a different
methodology or level of logistics support. When used in
this context, the figure should provide an accurate assess-
ment of the relative effectiveness of two spares allowance
policies.
3
?l 34
1*-*j
VI. EXAMPLE OF TIGER ANALYSIS
A. EQUIPMENT CONFIGURATION AND FAILURE RATES
1. Block Diagram and Operating Rules
As an example of the use of TIGER proposed in this
thesis a hypothetical video display unit will be analyzed.
The unit consists of a power section; signal processing
section; and video display section. The required reliability
block diagram is shown in figure 4.
POWER SECTION
il/
SIGNAL PROCESSING SECTION
(1 COPLRCIRCUIT BOARD - BI FUSE -B 2)
VIDEO SECTION
(2) CIRCUIT BOR - R T- (3)
(3) CIRCUIT BOARD-AE S N
Figure 4
3S
POEjETO
The three sections are connected in series to form the
entire unit. Only one of circuit board A is required to be
'up' in the power section, and two of circuit board B in the
signal processing section. The failure of two of either
circuit board A or B or the failure of any other single part
will cause system failure.
2. Failure Rates
The following is a list of the BRF for each part and
corresponding MTBF:
ITEM BRF MTBFSwit- .-69 7W-0Fuse - A 2.50 3506Transformer .17 51565Circuit Board - A 2.10 4174Coupler .23 38113Circuit Board - B 2.50 3506Fuse - B 3.60 2435Rheostat .12 73050Circuit Board - C 1.20 7305Circuit Board - D 2.20 3985Circuit Board - E 1.70 5156Video Screen .20 43830
B. LOGISTIC SUPPORT (COSAL) MODELS USED
The COSAL models evaluated were the standard .25 FLSIP
and a modified FLSIP as proposed by the CNO Shipboard Parts
Allowance Policy Study (Ref. 3). This modification consists
of changing the FLSIP cut point to .1 (one demand in ten
years) and providing an allowance quantity of two (vice one)
for those items with a BRF between 2.0 and 4.0.
36
LA-~
C. RESULTS OF ANALYSIS
1. Results of TIGER Simulation
The following tables provide a summary of the rele-
vant output from the two TIGER simulation runs for 90 day
missions. The actual computer output is self explanatory and
a sample is included as a separate section of this thesis.
The percent unavailability column indicates the percent of
unavailability caused by each item.
.25 FLSIP (Availability .7229)
SPARES SPARES FAIL/ PERCENTITEM STOCKED USED MISSION UNAVASw-Itch o 7.02-5 3.5Fuse - A 1 .50 .637 14.54Transformer 0 .00 .042 6.42Cir Bd - A 2 .96 1.05 6.77Coupler 0 .00 .064 9.35Cir Bd - B 4 1.84 1.897 .81Fuse - B 1 .57 .793 24.01Rheostat 0 .00 .030 3.74Cir Bd - C 1 .27 .318 3.64Cir Bd - D 1 .43 .541 11.99Cir Bd - E 1 .34 .416 7.07V. Screen 0 .00 .052 8.29
.1 MOD FLSIP (Availability = .9064)
SPARES SPARES FAIL/ PERCENTITEM STOCKED USED MISSION UNAVASwTch 0 .- -.T=7 W.5
* Fuse - A 2 .59 .607 5.41Transformer 1 .05 .054 .75Cir Bd - A 2 .92 1.015 24.70Coupler 1 .06 .067 1.23Cir Bd - B 4 1.84 1.897 2.58Fuse - B 2 .79 .844 18.19Rheostat 1 .04 .044 .00Cir Bd - C 1 .27 .310 13.43
* Cir Bd - D 2 .53 .553 5.42Cir Bd - E 1 .35 .414 18.99V. Screen 1 .04 .046 .74
37
2. Interpretation of Results
As would be expected, the .1 Mod FLSIP provided a
greater depth and range of spares than the .25 FLSIP. The
addition of seven more spares resulted in an increase in AVA
frum .7229 to .9064, a significant increase. For the .25
FLSIP run, the item accounting for highest percentage of
availability is fuse - B, with 24.01 percent. Since FLSIP
provides a 90 percent confidence level of protection for
those items with a BRF '4.0 (- I/qtr), the BRF of 3.60
places the fuse just below this cut and therefore it is
allocated only one spare. For the .1 Mod FLSIP run fuse - B
no longer is the largest contributor to unavailability.
Circuit board - A is the largest, accounting for 24.70 per-
cent of the unavailability. If further incremental improve-
ments were to be made to the .1 Mod FLSIP COSAL, the first
additional spare should be circuit board - A followed by
circuit board - B, fuse - B, and so on down the list of
unavailability percentages.
The difference in AVA for the two COSALS is the most
important statistic. If availability in the range of .9
were required for the system, the .1 Mod FLSIP should be
used. If however, the system were not that essential, the
.7 availability provided by FLSIP should be used to enable
scarce spares funding resources to be used on more essential
systems.
'3
: 38
it
VII. SUMMARY AND CONCLUSIONS
This thesis focused on one basic problem; that of pro-
viding logistics support for Naval units afloat. Current
guidelines and measures of effectiveness were presented
along with several of the methodologies by which the policies
are being carried out.
The NAVSEA TIGER reliability block diagram simulation
program was introduced as a currently used method of evalu-
ating ship reliability and also as a proposed method of
generating allowance documents. A key input to any relia-
bility calculation is the MTBF. The use by the Navy of a BRF
vice MTBF was reviewed and a solution proposed to enable BRF
to be used as an input to the TIGER simulation.
A technique for using TIGER to evaluate the effect of
various spares allowance policies upon system availability
was introduced, followed by an example of such an analysis.
The Navy is interested in providing logistics support
so as to maximize the operational availability of its ships
)within given resource constraints. Mathematical models
designed to allocate spares while maximizing system availa-
bility require extensive amounts of data (much of which is
either not available or retrievable by computer). They are
computationally infeasible to implement on a Navy-wide basis.
Thus, it appears that the Navy will continue to use simpler
3
p 39
parts-counting models such as those described in this thesis.
No claim of optimality with respect to 'system availability'
can be made with such simple models that make no attempt to
consider the system as anything other than a collection of
parts.
The models that are being used are regulated by control-
ling the values of certain parameters such as FLSIP cut
points or essentiality codes. Since there is no way to
analytically relate these models to system effectiveness, a
tool such as the TIGER simulator is needed to evaluate the
future impact on system availability of a given provisioning
or support policy. The assumptions required to perform this
type of evaluation have been discussed throughout this
thesis.
The following are recommendations for additional work in
the topic of this thesis or for additional uses of the TIGER
simulation:
1. Use as an evaluation tool for various provisioning
models.
2. Use to evaluate maintenance policies and their
effect on required manning levels.
3. Use as a system design tool.
4. Use on new equipment being introduced into the fleet
to establish a FLSIP cut point. Code equipment with this
cut point instead of the vital/non-vital codes currently in
use, and use this cut point when preparing the COSAL.
40
2 ! " -
S. Evaluate the effect of the assumptions made in this
thesis and other problems such as the gradual degredation of
equipment (not simply up or down) and the effect of the
annual revisions to the BRFs.
)
i 41
...
APPENDIX A
ACRONYMS
Ao Operational Availability
AVA Availability
BRF Best Replacement Factor
COSAL Coordinated Shipboard Allowance List
CNO Chief of Naval Operations
EST Estimate
FBM Fleet Ballistic Missile
FFG Guided Missile Frigate
FLSIP Fleet Logistics Support Improvement Program
MCO Maintenance Criticality Oriented
MEC Military Essentiality Code
MRU Minimum Replacement Unit
MTBF Mean Time Between Failure
MTTF Mean Time to Failure
MTTR Mean Time to Repair
NAVSEA Naval Sea Systems Command
NPS Naval Postgraduate School
PMR Preventative Maintenance Requirement
RED Readiness
REL Reliability
R N Reliability/Maintainability/Availability
'1
SPCC Ships Parts Control Center
SSN Fast Attack Submarine (Nuclear)
TIGER Simulation Program Name
TOR Technical Overide
4
,, 43?
Ai
]/
APPENDIX B
TIGER PROGRAM VARIABLES LIST
The following is a list of the variables used in the
TIGER program and their respective usage/definition. All
variables which were used in this thesis are included along
with some from other optional parts of the TIGER program.
Numbers at the right indicate the data card on which the
variable is input into the program.
A Subroutine DEMO producer risk 21A
ACMMH Average corrective manhours per mission
ADT Administrative delay time
AENDT1 Downtime in remainder of phase due to abort
AENDT2 Downtime in remainder of mission due to abort(up to current phase)
AFM Average failures per mission
ALDONE Sum of three DONE(I);if zero, skips spare printout
APPL Bad apple unreliability and
unavailability printout 21
AVA Average availability or availability
AVAINS Instant availability
AVAl Average availability
AVAL Average availability
AVGCST Avergae cost per hour of repairman 7M
B Subroutine DEMO consumer risk 21A
4
14
I II I I I I I I II I II I I I
BAPRIN Bad Apple printout indicator, when equals-1, print
BILL Temporary variable used to integerize the
number of spares
BLNK Four character alphabetic blank
COUNTB(1) Number of failures for equipment I
DAY(IX) Occupation symbol 1SA,M
DELT Time Difference
DEMO Probability ratio test plan for system 21
DMNO Same as DEMO
DNTl Total system downtime in phase
DNT2 Total system downtime in mission
DONE(I) Average number of spares used from ship,tender, depot(I=1,3)
DUM(J) Dummy variable to read Fl
DUMMY Skill types
ENDPHA End of phase time
EQUIP(I) Person type numbers of people who couldbe operating this type of equipment SG
ETIME Event time
EX(I,J) Administrative delay time (U,W)
F(I,J) Same as Fl
FCOUNT Real value of JCOUNT
* Fl Alphabetic equipment description 8
GMMA Alphabetic request for GAMMA subroutine 21
HAD DEMO X-axis accept intercept 21A
HRD DEMO X-axis reject intercept 21A
* I Various indices; equipment type number 8
45
IABC Index
IAUP Instant availability (up for entiresimulation)
IAUPl(I) Instant availability (up at beginningof sequence
IAUPZ(I) Instant availability (cumulative up atbeginning of sequence
IB(I) Group number and equipment and groups
which make up the group 18
IBLANK 14 alphabetic blank spaces
IBM Equipment type number
IBNUM(I,J) Number of configuration matrix cards inphase
ICHLD Child in reliability tree
ICRI Subsystems exceeding mission allowabledowntime (TAD2)
ID Alphabetic system name 16,17
IDIFF Total equipment failures (all types)
IDUM Same as IUT
IEQ Absolute value of IEQU(J)
IEQU(I) Equipment type array
IFF Number of failures
IFFEOP Same as ISW
IFLAG Repair option in each phase 6
IFR Number of repairs
IGRP Equipment group
II Spare location (ship, tender, depot)
III II-1
IIUSED(I,J) Spares used per equipment type from eachlocation
4: 46
L /
IK Phase indicator
IK2 Phase indicator
IK3 Phase indicator
ILB Counter for NEQ
ILL Phase subscript for VDC(IU,ILL)
IND Equipment type
INDEX Index; equipment number
INEWA Index used to rank equipment bynumber of failures
INMI(I) Number of missions run
INOABT(I) Number of aborts in the sequence
INREJ Not used
INUM Maximum number of mission repetitions (50)
IOR Number of equipment operating rules
IPTR Parent/Child index
IPRNT Parent reliability tree
IRULE Equipment operating rule card 19
ISEED Random number seed 2
ISO +=string; -=standby
ISPARE(I,J) Quantity of spares at ship, tender,depot is
ISS System/subsystem identification number 16,17
ISSA(I) Phase allowable downtime
ISTB(I) Equipment operating rules 19
ISUM Summation
ISW Subsystem status (l-up, -l-down)
ISSC Subsystems exceeding allowable downtime
/
ii 47
I- - / - ,
ISYS(K) System in phase K
ITEMP System status indicator
ITEMP2 Subsystem status indicator
ITIME Number of sets ZIA
ITER Number of simulations per set 21A
ITOTAL Integer value of total
IU Variable duty cycle (IUI(I))
IUI(I) Variable duty cycle indicator 8
IUNLIM Alphabetic 'unlimited spares'
IUT Same as IDUM
IUSED(I,K) Spares used from ship, tender, depot
IV Variable duty cycle indicator (IUI=IV) 9
IVALUE(I) Temporary variable for IB or ISTB
IX NUM+I
IXX Equipment type
IXXT Phase type
J Various indices; equipment type
JA Index for 1B
JB Index for IB
JBB Phase sequence number
JBB1 JBB-l
JC Current timeline
JCC Number of timelines
JCOUNT Number of failed equipments
JIND Equipment type
JNUM Integer of XNUM
4
, 48
!-.
K Various indices
KAA Mission number being simulated
KAB Mission number being simulated
KD Trucation line accept
KEQ Equipment number
KEQU(I) Number of failures for equipment type I
KID Dummy variable
KID1 Equipment group
KID2 Equipment group
KK Same as LL; index of equipment number
KKK Phase in mission
KKK2 Same as KKK
KOPT Printout option switch 5
KS(I) Output options for KOPT 5
KSS Index
KT IB( , ,l), or number required up in group
KI Equipment type; trail shape parameter
L Same as LL
LCL Lower confidence limit
LL Phase type number 16,17
LLL Duration of phase sequence
LOAD(I) Equipment numbers assigned to equipmenttype 12
MAXIB Maximum number of configuration matrixcards (300)
MAXNEQ Maximum number of equipments (500)
MAXNPH Maximum number of phases (6)
49
MAXRUN Maximum number of mission (1000)
NIAXSEQ Total number of phases
MAXSS Maximum number of subsystems (31)
MAXSTD Maximum number of equipment operating rulecards (49)
MAXTYPE Maximum number of equipment types (200)
MDT Estimator of MTTR
MKBA Bad Apple equipment vector
MM 0
MTBMF Mean time between mission failures
MUT Instanteneous MTBF parameter
Ml Trial scale parameter
N Counter; NSS+1
NEQ Equipment type counter
NLINE(l) Number of configuration cards in phase
NL NLINE(LL)
NN Index
NMAX Maximum number of missions 2
NOPT Optimal number of mission 2
NPH Number of phases 2
NRO Number required operating 18
NSS Number of subsystems in phase 16
NTY Last number of equipment types
NTYPE Equipment type 12
NTl Equipment type number
NUM Mission number counter
'so: 50
I
PERC Percent unreliable
PL Reliability specification 2
R Dummy variable used to find next eventtemporary variable used to calculate VDC;discrimination ratio 21A
RDT Running down time
RED Readiness
REDADl(I) Adjusted time for readiness calculationin phase
REDAD2 Adjusted time for readiness calculationin mission
RED Readiness
RED2 Readiness
REL Reliability
RELGA(JBB) Reliability (RELPY) for phase sequence
RELPY Reliability up to and including phasejust completed
REPOL Percent of repairs performed aboard ship 7
RN Random number
RIN3 Random number
RUNID Alphabetic program identification line 1
SLD Slope 21A
SPRS Alphabetic request for SPARES output 21
SR Intermediate value used to calculate ST
SSTINE(I,J) System/subsystem allowable sustaineddowntime 16,17
ST Intermediate time
STEPHAS Accumulated phase time
SUMX Total simulation time
51
SUMX2 Sum of SUMX squared (for variance
calculation)
SX Spares multiplier
T Duration of phase
TABORT Time of abort
TACMMH Total average corrective maintenancemanhours/mission
TAD1 Same as SSTIME
TAD2 Mission allowable downtime 7
TAFM Total average failures per mission
TDEOP Time down at end of phase
TDOWN Time system went down
TIMA(I) Cumulative phase time
TIME Simulation clock time
TITLE(K,N) Alphabetic subsytem title
TNMI Real value of INMI(JBB)
TOTAL Number of failed missions
TR Temporary variable used to find maximumunavailability/reliability
TRR Same as TR
TP Same as TIME
TTEMP Downtime
TTF Time for failure
TTR Time to repair
K TTl Phase length
TTZ(JBB) Cumulative time of phase lengths
TT3 Cumulative phase times
5
I - -
TYCOON(I) Downtime for equipment
TYCUM Unavailability
TYCUM2 Percent unavailability
Ti SSTIME( , ,l)
T3 Downtime
T3SUM Cumulative downtime
U Duty cycle utilization 8
UNAVA Unavailability
UNREL Unreliability
UP1 Time system up in phase
UP2(JBB) Cumulative system uptime
UP3 Cumulative system uptime
UP4 Cumulative system uptime
V Administrative delay time(tender to ship) 8
VAR MTBMF variance
VDC(I) Duty cycle utilization duringeach phase 9
VMTTR(I,J) Variable mean time to repair 10
W Administrative delay time (depot toship) 8
X Various; XMTBF; event indicator(+ fail; - repair)
XAV Instant availability
XAVI Instant availability
XCUM Successful missions in last 50
XDWN Number of mission failures (XNUM-XTCUM)
XIAUPP Real of IAUP
S3
I
XIAUPI Real of IAUPI
XID Alphabetic ID
XIFF Real of IFF
XIRR Real of IRR
XK Standard deviation for lower confidencelimit 2 2
XKAA Real of KAA
XLCLA Lower confidence limit of 90 percent
XM XMTBF Multiplier 7
XMDT System man down time
XMTBA Mean time between mission failures
XMTBF Mean time between failures 8
XMTTR Mean time to repair 8
XMUT System mean up time
XMl Same as XT
XNO Number of non aborts
XNUM Real of NUM (total missions run)
XPCAP Reliability
XPLCL Lower confidence limit
XT XMTBF multiplier 7
XTABT(I) Time of abort mission I
XTCUM Cumulative successful missions
XXT(I) Phase type (I odd); Duration (I even) 3
XXX XMTBF or VMTTR
X2 X squared
Y Same as XMTTR
YD Truncation line accept 21A
54
APPENDIX C
SPARES SUBROUTINE VARIABLE LIST
CUT FLSIP cut point
DUM Dummy variable
EX90DD Expected 90 day demand
ITMPOP(I) Number of equipment type Iin reliability block diagram
K Counter
KFACT K factorial
PRBSUM Poisson probability summation
SPRI-14 Various user defined input variables
55
!-
APPENDIX D
MODIFICATIONS TO TIGER PROGRAM INPUT
To use the GAMMA and DEMO options, the end of the main
section of the program must be changed to the following:
1210 IF (GMMA.EQ.BLNK) GO TO 1230
1220 CALL GAMMA
1230 CONTINUE
IF (DMNO.EQ.BLNK) GO TO 1240
CALL DEMO
1240 STOP
END
Subroutine GAMMA, function GAMF, subroutine DEMO, function
CHISQ, subroutine TGEN, and subroutine CKTP must be added to
the program deck (note: none of these have been utilized or
verified for use on the NPS computer).
The following changes were made to the original input
deck:
Card 2 - INREJ replaced by ISEED; the random number generator)
seed.
Card 14 - If spares subroutine is desired, enter 999. for SX.
Fourteen variables (SPRI,SPR2,...,SPRl4) may then be read
into the spares subroutine in F4.0 format starting in
column 25.
56
I. -
These changes are incorporated into the input require-
ments shown on the following pages. They should be used
when prepaxing the TIGER data input deck.
5
4r
57
LL,
4.)0 '0I
0 4) 4) *i( co44 >..C 4' U r- -4
:3 A42 X4 0 4 u4) 4)0
0 *tn 0 U0 10 U al0 C .' C: -4 10x
4J4)4 40+ 4) 4) 0 0 r0 $-.' ..oC 1~ *-4 44 tn W0n, 0 Udr n44 C 3 0 t
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00 'd r4 0 0$-4 0-CU4 41b4) 04-4 Wn C (flCU 3 + r
0 +- .0 111 =a jCD=0C4a +j 1-- 0 0 n.u00 =
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LIST OF REFERENCES
1. Naval Sea Systems Command Report TE660-AA-MMD-010,Tiger Manual, January 1980.
2. Chief of Naval Operations Instruction 4441.12A, SupplySupport of the Operating Forces, 9 August 1973.
3. Center for Naval Analysis Memorandum (CNA)80-0881,Third Advisory Committee Briefing on Shipboard PartsAllowance Policy Study, by Cdr. J. Bagby, 19 June 1980.
4. Learmonth, G. P. and Lewis, P. A. W., 'NavalPostgraduate School Random Number Generator Package',Naval Postgraduate School Report NPS5SLW3061A, June1973
5. Buckberg, M. L. and Vail, J. A., 'DDG-47 ReliabilityEngineering Analysis,' Naval Engineers Journal, v. 90,no. 3, p. 85-90, June 1978.
6. Naval Sea Systems Command Report 313-110-79, Reliability/Maintainability/Availability Design Data Bank, September1979.
7. Judge, S. D. and Luetjen, P., 'Determination ofShipboard Repair Parts Level,' Naval Engineers Journal,v. 91, no. 2, p. 37-43, April 1979.
8. Department of Defense Military StandardizationHandbook MIL-HDBK-217C, Reliability Prediction ofElectronic Equipment, 9 April 1979.
9. Straub, D. R., 'Differences Between Failure Rates andBest Replacement Factors,' Navy Supply Corps Newsletter,v. 42, no. S, p. 35-38, May 1979.
10. Esary, J. D. and Richards, F. R., Some Hostile CommentsAbout the Definition of Operational Availability, paperpresented at 44th Symposium of MORS, Vandenberg AFBCalifornia, 5 December 1979.
114
p
INITIAL DISTRIBUTION LIST
No. Copies
1. Defense Technical Information Center 2Cameron Station
Alexandria, Virginia 22314
2. Library, Code 01422Naval Postgraduate School
Monterey, CA 93940
. Department Chairman, Code S 1Department of Operations ResearchNaval Postgraduate SchoolMonterey, California 93940
4. Assoc. Professor F.R. Richards, Code 5Rh 1Naval Postgraduate SchoolMonterey, California 93940
S. Professor J.D. Esary, Code 55Ey1~Naval Postgraduate School~Monterey, California 93940
6. CDR. W.E. Daeschner, SC, USN, Code 04A 1Naval Supply Systems CommandWashington, DC 20376
7. CDR. James Bagby, USN 2Center for Naval Analysis2000 North Beauregard StreetAlexandria, Virginia 22311
8. Mr. Palmer Luetjen, Code 31331 1Naval Sea Systems CommandWashington, DC 20362
9. LT. J.E. Leather, SC, USN 262 Shongum RoadRandolph, New Jersey 07869
115
