USAAMRDL-TR-75-51 CH-54 OPERATIONAL STATISTICS / ^ 1 f*,, n % orsky Aircraft Division Ited Technologies Corporation g>tford, Conn. 06602 CM c bruary 1976 SaÜA nal Report 'i' Approved for public release; distribution unlimited. 5 r^ r »., ^ r7r\fp;":;y-::.;'-;n npf^" ... t.:- ,_. .i J^.iJ.,.'.! MAR 11 1976 D d!J Prepared for EUSTIS DIRECTORATE U. S. ARMY AIR MOBILITY RESEARCH AND DEVELOPMENT LABORATORY Fort Eustis, Va. 23604
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EUSTIS DIRECTORATE U. S. ARMY AIR MOBILITY RESEARCH AND DEVELOPMENT LABORATORY
Fort Eustis, Va. 23604
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EUSTIS DIRECTORATE POSITION STATEMENT
The CH-54 helicopter has been validated in the Army Reliability and Maintainability (R&M) Model. A factorial analysis was used to design a set of simulation experiments to determine model sensitivity, credibility, and sufficiency. Changes in operational . availability resulting from changes in TBO policy, major inspection policies, failure rates, Not Operationally Ready Supply (NORS) rates, and utilization rates were consistent with actual data from the field.
The conclusions contained herein are concurred in by this Directorate.
The technical monitors for this contract were Mr. Howard M. Bratt, Mr. Robert L. Walker, and Mr. Gary R. Newport, Military Operations Technology Division, Eustis Directorate.
DISCLAIIVIERS
The findings in this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents.
When Government uiawings, specifications, or other data ai.. used for any purpose other than in connection with a definitely related Government procurement operation, the United States Government thereby incurs no responsibility nor any obligation whatsoever; and the fact that the Government may have formulated, furnished, or in any way supplied the said drawings, specifications, or other data is not to be regarded by implication or otherwise as in any manner licensing the holder or any other person or corporation, or convoying any rights or permission, to manufacture, use, or sell any patented invention that may in any way be related thereto.
Tiade names ciluil in this repurt do not constitute an official undorscnienl or approval of the use of such commercinl hardware or software.
DISPOSITION INSTRUCTIONS
Destroy this report when no longer needed. Do not return it to the originator.
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(Continue on raver»» a'd« II n«ce«aa nd Identity by block number) i&v [ABSTRACT
The purpose of the CH-5^ Operational Statistics program was to validate th Ch-'yh helicopter in the Army's tactical aircraft reliability and maintain- ability model and to analyze the results obtained from the factorlally designed arrangement of simulation runs on sensitivity, credibility, and sufficiency. Changes in utilization, failure rate, N0RS waiting time^
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20. *» TBO concepts, major inspecLion durations, and repair/replacement time dis- tributions were studied. Effects on operational availability, intrinsic availability, unscheduled elapsed maintenance downtime (including and ex- cluding NORS time), and mission accomplishment were evaluated.
A baseline model was established by making successive simulation iterations and refinements until all output statistics tested fell within the allowable statistical range of the expected CH-'^H R8;M characteristics and operational conditions. ,ifl A
/v Among the ma\or findings of this program were:
a) Simulation error was very large, but could be reduced substantially by employing a factorial arrangement of simulation runs.
b) Simulation error could be further reduced if the model's logic were changed in the method of simulating failures.
c) Despite the large simulation error, sensitivities were able to be established for most parameters studied. Low utilization for the number of aircraft simulated was probably the primary cause for little or no change in mission accomplishment.
d) Types of repair/replacement distribution assumed do not alter the simulation results, provided the mean time to repair/replace value is correct.
e) Short-term scheduled maintenance requirements of 30 hours between major inspections as opposed to longer term "periodic" scheduled maintenance of 100 hours show indications of compromising opera- tional availability and maintenance man-hour resources.
The study results were substantiated on a rigorous statistical basis.
UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAOEftWian »•(• Enl.red;
SUMMARY
The CH-5^ Operational Statistics program was performed under Contract DAAJO^-T^-C-OOö^ for the purpose of validating the CH-51* helicopter in the Army's tactical aircraft Reliability and Maintainability (R&M) model and to analyze the results obtained from the factorically designed arrangement of R&M simulation runs on sensitivity, credibility, sufficiency and applica- 1 ion regimes.
The NORS and cannibalization subroutine was employed using CH-5^B ficxd data gathered through the ORME^ program and the subroutine was exercised throughout the study effort. The studies showed that employment of the NORS and cannibalization subroutine used in conjunction with an 8 hour a day, 5 days a week peacetime utilization introduces very large variation into the model. As a consequence, simulations covering a company unit operating period of 18 months were required to minimize this variability.
The CH-5^ program provides a new dimension into the study of simulation results in that it provides a statistical methodology for the acceptance or rejection of simulation results as sufficiently representative of known field flight operations and for the determination of significant fiimulation results.
A baseline model was established by making successive simulation iterations and model refinements until all output statistics tested fell within allow- able statistics limits of the expected R&M characteristics and operational conditions of the CH-^kB. Having established the baseline, changes in utilization, failure rate, NORS waiting time, TBO concepts, major inspec- tion durations and repair/replacement time distributions were studied.
Significant results found during this study were:
1) The simulation error associated with the operational availability model output is very large and hampers the ability of the model to measure the effects of major changes in Reliability and Main- tainability aircraft characteristics.
2) Despite the large simulation error, the model generally provides the expected results, for example, increasing either utilization, failure rate or NORS waiting time by 20% produced about the same
Note (l/: The ORME program which was completed in mid 197^ was a U. S. Army-Sikorsky Operational Reliability/Maintainability Program established to collect and evaluate Cti-^h R/M field data by trained R/M engineering personnel. Its purpose was to construct accurate and timely data profiles of failure and maintenance problems observed under monitored operational conditions and establish failure trends in order to intensify R/M improvement in current and future helicopter designs.
net effect, i.e., that of decreasing operational availability by 3%. A notable exception of this was found in attempting to measure the effect on mission accomplishment w üro the simulation error totally masked any cause/effect relationship induced by increasing NORS, failure rate, and utilization. Low utilization for the number of aircraft simulated appeared to play a wost significant part in causing little or no change in mission accomplistiment.
3) The ability to measure changes in operational response was enhanced by the use of the factorial analysis procedures in the study. The use of the factorial approach in this study not only minimized the influence of simulation error which threatened to cloud the determination of real changes in model output, but also substan- tially reduced the number of simulation runs required to perform the analysis. In many cases this reduction in runs was by a factor of 3 to 1.
The simulation error of this model is large and the number of iterative aiaulation runs required to establish the validity of the model and to ptrform sensitivity studies was excessive despite the mollifying influence of the factorial approach. A method is recommended for minimizing the simulation error of the R/M model which will have the combined effect of reducing the number of iterative runs required and improving the sensitivity of the model. This recommendation involves a change in the method of simulating failures according to "when discovered" events.
PREFACE
The work for this sLudy was authorized by Contract DPJ\J02-lk-C~006h by the Eustis Directorate, U. S. Army Air Mobility Research and Development Laboratory, Fort Eustis, Virginia, under the technical cognizance of Mr. Howard Bratt, Mr. Gary Newport and Mr. Robert Walker.
The Sikorsky Aircraft personnel involved in performing and contributing to this study were:
Mi. A. A. Wolf, Supervisor of Reliability and Maintainability
Mr. R. W. Caseria, Reliability Engineer and Program Manager
Mr. J. V. Stern, Computer Programmer
Mr. N. T. Spencer, CH-^ Field Reliability Engineer
Mr. C. D. Holbert, Maintainability Engineer
Mr. J. K. Bosse, Computer Programmer
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PRECEDING PAGE BLANK-NOT FILMED
TABLE OF CONTENTS
PAGE
SUMMARY 3
PREFACE 5
LIST OF ILLUSTRATIONS 8
LIST OF TABLES 9
INTRODUCTION 11
DISCUSSION 12
CH-^B Aircraft Description 12 CH-5I4B Aircraft Operation ih CH-5I+B/R&M Model Characteristics 17 Validation of the CH-^B , . . 17 Sensitivity Analysis of the CH-5^B Model Using Factorial Analysis Approach 22
CONCLUSIONS hi
RECOMMENDATIONS h2
APPENDIXES hk
I. Element Identification and Failure Rate kh II. CH-J^B Model Input Function Definition 50
III. CH-5itB Model Input Function Listing 57 IV. CH-5^B Model Program Update and Program Listing with Necessary
Modifications to the Government-Furnished Model Identified 80
V. Factorial Approach to Simulation Model Sensitivity Analysis 125
LIST OF SYMBOLS AND ABBREVIATIONS 136
LIST OF ILLUSTRATIONS
FIGURE PAGE
1 CH-^B Model Input/Output Description 13
2 Convergence of CH-^B/R&M Model Output Statistics .... 20
3 Percentage Difference Between Statistical Output of the Two Stability Runs with Least-Squares Fit 23
4 Utilization Boundry 27
5 Test Regxon Studied 2?
6 Operational Availability Contours 36
T Alternative Elapsed Maintenance Time Distributions ... 30
8 Observed Operational Availability Values 127
LIST OF TABLES
TABLE PAGE
I System/Event Maintenance Action Distribution l6
II ORME Verification Statistics 19
III Comparison of Baseline Simulation Model Statistics With Expected Baseline Values 25
IV Simulation Statistics - Comparison of Expected Values and Simulation Statistics for Factorial Test Points .... 28
V Analysis of Simulation Error 31
VI Simulation Statistics for Various Test Conditions 32
VII Comparison of Actual Difference of Expected and Observed Values and the Allowable Difference 33
VIII Factorial Analysis of Operational Availability 35
IX Significant Effects from the Qualitative Factorial Analysis 39
X Element Identification and Failure Rate ii5
XI On and Off Aircraft Maintenance Requirements 55
XII Factorial Analysis Worksheet for Operational Availability . 126
XIII Factorial Analysis of Unscheduled Elapsed Maintenance Down Hours With NORS, Failure Rate, and Utilization as Factors . 129
XIV Factorial Analysis of NORS Plus Unscheduled Elapsed Maintenance Down Hours With NORS, Failure Rate, and Utilization as Factors 130
XV Factorial Analysis of % Intrinsic Availability (Flight Hours/Flight Hours + Unscheduled Down Hours) With NORS, Failure Rate, and Utilization as Factors 131
XVI Factorial Analysis of % Intrinsic Availability (Flight Hours/Flight Hours + Unscheduled and Scheduled Down Hours) With NORS, Failure Rate, and Utilization as Factors .... 132
XVII Factorial Analysis of Direct Maintenance Man Hours/ Flight Hour With NORS, Failure Rate, and Utilization as Factors . . . ; 133
LIST OF TABLES (CONTINUED)
TABLE PAGE
XVIII Factorial Analysis of % Mission Accomplishment (Missions Completed/Missions Called) With NORS, Failure Rate, and Utilization as Factors 134
XIX Factorial Analysis of NORS Hours With NORS Component Waiting Time, Failure Rate, and Utilization as Factors 135
10
LNTHODUCTION
This program was undertaken to validate the Army R&M model for use in simulating CH-^B operation. A secondary but equally important purpose was to incorporate some statistical rigor into the measurement and inter- pretation of the simulation results.
The information collected and analyzed during this program is presented in the following seven sections:
(1) CH-^B Aircraft Description
(2) CH-5I+B Aircraft Operation
(3) R&M Model Data input for CH-^tB
(U) R&M Model Program Updates to Accommodate the Cll-^B Aircraft/ Operation
{5) Validation of the CH-^B Version of the R&M Model
(6) Statistical Analysis of Simulation Results
(7) Conclusions and Recommendations
The CH-5^B field experience used in constructing the CH-5^B version of the R&M model was primarily taken from the Operations Reliability/Maintain- ability Engineering (ORME) program. This was an Army/Sikorsky data collection and product improvement program which included 3 years of CH-5^B operation by 25 aircraft. The ORME program provided the expected values used in the CH-51+B/R&M model validation.
The sensitivity studies were based on varying certain aircraft and opera- tional factors in a factorial design arrangement to improve the statistical interpretation of the simulation results. The methods of varying these factors were optional in some cases. In the case of utilization, this chang. was produced by varying the number of mission launches per day as opposed to varying the number of aircraft required for a mission or the mission duration. The NORS factor was varied by changing the delay time to acquire a spare rather than changing the probability that a spare part was needed but not available.
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DISCUSGION
The CH-5^B model is a modification of the UH-1N R&M simulation model which was supplied to Sikorsky Aircraft by the Eustis Directorate. The first part of this discussion describes the CH-^B aircraft characteristics and CH-^UB operational environment that are being simulated. As part of the aircraft description, Appendix I is provided to identify the elements of the CH-^hB and their failure rates. Following this information is a discussion describing the specific input and model logic changes incorpo- rated into the original UH-1N R&M model Lo construct the CH-^Uti model. Appendixes II, III, and IV further identify these modifications. The last part of this discussion describes the CH--5^B model validation effort and a statistical analysis of the simulation results of running the model under a variety of alternative operating conditions and maintenance concepts, and the conclusions and results derived therefrom. Appendix V provides additional detail on the factorially designed statistical analysis performed in this program. Figure 1 illustrates the input, constraints and output that are essential to the CH-5^B model described herein.
CH-^B AIRCRAFT DESCRIPTION
The CH-5^B is a crane-type, ^C^OOO-lb category helicopter. It has been used extens:' /ely in Southeast A.sia to move heavy Army equipment and to retrieve downed aircraft. The operation simulated in this program, however, is peacetime, state-side operation.
For the purposes of the R&M model input function structure for failure, repair, and replace information, the CH-5^B has been identified according to the following subsystem/component breakdown, which has been described as consisting of 20 subsystems comprising a total of 2Q6 components. The categories of main and tail rotor blades, engines and fuel controls are represented by more than one component element to permit tracking each blade, etc., individually for monitoring their scheduled TBO removal times. The system codes to be used in describing the 20 subsystems and their components are consistent with those used in the Operational Reliability/ Maintainability Engineering (ORME) program and are identified below.
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The individual component identifications and the failure rates observed in the field relative to the components identified are contained in Appendix 1, This information was taken from the ORME program and is representative of the 3-year history reported in SER-61+3Ui*, Revision K..^ The time change components, as identified in the CH-5^B Organizational Maintenance Manual, TM 55-1520-217-20-2, are shown below with their high time removal limits.
Components
Main Rotor Head Tail Rotor Head Main Rotor Blade Tail Rotor Blade Main Gearbox Intermediate Gearbox Tail Gearbox AECS Servo Assembly Fuel Control Engine Cargo Hoist
Number of Items TBO (Hr)
1 800 1 800 6 2500 14 1600
1 625 1 1200 1 1200
1 1200 2 800 2 800 1 21+0(2)
CH-5^B AIRCRAFT OPERATION
The CH-5^B baseline operation is comprised of the following information.
. CH-51tB Company Unit = 9 aircraft . Operational Week = 5 Days . Operational Day = 8:30 a.m. to k:30 p.m. . Number of Standby Aircraft = 1 (of the 9) aircraft . Number of Holidays and General Inspection Nonflying Days = 18 Days per year
. Flight Hours for a 9-A/C Company Unit for 18 Months (28 Days/Month): 239^ Hr, 1596 FH/Year, ik.Q FH/AC/Month
. Operational Availability = 5k.5%
(1) Geffert, G. , and Holbert, C. , Operations Reliability/Maintainability Engineering Program Quarterly Evaluation Report, Sikorsky Aircraft, SER-6U31+1+, Rev, K, May 15, 197^
(2) Since the cargo hoist is used for no more than 10^ of the missions, the simulation model input actually reflects 21+0/.1 = 21+00 hours.
The company unit maintenance force used in the baseline operation is as follows :
Maintenance Specialist
a) A/C Maintenance Tech. b) Helicopter' Repairman c) Electrician d) Avionics Mechanic e) Airframe Repairman f) Engine Repairman g) Tech. Inspector h) Hydraulic Repairman i) Power Train Repairman j) Flight Engineer
To provide a realistic distribution of failures for the various operational events for the baseline, information was taken from the CH-5^ ORME program. Specifically the information was taken from the ORME Discrepancy/Corrective Action Reports. "When discovered" data and, in the case of in-flight aborts, the effect on mission data from these reports were used. The rela- tionship between the data as collected through the ORME "when discovered" codes and the R&M model's operational events is shown below. In the cases of special inspections, acceptance inspections, transfer inspections and "on ground - not covered by above" actions, some engineering judgement was required to appropriately enter this data into th,-? model. These judgements are indicated below and were made based on discussions with Sikorsky ORME reliability engineers and with the manager of the ORME program.
Relationship of ORME Data to R&M Model Requirements
ORME R&M MODEL
J Exterior & Interior Checks — AFP Start to Takeoff In-Flight On Ground to Eng. Shutdown'' Daily Inspection Intermediate Inspection Periodic Inspection — Special Inspection rrr Acceptance Inspection Transfer Inspection^)
On Ground - not covered by above
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Preflight In-Flight In-Flight Aborts (as further deter- mined by "effects on mission" code) Daily Inspection Intermediate Inspection Periodic Inspection Prorated over 1, k, 3, and 6 above Not Included Not Included Prorated over 1, k, 5, and 6 above
Table I shows the number of observed M.A.'s in the 9172 CH-5l*B flight hours (including those M.A.'s prorated) and the resulting system by system cumu- lative probability distribution for each aircraft operational event.
(3) M.A.'s discovered daring acceptance and transfer inspections together accounted for only .6% of the total M.A.'s and were not included since they occurred before, or were found after, the normal operation/mainte- nance cycle of the CH-5^.
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The Cti-'jkh H&M model incorporates an 8 hour a day, '; day a week, 28 day a month operation. The company unit strength of 9 aircraft has a flight operational requirement of approximately lH.8 flight hours per aircraft per month. Preflight, daily, intermediate, and periodic inspections are re- quired. The average mission duration is 1.9 hours with .7 hours required for test hops. The model is detailed to reflect the failure rates, mainte- nance manhours to repair and to replace, and the elapsed maintenance times on approximately 300 components. Abort data, probability of the aircraft being not operationally ready, and requirements for test hops are also defined for these components. This information is covered in detail in the two previous sections and in Appendix 11.
VALIDATION OF THE CH-b^B
The validation of the CH-5^B simulation model consists of three essential steps: the establishment of the CH-5^B baseline model expected values as determined from OHME data, the evaluation of the simulation error associ- ated with the CH-^B/K&M model, and finally the verification that the model has been revised and refined to agree with the expected values within the allowable tolerance permitted by the simulation error.
Table II contains the expected values for the baseline simulation. These are key field experience statistics collected through the CH-5'+B ORME pro- gram which provide the basis for validating the CH-5^B simulation model output values as representative of CH-S^B field experience. The information reflected in the table was accumulated over a 36-raonth period that extended from 1 April 1971 to 31 March 191^- The operational sites monitored were Ft. Eustis, Ft. Sill, Ft. Rucker, and Ft. Wainwright.
The CH-54B ORME program report SER-61t3^ , Revision K, reflected a history of ^(22,592 total aircraft hours, of which 9171.6 were flight hours. Of the 422,592 hours, 55^ were discounted because they were associated with a downed Alaskan aircraft in which parts were not ordered for its re- activation. Total accountable aircraft hours were, therefore, ^22,592 - •?5hk, or 417,0^8.
Because of the low CH-51+B utilization, i.e., 9171.6 flight hours in itl7,Ol48 total hours, or 2.20^ utilization, and because of the added simulation variation resulting from the incorporation of not operationally ready due to supply (NORS) and ca-mibalization data into the CH-5^B simulation model, runs simulating l8-month company unit operation were needed to provide sufficiently accurate simulation output statistics for meaningful analysis. The need for the l8-month simulation runs is discussed further in the next section. As a result of the l8-month simulation duration, however, 9 air- craft x 2k hours per day x 28 days per month x l8-months, or 108,86it accountable aircraft hours, were reflected in the simulation runs. This resulted in a 9171.6 flight hour x {löQ,%k/kn,0hQ) or a 239^.1 flight hour requirement for the l8-month baseline CH-'^B simulation.
17
Tutal L'ailure rales and abort rales shown in Table 11 have been taken from the .'iriK-O'ij't't, Revision K, and the failure rat« distribution has been de- rived i'roin the study of the UHMK Discrepancy AcMon Reports. The failure rates include both primary and secondary failures. They specifically ex- olude corrective maintenance actions found to be needed during acceptance and transfer Inspections which account for .6 percent of the total correc- ' ive actions observed In C\\-Cjhli operation. C'anniballzation M.A.'s which are incorporated into the model by way of probability of cannibalization indices and scheduled component replacement actions which are taken care of through the scheduled TBO subroutine are also excluded from these rates. Therefore, the model failure rate descriptions together with the M.A.'s accounted for by the cannibalization and scheduled TBÜ subroutines approx- imate (J').h percent of the total observed CH-'JiB M.A.'s. The failure rates shown in Table II translate into the followinr •v.pected number of failures for the various Cli-'^hh operational events, based on the expected 239^ flight hours.
Cti-jhli invent Fail. Rate x Kit. Time = Expected Failures
Preflight .03069F/Hr x 239^ Fit. Hr = 73 Failures inflight .16333F/Hr x 239k Fit. Hr = 391 Failures rnflight Abort . 0l8l0F/Hr x ?391( Fit. Hr = 1+3 Failures PMI .02213F/Hr x 239^ Fit. Hr = 53 Failures Dally .12093F/lir x 239^ Fit. Hr = 290 Failures PMP .109,4 2F/Hr x 239-'* FU. Hr = 262 Failures
To determine what simulation duration was appropriate for estimating simulation error and for the factorial analysis study, the stability of the output statistics was analyzed over an Id-month period.
Figure 2 shows the convergence of important statistics exhibited by the CH-'jhii version of the R&M model over the simulation duration. To provide these statistics, two simulation runs were made under identical conditions, except for different random number sequercss, and statistics were collected after each 2-month interval for the duration of the 18-month simulation. To highlight the variation of output values as the simulation progressed, the statistical value accumulated to the end of a period was compared with the value reflected at the end of the previous interval, and the percentage of differences was computed and plotted. The values were plotted through the löth month. The plots were examined first to see whether any systematic error was evident. If the trend lines fc- the simulation runs reflected values that were consistently plus or consistently minus, then it would be reasonable to conclude that the mod il has not stabilized and was still seeking its normal long term, average operational condition. Review of this figure shows no evidence of systematic error. Second, the plots were examined to evaluate whether the improved stability of the 18-month statis- tics was sufficient to warrant the longer simulation running time. The plots showed no profound change in the stability of the statistics after the 10th month. The low CH-5^B utilization, however, was known to cause high simulation error which could cloud the true operational characteristics. To obtain a better appreciation of this simulation error, statistical outputs from the two different runs were compared with particular attention paid to
18
TABLE ll. ORME VERIF'TCATIOiJ STJ\'l'IS'flCS
CH- 54R Ope rati o nal Data (April ' '11 to March •·(!l)
Total Airc r a ft Hours ( I nclude 21a Hr a Day , 7 Days a Week Accoun ab ility )
To tal Ac ive ho urs
To o l Fli gh t Hours
F'libht iiour s per A/C per ?~ont.h
Total Failur e Rate
To al Abort Rate
F'nilu r e Hate Di s t r ibution
r eC'litht In flight Daily PMI !1-IP
~umber of F' l i ~ts
T s t Hop F' li gh flours ( Subeate~;ory or t he 917 1. 6 F'li~;ht. Hours)
Ope r uti ng and Heady !lours
Oper·at i onal Avul l llbility = (227 , 248t417 ,048) X 100
19
Dut<: Sou.r ce & Value GER- 61, 344 OHME lJiscr e p/
Rev. K tor r . Act. Hpt.s .
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'igure 2. Cuuvergence of CH-^iB/R&M Model Otitput Statistics.
20
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Figure 2. (Continued!
21
the 10th through loth month region. Least squares trend lines using the data I'rora the 101,li through the löth month were computed and drawn. The dilTerences in statistical values between the two runs are shown in Figure _J,, together with the trend lines. based on these trend lines, about a 25 per- cent reduction in scatter between the two runs, when averaged over ail eight statistical trends studied, was achieved. Operational availability and mission accomplishment did not exhibit the characteristic improvement, how- ever, the fluctuation of these statistics is such that exceptions to the normal trend will frequently occur. The important fact is that a general improvement in statistical scatter has beeti achieved by extending the simulated duration to 18 months. Therefore, to help guard against the adverse effects of large variation, the l8-month runs were considered desirable and were used in the subsequent studies.
Table 111 compares the baseline simulation model statistics with expected baseline values. Four separate l8-month simulation runs were made with the CH-^B baseline model with the random number seed changed. These four runs permitted the evaluation of the error inherent in the simulation model it- self. Table 111 shows the expected values for the subject baseline model and the simulation deviation allowed from the expected values as determined from the four simulation runs referred to above. If the specific simula- tion run output statistics deviate from the expected values by more than the allowable values, the run is judged to be nonrepresentative of the expected values and further refinement of the model is required. The allow- able deviation has been determined on a rigorous statistical basis and conforms to a level of significance criteria of a = .01. This means, given that the model is truly representative of the expected values, there is only a \% chance that a specific simulation statistic will deviate from the expected value by more than the allowable deviation value. Conversely, since this possibility is so remote, if a value does fall outside the allowable limit there is sufficient statistical justification to conclude that the simulation model does not fully represent the expected value and further refinement is required.
After successive simulation iterations and refinements to the model, a baseline model was established in which all output statistics tested fell within the allowable statistical limits; i.e., the resultant model was found to adequately represent the inherent R&M characteristics of the CH-5^B when flown in accordance with those operational conditions reflected in the ORME operational data. As indicated above, Table V shows the allowable deviation and the actual difference recorded between the baseline model statistics and the expected values. In all cases these differences were within the allow- able deviation, thus giving statistical credibility to the baseline model as adequately representing the expected values.
SENSITIVITY ANALYLSES OF THE CH-^B MODEL USING FACTORIAL ANALYSIS APPROACH
Two factorial analyses were selected for study, one having quantitative in- put levels of utilization, failure rate and not operationally ready due to spares (NORS) varied, and the second having the qualitative factors of major inspection maintenance concepts, elapsed repair/replacement time distribu- tions, and on-condition removals studied.
22
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The first factorial analysis was originally set to study the effects on operational availability and other output statistics caused by changes to the baseline ranging from -25 to +25 percent for NORo and 0 to +20 percent increase in utilization and failure rate. These points of consideration were the corners of the right-hand cube shown in Figure h. When these test conditions were studied, an upper bound was discovered to exist beyond which the company unit utilization could not be reached. This required a change in the study points for the factorial analysis from a center point that measured the baseline (BL) plus 10 percent utilization and an upper set of points that evaluated BL plus 20 percent utilization to equivalent points for the factorial analysis measuring BL minus 10 percent and BL minus 20 percent. in Figure k the left hand cube shows the changes required in the test region due to the utilization limit. Figure 5 shows each of the test conditions simulated and studied. These test conditions are identified in terms of flight hours per aircraft per month for utilization, failures per hour for failure rate, and percentage increase/decrease in NGRS for supply. Table IV shows these test condition values and the associated expected values of key operational parameters. The test conditions were simulated for the revised set of study points. Test point 5 was repeated four times and Table V shows the results. These four runs were discussed in relation to measuring the simulation error rela'.ive to the baseline run and are used throughout the analysis to justify computer runs being suffi- ciently close to the expected values to be statistically acceptable at the .01 level of significance. To compute the 1 percent level of significance, the standard deviation was computed for each significant statistic and multiplied by the normal distribution coefficient of 2.576, which corre- sponds to the 1 percent level of significance. As indicated above, all baseline values were checked with this deviation criterion to prove that the simulation results were sufficiently close to the expected values to be accepted as representative of the 0RME operational statistics expected values.
iterative computer runs were made at each of the study points until they were in the region of acceptability. One point was found to be out of limits. Condition 3, which was felt to be influenced by the utilization boundary, was out of limits. However, this point was accepted for the analysis because the expected flight-hour value could not be reached despite several attempts to get. closer to the expected value. Saturating the flight schedule would permit the flight-hour value to be reached, but this would distort other important output statistics such as mission completion values. Although the analysis is slightly distorted by the use of this study point result, the distortion was not considered, in an analysis of this sort, to be sufficient to seriously jeopardize the overall study results. In the factorial analysis employed, the low and high utilization points are averaged over four values each, and therefore, any error is desensitized by this averaging process. Table VI shows the simulation statistics generated for the various test conditions. Table VII shows the difference between the values expected at each study point and those observed after successive iterations. Test point 1 shows an out-of- tolerance condition for inflight failures, but since at the total failure level the number of failures observed was in tolerance., the run was consid- ered to be acceptable. It should be noted that Table VII defines over 100
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tests of significance al the 1 percent level; therefore, it is highly likely that one statistic in 100 would be found slightly out-of-tolerance. Test point j has already been noted. Afte'" several iterations, the computer run exhibiting the closest value to the expected utilization was chosen for the analysis with ^he recognition that some error would be introduced into the analysis.
The first factorial analysis includes a study of the eight basic factorial analysis points to ascertain how, for example, the simulation output opera- tional availability changes in relation to discrete changes in utilization, failure rate and NORS levels. It also includes the incorporation of the center point data to assess the curvature associated with the surfaces reflecting constant operational availability. The definition of operational availability used here is
Operational Availability =
Flight Time + Ready Time
Fit. Time + Ready Time + Corr. Maint. + Prevent Maint. + Supply & Admin. Downtime
Table VIII shows tne factorial analyses results for operational availability. Table XIII in Appendix V shows in expanded arithmetic detail the information contained in Table VIII. The values for availability have been taken from Tables V and VI. Several observations must be made before proceeding. First, from a statistical viewpoint, there are eight degrees of freedom (df) associated with the data shown in the "Aircraft Availability Values" column since the data is derived from eight distinct test points. In the center point evaluation of the simulation error, four test points, and therefore a df of four, are reflected: one associated with the mean and three associ- ated with the variance. Using an F level of significance test, the computed effects can be analyzed to determine whether they are true effects or simply perturbations due to simulation error. Bases on an a = .05 and the df information above, if the F statistic (equal to the mean square value divided by the simulation error) exceeds the F distribution value for a .05 level of significance with 1 df in the numerator and 3 df in the denomina- tor, then the effect associated with the mean square is judged to be a real effect. The critical Fj^ 3 distribution value for a = .05 is 10.1, and the F statistic in the case of the NORS effect is l&J.12/h.06, or 1+1.3- There- fore, the change in operational availability due to the computer input change in NORS level is real, and the best estimate of this change is -9-16 percent in operational availability when the NORS level is changed from its low to its high value. The changes in operational availability due to changes in failure rate and utilization are also found to be real.
This information coupled with the center point data permitted the drawing of operational response surfaces. These surfaces are shown in Figure 6 together with the contour lines of constant operational availability dis- played on each face of the cubic space studied.
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36
From Lhe analysis of the first factorial arrangement as it applies to operational aviilabiLlty, the folJowing conclusions are drawn.
(1) The simulation error in relation to the operational availability model output is large and hampers the ability of the model to measure the effects of major changes in aircraft R&M characteristics. As a consequence, the contour lines and surfaces of constant operational availability shown in Figure 6 must be somewhat uncertain.
(2) Despite the large simulation error, the model yields consistent re- sults; for example, decreasing the utilization by 20 percent has approxi- mately the same effect on operational availability as decreasing failure rate by 20 percent. The utilization decrease results in about L),h percent- age decrease in availability; failure rate results in about 6.^ percent. The NORS level was decreased about hO percent and resulted in a proportional 9.2 percent increase in availability.
(3) The consistency is enhanced by the employment of the factorial arrange- ment. Although only eight test points were used to measure the effects of changes in utilization, failure rate, and NORS, the factorial arrangement permitted all eight test points, four at the low factor level and four at the high factor level, to be used to measure each factor response. This provided a major improvement in accuracy per test point over an arrangement which would measure each factor separately.
{k) Because of the high number of computer iterations required to "home in" on the factor levels of utilization and failure rate, especially failure rate, the study was limited to tue factorial analysis indicated in the statement of work; however, a more forceful and exacting experimental design could be employed, if the required number of iteration runs could be cut down. The experimental design referred to is called the central composite design and is discussed in 0. L. Daves book on Experimental Design.^) This test design would provide a major improvement in computing i^he response surfaces. Figure 6 is simply a synthesis of the 8-point factorial analysis results shown in Table VHI and the center-point analysis also shown in that table.
To evaluate the overall sensitivity and credibility of the CH-5^B model, several output parameters were evaluated on a statistical basis. Three levels of significance were used: a = .10, where the results were consid- ered to be significant; a = .05, where the results were considered to be highly significant; and a = .01, where the results were considered to be very highly significant. The reason for considering several levels of significance is that an overall appreciation of the model's output is the focal point of this part of the evaluation, rather than decisionmaking. In a decision situation, one level of significance would be chosen based on
[h] Daves, Owen L., DESIGN AND MALYSIS OF INDUSTRIAL EXPERIMENTS, Second Edition, New York, Hafner Publishing Company, 1903, pp 532-553.
37
the consequences of making a wrong decision. In this evaluation the interest lies in the question; do the expected effects show up using this model, and how pronounced are those effects? In other words, are the effects believable, and how sensitive is the model to changes in aircraft quality or operational conditions? Table IX contains a listing of the effects shown to be significant, and Appendix V shows the computational detail establishing these effects as significant.
Failure rate, utilization, and NORS waiting time were the factors varied. The output values selected for study were unscheduled elapsed maintenance down hours; NORS hours plus unscheduled elapsed maintenance down hours; percentage of intrinsic availability where intrinsic availability measured the proportion of flight hours to flight hours plus unscheduled down hours and also the proportion of flight hours to flight hours plus scheduled and unscheduled down hours; direct maintenance man-hours per flight hour; per- centage of mission accomplishment; and finally, observed NORS hours.
Table IX contains a summary of the responses found to be significant and estimates of these responses. The expected responses are summarized as follows. An increase in NORS waiting factor should adversely affect all the output statistics except those that measure active maintenance down time alone, namely, unscheduled elapsed maintenance down hours and direct maintenance man-hours per flight hour. An increase in failure rate should adversely affect all the output statistics. Finally, an increase in utilization should adversely affect all output statistics except intrinsic availability and direct maintenance man-hours per flight hour which would be expected to remain constant with increased flight hours.
The consistency of the actual significant effects with those expected is apparent. The major exception to this is in mission accomplishment, where it is expected that increases in NORS time, failure rate or utilization would cause less aircraft to be available and therefore less chance of performing and completing a mission that is called. In this instance it must be concluded that ehe model is not sensitive enough to measure the change in mission accomplishment for tue changes in the levels of the factors analyzed. Another exception of concern was in direct maintenance man-hours per flight hour, where an increase in utilization has resulted in a decreased value for this statistic. Reflecting on the reasons that could cause this phenomenon led to an investigation of the difference in scheduled maintenance requirements per flight hour for both daily and preflight inspections. The four low utilization runs showed the need for .692 daily per flight hour and .727 preflight per flight hour, and the four high utilization runs showed .600 and .702 respectively. As the utilization goes up, therefore, the need for additional dailies and preflights goes uv much more £,lowly, resulting in the lower scheduled maintenance man-hour per flight hour requirement. Table IX shows that the best estimate of the difference ,-.n direct maintenance man-hours per flight hour is -.57. Since it takes 5.'» man-hours per flight hour for performing daily inspections and 1.8 for preflights, the expected difference from this source should be
(.600 - .702) 5.1t + (.692 - .727) 1.8 = -.61
38
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Again this shews the consistency of the CH-5^B model and shows that, relative to certain statistical output, the model has a very sensitive response.
The above analysis is a further indication of the areas of sensitivity and lack of sensitivity produced by the CH-5^B model, and of the care that must be exercised in the interpretation of results relative to the simulation error. The factorial analysis method employed here provides a viable and efficient method of minimizing the effects of this simulation error and should be seriously considered for use in all subsequent simulation studies of this type.
hO
CONCLUSIONS
Conclusions are presented Tor five general area:;: the variation associated with the model; the adequacy of the C!i-5^B model; the conclusions derived from the factorial analysis varying factors of NORS waiting time, failure rate, and utilization; the conclusions derived from the factorial analysis varying factors of major inspection policy, TBO policy, and repair/replace- ment time distribution; and finally, the conclusions derived from the sta- tistical methodology employed.
The CH-ljhb model evidences a very large variation in operational availabil- ity and other output statistics. A large part of this variation is associ- ated with the use of the NORS and cannibalization subroutines. Also, a low daily utilization of aircraft contributes to this variation. Despite this variation, the model yields statistical output that is consistent with expected changes in operational parameters.
The CH-5^B baseline model was verified to reflect known CH-5^B field opera- tion as reported by the ORME field data collection program. This veri- fication of tne baseline model established that, within the error inherent in the model itself, the utilization, failure rates, and other aircraft/ operational parameters were found to be representative of the ORME field data.
The simulation error associated with CH-5^B R&M simulation model output was large but, due to the improved ability of the factorial analysis procedure to measure operational responses, changes in NOR waiting time, failure rate, and utilization factors, provided statistical output that was consistent with expectations and was relatively sensitive. For example, increasing either utilization, failure rate, or NORS waiting time by 20% produced about the same net effect of decreasing operational availability by 3%- This con- sistency and sensitivity were true for all statistical output studies, which included measures of intrinsic availability, direct maintenance man-hours per flight hour, unscheduled elapsed maintenance down hours, and not opera- tionally ready time due to spares. The lone exception to this sensitivity was in the measurement of mission accomplishment (ratio of missions called to missions completed). Increased NORS waiting time, failure rate, or utilization would be expected to reduce mission accomplishment, but it was found that the model was not sufficiently sensitive for the prescribed 18- month simulation operation to measure this reduction.
The final conclusion is that statistical procedures are required to analyze the R&M model simulation output if real effects are to be discerned from random scatter and that factorial analysis is an important statistical procedure to minimize the required number of simulation runs.
ill
RECOMMENDATIONS
i. The CH-'^B model, which incorporates NORS data, evidences large varia- bility in its simulated output, making it difficult to measure effects and creating an unnecessary number of iterative runs to home in on the failure rates associated with the specific condition simulated. This large varia- bility is associated with how the basic R&M model is constructed and is inherent in the UH-1N model as well as the derivative CH-5^B model. In the daily inspection, for example, a probability distribution of the number of failures is input to the model based on an expected number of daily inspec- tions. Since the number of dailies can easily vary by T^5 as is reflected in Table VIII in the spread of daDly inspections for different random num- ber seeds, this variability is added to that created by the probability distribution of the number of failures. This probability distribution reflects the Poissun distribution based on the exponential time to failure, which implies a totally random occurrence of failure. The Poisson proba- bility distribution already reflects the maximum spread of failure rates that should be expected. The introduction of variation due to the number of dailies unnecessarily and unrealistically magnifies this variability. It is recommended, therefore, to substantially reduce the computer time for the same simulation accuracy or, conversely, to substantially improve the accuracy for the same simulation time, that the model be changed in the method of simulating failures. Rather than simulating the number of fail- ures each time a daily occurs, simulate failures independently of the events and then assign them on a probability distribution basis to the various events. This approach would not only eliminate unrealistic model variabil- ity, but would do it in a way that would simplify the model input function requirements.
The Reliability and Maintainability (R&M) Model currently used by the Eustis Directorate, USAAMRDL, has been modified to incorporate the failure methodology outlined above. The GAMMA distribution is used to compute the time to next failure, for each component, in terms of aircraft operating hours. When the aircraft reaches the precomputed operating hours, the component fails. Monte Carlo techniques are employed to determine if the failure is discovered at the time of failure, in subsequent missions, or in an inspection event, such as daily, preventive maintenance periodic (PMP), etc. The failure is placed on a list of other failures awaiting discovery when the appropriate event occurs.
2. It is further recommended that a statistical methodology be established for use in subsequent studies employing the R&M simulation model or the ARMS model. This methodology should be based on the statistical procedures put forth in this study. This methodology should encompass:
a) Evaluation of simulation error. b) Validation of baseline model as consistent with expected values
using a level of significance criterion in conjunction with simulation error measurement.
c) Use of factorial analysis procedures to evaluate alternative operational conditions.
^2
d) Use of central composite design where response surface studies are desirable.
The establishment of such a statistical methodology would substantially enhance the efficiency of performing these studies, would produce improved sensitivity analyses, and would provide a better grasp and understanding of the trends brought about by changes in aircraft/operational character- istics .
h3
APPENDIX I ELEMENT IDENTIFICATION AM) FAILURE RÄTE
Table X contains the numerical codes used to identify the subsystems and elements of the CH-5^B. The element nomenclature and the failure rate associated with each element are identified in this table.
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^9
APPENDIX II C\l-5hB MODEL IMPUT FUNCTION DEFINITION
The K&M model input data as organized from the ORME information base is described for the various functions below. These functions relate an independent value in the simulation model to a dependent value, and through these functions , the specific CH-5^B aircraft/operation characteristics are introduced into the R&M model. For example, when the daily inspection logic is encountered in a model simulation and the probability of success- fully passing the inspection without discovering a failure is required. Function 2, independent value l6, is located and the CH-5^B value of .8l378l is introduced into the simulation as that probability. This input data described is for the baseline model which has been used in the validation of the CH-5^B. Appendix III contains a detailed listing of all CU-^hB input functions.
Function 1
An average 1.9-hour single-point winch mission configuration flight was considered.
Function 2
Probability values for successfully passing various ground events without discovering a failure, to be used in the CH-5^ baseline simulation, are given as follows:
11 (Turnaround Insp.) .999999 16 (Daily Insp.) .813781 17 (Periodic Insp.) .000020 21 {% Good Parts from Supply) .96OOOO
Events 1, 5, and 11 were, in effect, ignored by entering a probability of success of certainty into the function, since based on observations of Sikorsky ORME reliability engineers, these three ground events do not occur in CH-5UB operation. Probability values for events 2, 8, l6 and 17 were based on actual CH-5iiB failure rate records as reported by the ORME program. The probability value for event 21 is based on discussions with ORME reliability engineers, and its relatively high rate of bad parts from supply is born out by a joint AMRDL/Sikorsky helicopter maintenance effectiveness analysis study.'5)
The probability of no maintenance action diseovereu during flight is .737^7?. This was determined from the OHME Program Quarterly Evaluation Report, SER-6^3^^, Revision K. The "when discovered" summary of the number of maintenance actions of Table II shows 1^98 M.A.'s in 9172 flight hours, or a .1033 rate of corrective maintenance actions to flight hours. For a 1.9-hour mission and a .7-hour test flight, the probabilities of sustaining no M,A.'s are
P(0) = e--l633 x 1.9 = .7332 & p(o) = e-.l^3 x .7 = .8920.
Aborted missions reduce the average mission time, resulting in the higher function 3 values.
Function h
From SER-6U3W, Revision K, the average flight durations were found to be between .7 and .8 hour for test hops and between 1.8 and 1.9 hours for single-point winch. Because .7 and 1.9 yielded the closest baseline flight hours, they were chosen.
Function 5
From SER-6I43W, Revision K, the probability of no abort given a M.A. in- flight was found to be .8892. Data from this SER showed l66 aborts in 1^98 in-flight failures, or probability of abort equal to
166 = .1108 1^98
Therefore, P(no abort) = 1 - .1108 =
Function 6
This function defines the number of maintenance men, the maintenance work centers, i.e., the maintenance manpower specialty codes, and the elapsed maintenance times, as observed in the ORME preventive maintenance repor- ting forms to perform the preflight and daily inspections. The function reflects the following information:
Preflight requires two helicopter repairmen for .9 hour.
Daily requires two helicopter repairmen for 2.7 hours.
Function 7
The logic in the R&M model is so constructed as to reverse the priority convention used in the basic GPSS computer language. The priority values referred to in this function are for obtaining manpower to perform the various inspection events. This maintenance priority function, therefore, assigns the lowest priority numbers to the highest priority events. As
51
noted in the following assignment, of priority numbers, the highest priority event is prel'light, followed in order by daily, PMI and FMP inspections. These priorities agree with actual CH-5'iB operations as observed by Sikorsky ORME reliability engineers.
Function T values are:
Event Priority No.
Preflight 5 Daily 15 PMI 29 PMP 30
Functions 10, 11, 12, ih and 3t>
These functions have been revised to simulate CH-5'+B maintenance frequen- cies. The functions define the probabilities of multiple maintenance actions (M.A.'s) given that at least one M.A. has occurred. These func- tions provide the information for during flight, preflight, daily inspec- tion and intermediate inspection, respectively. Since it was not feasible to construct this information from the ORME data base, the functions were derived using the assumption that the probability of a given number of M.A.'s follows a Poisson distribution. In functions 2 and 3, the proba- bilities of zero M.A.'s are defined for the various events, i.e.:
P(0) = e~" where X = the frequency of the M.A.
the P (at least one M.A.) = l-P(o)
The Poisson distribution defines the probability of x occurrences by the formula
P(x) = X^e^/x!
Therefore, the probability of x M.A.'s given that an M.A. has occurred is provided by the equation
P(x)/1-P(0) = (Xxe"X/x!)/( l-e~X)
Specific values for these functions can be observed in Appendix I.
Functions "1^ and 23
These are sorting functions which permit the R&M model to sort down from the aircraft to the system and to the component within the system to identify the item causing the M.A. The functions have been revised to account for intermediate inspections. Specifically, these two functions direct the R&M model to other functions which describe the probability that an aircraft M.A. occurs in a given system and then to a second set of functions that describe the probability that a system M.A. occurs in
52
a given element or component. The (leocription of the two functions as t.hey relate to the various aircraft operational event:; is contained below.
These functions provide the probability of a system's sustaining an M.A. given that the aircraft has sustained an action for the events of in-flight, in-flight abort, preflight, daily, periodic inspection and intermediate inspection. The specific values contained in these functions are shown in Table I under columns headed Cumulative Probability.
Functions 25, 26, 27, 28, 29 and 58
These functions provide the probability of an element or component sus- taining an M.A. given that a particular system has sustained an action for the events in-flight, in-flight abort, preflight, daily periodic inspection and intermediate inspection respectively. For the CH-5^B, each of these functions contains approximately 300 data entries which describe the most significant components from the viewpoint of frequency of occurrence, expenditures of manpower, and impact on mission success. In order to keep the number of elements reasonable, the least important elements in each system were grouped into a catchall element where cumulative frequency, the average maintenance times, arid the most representative maintenance specialists were assigned to tbise catchall items. These 20 catchall elements accounted for slightl. over 30^ of all the M.A.'s.
A function 58 was added to this data set since the ORME data included the necessary information. 'It was not necessary to assume, as was the case in previous Army simulation efforts, that the same distribution of M.A.'s discovered during the more encompassing periodic inspection also applied to the intermediate inspection. The specific values of these functions are seen in Appendix III. These probabilities represent an actual couj;t and the resulting ratio of component maintenance actions within each sub- system as observed within each event.
^o) Aircrew inspection is covered in these functions because it exists in the H&M model supplied by the Army; however, it will not be activated in the CH-5^B simulations since the CH-5^B has no comparable event.
53
Funct, i crip 3.°, 3jj and 33
Funciioj, ;'' defines t-lio probability of a C11-5'J1' aircrafi'ü being not operationally ready (KOR) given a "no abort" in-flight M.A. This function, which prescribes a probability for each aircraft component, was generated from data taken from the ORME Discrepancy/Corrective Action Reports. The probab i 1 i t i er; were computed for each element by taking the proportion of in-flight "no abort" M.A.'s that were identified in these OKME reports as having caused the aircraft to be placed in a "downed" status upon comple- tion of the flight.
Functions 3^ and 35 reflect, for each CH-^ltB component, the computed, pro- protion of M.A.'s discovered in preflight and daily inspection, respec- tively, that down the .aircraft. The specific values of these functions are shown in Appendix III.
Functions 37, ^0, ^2, k3, 33, 31' and TO
These functions describe the on-aircraft and off-aircraft work performed to correct equipment discrepancies (maintenance actions) discovered during the course of equipment operation and inspection. The functions describe the number of maintenance men, their active working time, their specialty codes, and the mean elapsed maintenance time required to perform the correc- tive action for each component. These are "packed" functions in that their six-digit values convey two or three bits of information rather than the usual one bit of information. Where three bits are addressed, i.e., the six-digit values are in actuality three two-digit values, they are referred to as the A, ß and C packs or AP, BP, CP. Where two bits of information are conveyed by the function, the two three-digit values are distinguished by referring to AP and BP. Table XI describes the packed functions as they have been defined tr reflect the CH-5^B aircraft/operation. Also, the following comments are offered to further describe this information by identifying the sources and limitations of the ORME data used.
a) The remove and replace data contained in Functions 37, ^2, ^3 and 70 was derived from ORME Discrepancy/Corrective ActionEfeports , where the disposition codes were identified as:
Removed, Repaired, Reinstalled Removed, Repaired, Made Ready for Issue (RFl) Removed, Scrapped Removed, Returned to Depot Removed, Tested O.K., Made RFI
These Discrepancy/Corrective Action Reports included all time spent on removing the discrepant part and its replacement either with the same part or with a like item. In the first two cases above, however, some off- aircraft repair time is included. The error introduced by this fact is small since less than 15 percent of all removals observed fall into these two categories.
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from Discrepancy/Corrective Action Heports wliere the Disposition Code was defined as either "Repaired on Aircraft" or "Checked on Aircraft, Tested O.K."
i.-) Jn function 37, BP entries for each component have been set to ;'.t>ro. This was done because the ORME progrfxm did not contain data with which to measure the percentage of elements repaired given that they are received at G.."..
d) In functions ^0, '(2, and '-i3, the AP values were set to zero since the ORME program did not contain this information.
e) The ORME data shows, in many cases, that more than two maintenance specialties (work centers) were involved in correcting the faults associa- teu with each component. As a result, two things were done. First, since the specialty requirements were somewhat different for remove and replace, as opposed to on-aircraft repair, a separate function, function TO, was created to distinguish between the primary and secondary specialists required for remove and replace vs. those required for on-aircraft repair. Second, where there still remained requirements for more than two main- tenance specialties, their times were added to the primary or ;-( condary specialist category that they most closely matched. If no matcn existed, the limes were prorated over the primary and secondary work centers.
Function Mj
Al] CH-5'iB component elements were reviewed with ORME engineers to define test hop requirements. Based on this work, function kk has been revised to reflect CH-5^B test hop component candidates. Appendix III identifies each component which may require a test hop by associating it with a value one. Appendix IV shows a change in the probability of a maintenance action requirement which was selected in order to bring the test hop flight time to ^i.Sl percent of the total flight time as was reflected in actual CH-5^B operational history.
Function 71
Since function 70 was added to distinguish between work centers required for removal and replacement of a component, as opposed to its repair on- aircraft, an additional function is required to permit sorting the proper digits in the packed function. This function plus its associated variable statements (which also had to be added) are identified below.
71 Function PI, E3
V270 2 V269 3 V268
where V268 = FN70/10,000 for off-equipment W.C. V269 = FN70@ 10,000/100 for secondary W.C, R&R V270 = FN70 @ 100 for primary W.C, R&R
56
APPENDIX HI
CH-^B MODEL INPUT FUNCTION LISTING
The following is a listing of all the input function values used in the CH-5^B model. Frequent references to these fuuclions are made in the main body of the report.
46 FUNOTIÜN P22»L)296 ELEMENTS TAflLE CODE 00012990 0101 1 0102 2 0103 3 0104 4 0105 5 0106 6 00013000 mo7 7 nin« n nino o n« in in ni»i i i n i » ? 1 7 nnniimn
INI UAL INI 1i AL INITIAL INI UAL INI UAL INITIAL INI U AL INITIAL INITIAL INI UAL INI 11 AL INITIAL INI UAL INITIAL INITIAL INITIAL INITIAL INITIAL INI TIAL INITIAL INITIAL INITIAL INI HAL INITIAL INI UAL INI 11 AL INITIAL INI UAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL INITIAL
TIME BtTWEtN LAUNCH 2t3 TIME BETWEEN LAUNCH 2C3 TIMt BETWEEN LAUNCH 2t3 TIME BETWEEN LAUNCH 3(.4
TIMt BtTWtEN LAUNCH 3C4 TIME BETWEEN LAUNCH 3t,4 TIME BETWEEN LAUNCH 3t4
TIME BETWEEN LAUNCH 4ti TIME BETWEEN LAUNCH -VtOOsW TIME BtTWEEN LAUNCH 4t00:12 TIMt BETWEEN LAUNCH 3t,00!l2 TIME BETWEEN LAUNCH 4tÜ0:12 NÜ. UF LAUNCHES PER DAY NO. UF LAUNCHES NO. OF LAUNCHES PER DAY NO. UF LAUNCHES PER DAY
NUN FLYING HOURS WEEKEND FLYING HOURS WEEKDAYS
.•>LACK TIME TIMt FROM CALL TO LAUNCH
TIME TO PERFORM AIRCREW INSPECTION LAUNCH TIME TO REPLACE ABORTS PERCENT 1N-FLT ABORTS REPLACED NO STANDBY A/C BY MISSION TYPE FLT DURATION FOR ABORT REPLACEMtNTS00017010
CH-^B MODEL PROGRAM UPDATE MD PROGRAM LISTING WITH NECESSARY MODIFICATIONS TO THE GOVERNMENT-FURNISHED MODEL IDENTIFIED
PROGRAM UPDATE FOR THE CH-^UB MODEL
The program update for tLs CH-5^B model is contained in this Appendix. This update contains the reasons for all Sikorsky-initiated changes. Eustis Directorate initiated some changes to improve the overall model, and these changes are noted without comment. Certain specific changes made by- Sikorsky are of particular significance and are elaborated on below.
Incorporation of Log Normal Distribution
The log normal distribution has been incorporated into the CH-5UB baseline simulation model to replace the exponential distribution previously con- tained in the simulation model input function 36. The log normal (to the Base e) is more representative of the replacement and repair elapsed maintenance time distributions evidenced by the CH-5^B. Contained in figure 7 are graphs comparing the two distributions followed by pertinent facts about the log normal distribution used for CH-5^B simulation runs.
Exponential Log Normal
1000 2000 1000 2000
Normalized Elapsed Maintenance
Figure 7. Alternative Elapsed Maintenance Time Distributions
The elapsed maintenance time distributions of eight different CH-5^B com- ponents were studied to ascertain the most appropriate distribution for the CH-5^B- The eight components were singled out because they contained the most data. The shape of the observed distributions dictated that the log normal be used instead of the exponential distribution. Therefore, the exponential distribution with mean = 1000 was replaced by the log normal distribution with mean = 1000. The log normal distribution, which was found to best represent the eight observed distributions, reflected the following log values:
80
o , = Memi of the nuLural io^ oi" the variable x = 6,7^4 cr = Variance of Lhe natural log of the variable x = .2'j
THÜ Ini tialixation
The JH-^'iB l^&M model reflects that components reaching their TBO times are replaced with components having their full TBO time remaining. The simu- lation runs bear out the adequacy of present logic. Based on the TBO com- ponent scheduled removal times as defined under "Cll-'diB Aircraft Descrip- tion", the removal rate for all scheduled TBO replacements should approxi- mate 17 scheduled removals/1000 flight hours. The slightly higher value results from the interaction of the initialized component times and the first preventive maintenance £eriodic (i'MF) inspection. Because of the 100 flight hour duration between PMP's, components having less than 100 hours remaining before TBO expiration are replaced. This results in a slightly higher rate of replacement. This, however, is consistent with procedures practiced in the field.
Modified Daily Inspection Schedule
The daily inspection subroutine has been modified to eliminate the possi- bility of daily inspections being performed on overtime hours. This was in compliance with an Army request. This modification resulted in a less flexible daily flight schedule, since all flying and daily inspections as well as preflights had to be packed into the 8-hour operational day.
CH-^B MODEL PROGRAM LISTING WITH NECESSARY MODIFICATION TO THE GOVERNMENT- FURNISHED MODEL IDENTIFIED ' "" ^ "'
The following is a list of changes made tc the Government-furnished model to convert the UH-1N R&M model to conform to CH-'phE aircraft and operational characteristics. Changes made by the Government to update the original UH-IN R&M model are so noted with no further comment.
1. The change in the reallocation of functions, variables, full-word save- values, and transactions was necessary to reapportion the allocation of entities in the model to accommodate changes to simulate CH-5^B operation.
2. Variable 9 has been corrected to allow general use of the variable as well as inclusion of a snap feature.
3. Variable 19 has been modified to be general with respect to the ^Lart of the first shift.
h. Variable 38 has been generalized with respect to the end of the first, shift.
5. Per a Eustis Directorate correction, variable 73 is now correct.
6. Variable 233 has been added per Eustis Directorate directive.
7. Variable 238 has been added per Eustis Directorate directive.
01
8. Variables 268, 269, 270 have been added to provide different, centers for remove and replace actions. These variables decode the "packed" information contained in function 70.
9- Variable 267 was added to accommodate the scheduling of launch calls on a daily basis. This variable will define the half matrix to be used for that particular day's launches.
10. Boolean variable 11 has been changed per Eustis Directorate.
11. Boolean variable 19 has been changed per Eusv.is Directorate.
12. Half matrices 11-17 have been added for the daily launch schedule. Half matrix 11 is Monday's launches and matrix 17 is Sunday's.
13. Table 9 has been changed to give a more meaningful output of downtime distribution for the CH-5UB.
l^t. Table 18 has been added to tabulate the start of each daily inspection.
15- Table 19 has been added to tabulate the number of deferred maintenance actions caused by the aircraft at the start of the daily inspection.
16. Storages 33 through k2 have been limited to the levels defined by the CH-^B TOE.
17. The PMI has been added to function 7 (event code 8).
18. Function 15 has been modified to identify function 57 for the system failure for PMI.
19. Function 23 has been modified to identify function 58 for the element failure for PMI.
20. The log normal distribution has been substituted for the exponential distribution.
21. Function ^0 has been redefined as the skill codes (or work centers) for on-aircraft repair only. It was formerly the skill codes for on-aircraft repair as well as remove and replace.
22. Function I48 has been redefined as the probability of no cannibalization given a N0RS item.
23. Function 58 has been added to define the probability of element failure given system failure during PMI.
2k. Function 70 has been added to define separate work centers for remove and replace actions.
25. Function 71 has been added to use variables 268, 269, and 270 to decode the data contained in function 70.
82
26. In order to define the daily flight schedule in half matrices 1 through 17, these initial statements have been added. The structure is defined such that the rows and columns contain the data in the same matrix location as half matrix 1 formerly contained. Data other than flight schedule data is still retained in half matrix 1.
27. These initial statements were added per Eustis Directorate.
28. This initial statement defines save-value l601 as the time of the end of first shift. It is used in variable 38.
29. These model logic changes were added to define a flight schedule on a daily basis.
30. Changed per Eustis Directorate.
31. Number of TBO items to be initialized has been generalized.
32. Added per Eustis Directorate.
33. Added per Eustis Directorate.
3^. Added per Eustis Directorate,
35. Added per Eustis Directorate.
36. Table 18 added to tabulate time daily performed.
37- Table 19 added to tabulate number of deferred maintenance actions carried at the start of the daily inspection.
38. Added per Eustis Directorate,
39- Added per Eustis Directorate.
kO. Added per Eustis Directorate,
hi. Added per Eustis Directorate.
h2. Corrected per Eustis Directorate.
^3. Added to insure that if the item is a remove and replace action 100^ of the time, and if the random number comes up as 999, it still will be a remove and replace action,
hh. Changed to be consistent with the definition of function 38 being probability of part availability,
h1?. Logic change to assign remove and replace work centers from function 70 and on-aircraft repair work centers from function ^(0.
83
hb. Removed truncation of elapsed maintenance times. With the use of the log normal distribution of repair times in place of exponential, truncation of the distribution was not necessary.
I47. Added per Eustis Directorate.
kQ. Removed the test to put test hops in the second shift. The CH-5i+B is a one-shift operation.
U9. The CH-5^B baseline requires a .650 value in this statement to get the proper percentage of test hop flight time.
^0. Changed per Eustis Directorate.
51. Added to require secondary work centers for cannibali^ation remove and replace actions when needed.
52. Untruncated cannibalization remove and replace time to correspond with Cll-^B data.
53. Added per Eustis Directorate.
5*4. Report changed to more clearly output CH-5^B simulated operational statistics.
"MISSIUN FLYING HUURS* SAVEVALUE NUMbtRS P^+Kb "AIKCKAFT NUT AVAlLAbLt WHtN CALLED" MISSIUN XH f",*K* "MISSIUN LAUNCH CATt" SWITCH NUMbERS Pll+Ki3 »MISSION CYCLIC t-LYINO HOUR" SWITCH NUMBERS P'ftKU "MISSION CYCLIC FLY1NL. HÜUK" SWITCH NUMBERS P3-C1 CURRtCfEL) 11.5.74 (KNl«1000*RNl)iXl<y5 INITIAL DAYS SINCt PMP (P',7*(Cl/2<tO) )iX195 UAYi ilNCt PMP kNl*i000 + KNl SIX ÜICIT RANLtUM NUMBER ^b♦KJ MISSION STJKt ♦ LAUNCH oATt SWITCH NUMbERS Pü«-MJ "MISSION CYCLIC FLYING HUUK" SWITCH NUMBtRS Pö + Mö NUMbER UF tACH MISSION FCUwN WITHOUT MA'S PÖ + KÜ', SAVcVALUt NUMÜEkb - FLIGHT HOURS BY MISSION FNH/2 AbUKT FLIGHT TIME UURATION (MXiU.O+^O-V/üia^O TIME TO START OF IST SHIFT Cldli'fU TlMt OF UAY-TENTHS OF HOURS PltaMXU 1,10» ü=TIMt FOR ALTEKNATt OAl LY FNö/i.OOOO MANPOWER RtOUIREO FNo/100«100 WORK CENTER FNöaiOÜ MtAN ELAPSED TIME TU PfcRFUHM EVENT Pi7*d EVENT STORE NUMBER P2*32 WORK CENTtR UUtU£ ♦ 1ST SHIFT STORE NUMBERS P2*tJ 2NU SHIFT WORK CENTER STORE NUMBER PtZ*PZO MAN HOURS X J.OO P2*8 SAVtVALUt NUMbERS OF MMH VS. WORK CENTER P2*43-P'»»U SKILL LINK NUMBERS ü+bVl'. MATRIX COLUMN NUMoEk-PMP/PMI ELAPSE TIME K2+BV14*8 MATRIX ROW NUMötR-PMP UR PMI,MEN K,3*-BVU»6 MATRIX ROW NUMBtR-^MP OR PMI,TIME/MAN tZO-CidZttü TIME REMAINING SECOND SHIFT P3*P'. MAN HOURS X 100 P2+2C SAVtVALUt NUMb£RS-PMP/PMI MAN HOURS BY WORK C£ Xio01-ClS2'»C TIME REMAINING - FIKST iHlFT P4-P20 EMT IN EXCESS OF CURRENT SHIFT LENGTH P2*29 SAVcVALUt NUMBERS, NUMBER UF P2 MA'S/EVENT P1V+39 SAVEVALOt NUMBERS, NUMBER OF MA'S/PIV EVENT P3*100*P5 ELEMtNT NUMBER FN37/K100Ü PROBABILITY Of R ♦ R P22/100 ELEMENT SYSTEM NUMbtR Pi*2^ PAR..METER IDENTIFICATION - WOkK CEMTER
00002380 10 00002390 u TABLt FN».o,0 i l, 3GÜ CANNlBALIZtO PARTS 00002400 li TAbLt FN'tO ,0,1, JUO PARTS CAUSING NURS UR CANNIBAIZATION 0000/410 13 TAbLt FN'tb,0,1,300 PARTS K AND R BY SERVICE PLATOON 00002420 i'» IABLL
TIME FROM 00:12 TIME FROM 00:12 TIME FRÜH 00:12 TIME FROM 00:12
TO 1ST TO 1ST TO 1ST TO 1ST
TIME BETWEEN LAUNCH 11.2 TIME BETWEEN LAUNCH U2
TIME BETWEEN LAUNCH U2 TIME BETWEEN LAUNCH It/ TIME BETWEEN LAUNCH 203
TIME BETWEEN LAUNCH 2t3 TIME BETWEEN LAUNCH 2C3 TIME BETWEEN LAUNCH 213 TIME BETWEEN LAUNCH 3£.4
TIME BETWEEN LAUNCH 3C4 TIME BETWEEN LAUNCH 3£% TIME BETWEEN LAUNCH 3t4
TINE BETWEEN LAUNCH 4L5 TIME BETWEEN LAUNCH *&00il2 TIME StTMEEN LAUNCH 4100:12 TIME BETWEEN LAUNCH 3C00:12 TIME BETWEEN LAUNCH 4t00»12 NU. UF LAUNCHES PER DAY NO. OF LAUNCHES NO. OF LAUNCHES PER DAY NO. OF LAUNCHES PER DAY
FLYING HOURS WEEKEND FLYING HOURS WEEKDAYS
iLACK TIME TIME FROM CALL TO LAUNCH
TIME TO PERFORM AIRCREW INSPECTION LAUNCH TIME TO REPLACE ABORTS PERCENT IN-FLT ABORTS REPLACED NO STANDBY A/C BY MISSION TYPE
UA GtNfcRATt SPLIT SPLIT SPLIT SPLIT SPLIT SPLIT SPLIT ASSIGN ASSIGN ADVANCb TtST E SPLIT ASSIGN TEST GE AbSIGN ASSIGN LOOP SPLIT GATt LR TEST t ADVANCE ASSIGN GATE LR ASSIGN TcST NE TRANSFER SPLIT TRANSFER GATE LR GATE LR GATE LR ASSIGN ASSIGN SPLIT SAVEVALUE ALTER ALTER UNLINK LOOP TERMINATE ASSIGN TEST t TEST E HARK ASSIGN ASSIGN ADVANCE TEST G UNLINK SPLIT ASSIGN
AKW3V SAVEVALUE TRANSFER ASSIGN TRANSFER ASSIGN ASSIGN TRANSFER ADVANCE BUFFER LOGICS LOGICS ADVANCE PUEEtÄ
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ASSIGN ADVANLfc TEST Nt TEST Nfc LEAVE LEAVE TABULATE MSAVEVALUE SAVEVALUE SAVEVALUE UNLINK TKANSFhR SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE TRANSFER SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVtVALUE SAVEVALUE SAVtVALUE TRANSFER ASSIGN ASSIGN TRANSFER ASSIGN ASSIGN LINK TEST E TEST Nt TEST NL TbiT G DEPART ÜEPART LEAVE REHOVt: TRANSrER UbPARI TRANSFtR TEST G TRANSFER
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TEST t TRANSFfcR TfcST L SAVEVALUE SAVEVALUE SAVbVALUE SAVEVALUE TRANSFER ASSIGN ASS1UN ASSIGN TRANSFER ASSIGN ASSIGN ASSIGN TtST t DEPART ASSIGN PRIORITY PRIORITY ASSIGN TRANSFER LINK SPl iT TRANSFER
SAVtVALUt ASSIGN ASSIGN TABULATh TAfaULATt SAVtVALUt SAVtVALUL SAVLVALUfc SAVtVALUE SAVtVALUfc ASSIGN SAVtVALUt ASSIGN MSAVEVALUt ASSIbN TtST Nc MSAVtVALUt TtSl LE TABULATh SPLIT TEST E ASSIGN ASSIGN LÜÜP TEST fc TfcST E UNLINK SPLIT TEST t SAVtVALUE TRANSFER LÜOP TtST E TEST G GATb LS TRANSFER TEST NE ASSIGN ASSIGN TRANSFER LINK MSAVEVALUE TRANSFER ASSIGN TEST £ ASSIGN TRANSFER TEiT L TRANSFER TEST L TEST L TEST L TRANSFER
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ASSIGN 16,Kl 0002 7940 SPLIT l,RLARF,,21> 00027950 ADVANCE PI 00027960 TEST E bV19,Kl TEST FOR PREVENTING OFF SHIFT MAINT. 00027970 SAVEVALUE V232'».M1 00027980 SAVEVALUE 1425*,Ml 00027990 SPLIT ltRLAR6t.25 00028000 TRANSFER ,NPAA 00028010
NÜRCb SPLIT 1,NORCO 00028020 TRANSFER ,NORCE 00028030
NORCO ADVANCE PI 00028040 TRANSFER • CANO 00026050
NORA ASSIGN 23,7* 00028060 TP<;T F WA7.rM7k nnmnmn
112
TEST E WtNORL.KO ASSIGN l.KO GATE LS 22,NURC GATE LH 23 SCAN 12,14,Pl'f.>tN0RH SPLIT l.NÜRTf.bO SPLIT l,NÜRS,,60 SPLIT IiRLARF,t60 TRANSFER ,N0RJ
SAVfcWALUE SAVEVALUE AUVANLE LtAVE LbAVfc UNLINK UNLINK ASSIGN SAVtVALUE TEST L ASSIGN TEST G ASSIGN TEST G ASSIGN SAVtVALUE MSAVEVALUfc MSA VE.VALUE SAVEVALUE SAVtVALUE SAVEVALUE SAVtVALUE TEST t TABULATE TERMINATE SAVtVALUE TRANSFER SAVtVALUE TRANSFER SAVtVALUE TRANSFER ASSIGN PRIUKITY ASSIGN ASSIGN TtSI c ASSIGN ASSIGN ASSIGN ASSIGN SAVEVALUE MSAVEVALUt TRANSFER ASSIGN TKANSFER
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—— —-— ~— ——-— 00032680 2 00032690 SCENARIO SIMULATED 00032700 1 00032710 UNE PLATOON OF NINE CH-54B ARMY HtLICüPTERS 0003272Ü 1 00032730 FLYING PRÜGKAM CONSIST EL» UF FIVE FLYING DAYS PER WEEK 000327*0 1 00032760 MISSION LENGTH IS l.B HOURS 00032770 1 00032 790 LAUNCH SCHEÜULE DURING EACH FLYING DAY Ü0032800
00032810 00032820 0003/830 0003,28«) 00032850
I 00032860 UTHEK FLIGHT CONSIUEHAIIONS 00032Ö70 1 C0Ü32871 STANUbY AlRCRAhT READY AT ALL TIMES DURING THE SCHEuU*00032680
ALS. 00032890 1 00vl32 891 MISSION FLIGHT IS POSSIbLE UP TO IHIRTY MINUTES AFTER+00032900 TIME. AFTLK THIS INTERVALt FLIGHT IS SCKUbBED. 00032910 2' 00032920 MAINTENANCE CONCEPT SIMULATED 0003/930 I 00033000 PREVENTIVE MAINTENANCE DAILY (PMD> INSPECTIONS OCCUR »00033010
RAFT HAS FLUWN OR EVERY 72 HOURS IF NUT FLYING. 00033020 1 00033030 JNIERMcDIATE MAINTENANCE INSPECTIONS OCCUR EVERY 25 H»&0033ü3i
00033032 1 00033033 PLRI'JDIC MAINTENANCE INSPECTIuNS OCCUR EVERY 100 H0UR*00033034
00033035 2 00033O36 MAINTENANCE PEKSUNNEL ARE AVAILAULE btTWEEN 0830 AND ♦000330*0
IVt DAY FLYING PERIOD PER WEEK. 00033050 I 000330t>0 1 00033090 THE AIRCRAFT CONSISTS OF /9A ELEMENTS. THERE ARE 21 TȆ0033100
ENIS. 00033110 i 00-J33120 UROANIZATIUNAL MAINTENANCE INCLODtS, AN INTEGRATED DlR»00Ü33l60
ENANCt CAPAblLIlY. 00Ü3J170 1 G0ü3J18ü UFF EWU1PMENT CUMPUNEM MAINTENANCE IS DUMMIED OUT. 00033190 1 00G3322Ü CUNUEMNATIUN OR ^KTS STATUS IS DUMMIED OUT. 000332^0 I 000332*0 NGRi AND CANNIbALIZATIUN ROUTINE IS ACTIVE. 00033/*! / 000332*2 EVALOATIDN THIS SIMULATION RUN: €0033^50 1 0003326Ü bASIC CH-5*b MISSION AMD MAINTENANCE PHILOSOPHY 00033270
FACTORIAL APPROACH TO SIMULATION MODEL SENSITIVITY ANALYSIS
The factorial approach incorporated into this study is a powerful method of optimizing the number of test simulation runs to provide the output statistics required for analysis.
The purposes of this appendix are to give the statistical background upon which the factorial analysis is based and to provide the tables and statis- tical evidence of significant effects observed in other output parameters studied and referred to in the main body of this report.
The first step is to develop an independent estimate of simulation or experimental error. Table III in this appendix and Table VIII in the main body of the report, show four separate computer runs under identical condi- tions, except that the random number seed was changed. The variation, or simulation error, associated with operational availability was computed from these four runs by the following formula:
2( x. - x)2
_ Variance = N - 1 where x^ is the individual observa- tions, x is the mean of the observations, and N is the number of observa- tions .
Therefore, the variance associated with the output statistic of operational availability is
The second step is to see if the variation that occurs when a factor level is changed is consistent with this simulation variation, in which case there is no reason to believe that the change in the level of the factor produced any change in the output value. If the variation that occurs when a factor level is changed is significantly larger than the simulation variation, then there is sufficient statistical evidence to conclude that the change in the level of the factor has caused the observed change in the output parameter.
Consider the change in NORS level vs. the observed change in operational availability as shown in the following case. Note that these values are the ones recorded in Table XII.
125
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The Yates algorithm shown in Table XII is simply a mathematical procedure to facilitate the computation of effects. Using the availability values shown in Table XII and illustrated in Figure 8, the average effect on changing NORS level is
Now the variation associated with this estimate is
(36.63)2 = 167.72 8
If there is no real change in operational availability caused by the change in NORS level, then this variability reflects simply the variability associated with simulation error, i.e., it is simply another estimate of simulation error.
The distribution generated by taking the quotient of two independent esti- mates of the same simulation error is given by the F distribution. The appropriate F distribution is dependent on the number of degrees of free- dom associated with the numerator estimate and the denominator estimate.
Table XII shows that eight test points were used in generating the eight mean square values. There are eight separate bits of information used in the analysis; therefore, the data contains eight degrees of freedom. There are eight independent mean square outputs; therefore, there is one degree of freedom associated with each. In the case of the independent estimate uf simulation error, there are four bits of data and therefore four degrees of freedom associated with the data; one is associated with estimating the
127
mean, x, and the other three are associated with the estimate of error.
The NORS effect shows a variation value of 167.72 with df = 1, and the simulation variation value is ^.06 with df = 3. The F^ 3 distribution shows that at the a = .05 level of significance, given two independent estimates of the same error, the quotient of these two estimates should not exceed 10.1.
167.72 = i+1.31 i+.06
Since this exceeds 10.1, we must conclude that the deviation or difference observed in operational availability when changing from a low to a high level of N0R3 is not simply a manifestation of simulation error, but in actuality is a true effect caused by this change in NORS level. The best estimate of this change is a -9-l6% in operational availability.
The factorial analyses are performed for the following computer output values. Significant effects are asterisked in the table showing the fac- torial analyses, and these effects are summarized and discussed in the main body of the report.
1) Unscheduled Elapsed Maintenance Down Hours
2) NORS Plus Unscheduled Elapsed Maintenance Down Hours
3) Percentage of Intrinsic Availability for Flight Hours Divided by Flight Hours Plus Unscheduled Down Hours
k) Percentage of Intrinsic Availability for Flight Hours Divided by Flight Hours Pius Scheduled and Unscheduled Down Hours
5) Direct Maintenance Man-Hours Per Flight Hour
6) Percentage of Mission Accomplishment
7) NORS Down Hours
Table XII has been included to show the factorial analysis in detail. Table VIII in the main body of the report summarizes the factorial analysis findings for operational availability. Tables XIII through XIX summarize the findings for each of the seven model output statistics stated above.
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135
LIST OF SYMBOLS MD ABBREVIATIONS
oc level of significance
9 mean of distribution
cr standard deviation of distribution
A/C aircraft
act. action
admin. administrative
AFCS automatic flight control system
APP auxiliary power plant
avail. availability
coll. collective
cent. control
corr. corrective
cum. cumulative
discrep. discrepancy
EAPS engine air particle separator
EMT elapsed maintenance time
eng. engine
fit. flight
F.R. failure rate
GSE ground support equipment
HS highly significant
hyd. hydraulic
IGB intermediate gearbox
Insp. inspection
land landing
136
LIST OF SYMBOLS AND ABBREVIATIONS (CONTINUED)
luL. lateral
L.H. left hand
Lt, left
M.A. maintenance action
Math. mathematical
Mech. mechanism
M.G.B. main gearbox
M.L.G. main landing gear
MMH maintenance man-hours
MMH/FH maintenance man-hours per flight hour
MOS military occupational speciality
ME main rotor
MBH main rotor head
MTBF mean time between failures
MTBMA mean time between maintenance actions
MTBK mean time between removals
MTTR mean time to repair
No. number
NORM not operationally ready - maintenance
NORS not operationally ready - spares
ORME operations reliability/maintainability engineering program