NAVAL POSTGRADUATE SCHOOL Monterey, California THESIS APPROXIMATE CONFIDENCE LIMIT PROCEDURES FOR COMPLEX SYSTEMS by YEE, Kah-Chee September, 1991 WOODS Thesis Advisor: W. M. Approved for public release; distribution is unlimited. T2S93PP SECURITYCLASSIFICATIONOFTHISPAGE REPORT DOCUMENTATION PAGE 1a.REPORTSECURITYCLASSIFICATION 1b RESTRICTIVEMARKINGS UNCLASSIFIED 2a SECURITYCLASSIFICATIONAUTHORITY 3 DISTRIBUTION/AVAILABILITYOFREPORT Approvedfor publicrelease;distributionisunlimited. 2b DECLASSIFICATION/DOWNGRADINGSCHEDULE 4 PERFORMINGORGANIZATIONREPORTNUMBER(S) 5 MONITORINGORGANIZATIONREPORTNUMBER(S) 6a.NAMEOFPERFORMINGORGANIZATION 6b OFFICESYMBOL 7a NAMEOFMONITORINGORGANIZATION NavalPostgraduateSchool (Ifapplicable) NavalPostgraduateSchool OR 6c ADDRESS(City,State,andZIPCode) 7b ADDRESS(City,State,andZIPCode) Monterey,CA 93943-5000 Monterey,CA 93943-5000 8a NAMEOFFUNDING/SPONSORING 8b OFFICESYMBOL 9.PROCUREMENTINSTRUMENTIDENTIFICATIONNUMBER ORGANIZATION (Ifapplicable) 8c ADDRESS(Crty,State,andZIPCode) 10 SOURCEOFFUNDINGNUMBERS ProgramElementNo ProjectNo TaskNo WorkUnitAccession Number 11 TITLE(IncludeSecurityClassification) APPROXIMATECONFIDENCELIMITPROCEDURESFORCOMPLEXSYSTEMS 12.PERSONALAUTHOR(S) YEE, Kah-Chee 13a TYPEOFREPORT 13b TIMECOVERED 14 DATEOFREPORT(year,month,day) 15 PAGECOUNT Master'sThesis From To 1991,September 129 16.SUPPLEMENTARYNOTATION TheviewsexpressedinthisthesisarethoseoftheauthoranddonotreflecttheofficialpolicyorpositionoftheDepartmentofDefenseortheU.S. Government. 17 COSATICODES 18 SUBJECTTERMS(continueonreverseifnecessaryandidentifybyblocknumber) FIELD GROUP SUBGROUP CONFIDENCELIMITPROCEDURES,COMPLEXSYSTEMS,LIFETESTING, SERIESSYSTEMS,SYSTEMRELIABILITYRELIABILITY 19 ABSTRACT(continueonreverseifnecessaryandidentifybyblocknumber) Lowerconfidencelimitestimationproceduresforthereliabilityofseveralsystemsaredevelopedandtheiraccuraciesevaluatedusingcomputer simulation. TheproceduresusetestdataoncomponentsofthesystemwhichcanhavefailuretimeswitheitherexponentialorWeibull distributionsorboth. Testingscenariosforthecomponentscanbetruncatedbynumberoffailuresorbyplannedtesttimes. Althoughtheevaluationeffortwasfocussedonseriessystemsinthisthesis,theproceduresreadilyapplytoothersystemsasdescribedinthe thesis. Theevaluationsdemonstratetheprocedurestobequiteaccuratewhensufficientcomponenttestingisperformed. TwoFORTRANcomputerprogramswerewrittentoperformtheevaluation. TheyareannotatedinUsers'Guidesandcanbeusedtodetermine theaccuracyoftheseapproximatelowerconfidencelimitproceduresforagivenspecificsystemandassociatedsetofinputparameters. 20 DISTRIBUTION/AVAILABILITYOFABSTRACT 21 ABSTRACTSECURITYCLASSIFICATION J UNCLASSIFIED/UNLIMITtD J SAMEASREPORT J OTICUSERS UNCLASSIFIED 22a NAMEOFRESPONSIBLE INDIVIDUAL 22b TELEPHONE(IncludeAreacode) 22c OFFICESYMBOL W.M.Woods (408)646 2743 OR/Wo DD FORM 1473.84 MAR 83APReditionmaybeuseduntilexhausted SECURITYCLASSIFICATIONOFTHISPAGE AHothereditionsareobsolete UNCLASSIFIED Approved for public release; distribution is unlimited. Approximate Confidence Limit Procedures For Complex Systems by YEE, Kah-Chee SINGAPORE Operations Analyst, Ministry of Defence, B.Eng(Mech), National University of Singapore, 1987 Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN OPERATIONS RESEARCH from the NAVAL POSTGRADUATE SCHOOL September 1991 ABSTRACT Lower confidence limit estimation procedures for the reliability of several systems are developed and their accuracies evaluated using computer simulation. The procedures use test data on components of the system which can have failure times with either exponential or Weibull distributions or both. Testing scenarios for the components can be truncated by number of failures or by planned test times. Although the evaluation effortwas focussed onseries systems in this thesis, the procedures readily apply to other systems as described in the thesis. The evaluations demonstrate the procedures to be quite accurate when sufficient component testing is performed. Two FORTRAN computer programs were written to perform the evaluation. They are annotated in Users' Guides and can be used to determine the accuracy of these approximate lower confidence limit procedures for a given specific system and associated set of input parameters. m / \y^ v f^ 6.1 THESIS DISCLAIMER The reader is cautioned that the computer programs developed in this research may not have been exercised for all cases ofinterest. While every effort has been made, within the time available, to ensure that the programs are free of computational and logic errors, they cannot be consideredvalidated. Anyapplication of these programs without additional verification is at the risk of the user. IV