《船舶安全与可靠性理论》课程教学课件（英文讲义）Safety and Reliability Analysis Lecture 4/5

SafetyandReliabilityAnalysisLecture4Yiliu LiuDepartment of Production and Quality EngineeringNorwegian Universityof ScienceandTechnologyyiliu.liu@ntnu.noNTNU- TrondheimNorwegian University ofScience and Technologywww.ntnu.edu

1 Safety and Reliability Analysis Lecture 4 Yiliu Liu Department of Production and Quality Engineering Norwegian University of Science and Technology yiliu.liu@ntnu.no

DATA ANALYSISNTNU-TrondheimNorwegian University ofScience and Technologywww.ntnu.edu

2 DATA ANALYSIS

3Test-analyze-and-fix(TAAF)Phases6-7Phases2-3Phases4-5ReliabilityGrowthtestingGrowthindesignInitial designassessment(TEST)(ANALYZE)EngineeringRedesignanalysis(FIX)(ANALYZE)NTNU-TrondheimNorwegian Universityof梦ScienceandTechnologywww.ntnu.edu

3 Test‐analyze‐and‐fix (TAAF)

Classifications of testsTheaimof reliabilitytesting is described asto give objectiveand reproducibledata on thereliabilityperformanceofanitem.AcommonclassificationisaccordingtothepurposesoftestsReliability estimation testing- to estimate reliability parameters(quantitativeacceleratedtesting)Failureidentificationtesting-to reveal failuremodes and causes (qualitative acceleratedtesting,burn-intesting,prooftesting)Reliability comparisontesting-to comparedesign optionsin termsof reliabilityandfindtheoptimal (robustdesign)Reliability compliance testing-to check whether the reliability goals or specificationshavebeenmet,ordetermineswhetherpartsorcomponentscanbeacceptable.NTNU-TrondheimNorwegian University ofScienceand Technologywww.ntnu.edu

4 Classifications of tests The aim of reliability testing is described as to give objective and reproducible data on the reliability performance of an item. A common classification is according to the purposes of tests: • Reliability estimation testing ‐ to estimate reliability parameters (quantitative accelerated testing) • Failure identification testing ‐ to reveal failure modes and causes (qualitative accelerated testing, burn‐in testing, proof testing) • Reliability comparison testing ‐ to compare design options in terms of reliability and find the optimal (robust design) • Reliability compliance testing ‐ to check whether the reliability goals or specifications have been met, or determines whether parts or components can be acceptable

5Test-analyze-and-fix(TAAF)Phases4-5ThemaintasksinaTAAFprocessinclude1.Detectproblem(i.e.,deficiencyorReliabilityGrowthtestingweakness)assessment(TEST)2.Feedbackproblemtothedesigner(ANALYZE)3.Analyzeand redesign theproductto?correcttheproblemEngineering4.IncorporateredesignintotheproductRedesignanalysis5.Verifyfixbyoperatingtheproduct(FIX)(ANALYZE)NTNU -Trondheim莎NorwegianLUniversityofScienceandTechnologywww.ntnu.edu

5 Test‐analyze‐and‐fix (TAAF) The main tasks in a TAAF process include: 1. Detect problem (i.e., deficiency or weakness) 2. Feed back problem to the designer 3. Analyze and redesign the product to correct the problem 4. Incorporate redesign into the product 5. Verify fix by operating the product

Test and data analysisIn order to obtain information about a particular life distribution F(t) for an item(component/system),itisoftennecessarytocarryoutatestwherenidenticalitemsareactivated in order to record their lifetimes. The data set thus obtained is said to becomplete.Often we have to be satisfied with incomplete data sets.This may be because it isimpractical ortoo expensive to wait until all theitemshavefailed.Insuch situationsthedatasetissaidtobecensored.NTNU-TrondheimNorwegian UniversityofScienceand Technologywww.ntnu.edu

6 Test and data analysis In order to obtain information about a particular life distribution ܨሺݐሻ for an item (component/system), it is often necessary to carry out a test where ݊ identical items are activated in order to record their lifetimes. The data set thus obtained is said to be complete. Often we have to be satisfied with incomplete data sets. This may be because it is impractical or too expensive to wait until all the items have failed. In such situations the data set is said to be censored

Types of censoringCensoringof typelAll items are activated at timet=o andfollowed until failure or until timeto when theexperiment isterminated.CensoringoftypellAll items areactivated at timet =o, and the resultingdata set contains afixed numberrofobserved lifetimesandfurthermorewanttoterminatethetestasfastaspossibleCensoringof type IllAll items are activated at time t =O, and the test terminates at the time that occursfirst,toortherthfailure.CensoringoftypeIVn numbered identical itemsare activated at differentgivenpoint(s)in time.Censoringtimeisstochastic.NTNU-TrondheimNorwegian University of莎Science and Technologywww.ntnu.edu

7 Types of censoring • Censoring of type I All items are activated at time t =0 and followed until failure or until time ݐ ଴when the experiment is terminated. • Censoring of type II All items are activated at time t =0, and the resulting data set contains a fixed number r of observed lifetimes and furthermore want to terminate the test as fast as possible • Censoring of type III All items are activated at time t =0, and the test terminates at the time that occurs first, ݐ ଴or the rth failure. • Censoring of type IV n numbered identical items are activated at different given point(s) in time. Censoring time is stochastic

8Empiricaldistributiond(t)ationoftestingd(n(a)d(t)(b)NTNU-TrondheimNorwegian University ofScience and Technologywww.ntnu.edu

8 Empirical distribution

0NonparametricmethodsWedo not makeanyassumptionsabout the lifedistribution F(t)T;-potential lifecyleti-the observed value of T;ThesamplemeanSm1-1Thesamplevariancet?(t)2tPNTNU- Trondheim?NorwegianLniversityofScience and Technologywww.ntnu.edu

9 Nonparametric methods We do not make any assumptions about the life distribution F(t) ܶ௜ െpotential lifecyle ݐ ௜െthe observed value of ܶ௜ The sample mean ݐ ̅ ൌ 1 ௜ݐ ෍݊ ௡ ௜ୀଵ The sample variance ݏଶ ൌ 1 ݊െ1෍ሺݐ ௜െ ݐ̅ሻଶൌ 1 ݊െ1 ሺ෍ ݐ௜ଶ ௡ ௜ୀଵ െ 1 ௜ݐ ෍ሺ݊ ௡ ௜ୀଵ ሻଶሻ ௡ ௜ୀଵ

10EmpiricaldistributionLetF(t)denotethe lifedistributionfora certaintypeof items.Theempirical distributionfunctionisdefinedasNumberoflifetimes≤tFn(t)=nIf we assume that there are no ties in the data set, the empirical distribution function maybewrittenfort<t(1)Fn(t) :for t() ≤t<t(i+1);i = 1,2, .,(n - 1)n1fort(n) ≤tNTNU -Trondheim福NorwegianUniversityofScienceand Technologywww.ntnu.edu

10 Empirical distribution Let ܨሺݐሻ denote the life distribution for a certain type of items. The empirical distribution function is defined as ൌ ݐ ௡ܨ Number of lifetimes ൑ ݐ ݊ If we assume that there are no ties in the data set, the empirical distribution function may be written ൌ ݐ ௡ܨ 0 for ݐ ൏ ݐሺଵሻ ݅ ݊ for ݐሺ௜ሻ ൑ݐ൏ݐ௜ ାଵ ; ݅ ൌ 1, 2, . , ሺ݊ െ 1ሻ 1 for ݐሺ௡ሻ ൑ ݐ t