【正文】 Reliability 2 Overview of this module ?Basic concepts ?Parametric Analysis ?Nonparametric Analysis ?Redundancy Reliability Basic Concepts 4 What is reliability? ?Products and systems are expected to function at the point of delivery and for a certain time. ?Sometimes there are contractual terms determining the time a system is expected to function without a limitation, . warranty times. ?Reliability is ―Quality over Time”. So reliability has to be developed into a product or system. 5 Reliability = 1 – Failure to Reliability Cumulative Failures ? F(t) = population proportion failed by time t Reliability ? R(t) = surviving proportion at time t Probability Density Function ? “Histogram of Failures“ ? Gradient of Cumulative Failure Curve ? f(t) = dF(t)/dt Hazard Rate ? Instantaneous Failure Rate at a particular time ? h(t) = f(t) / R(t) t t t F(t) R(t) f(t) h(t) Reliability Three Graphs 6 F(t) f(t) R(t) h(t) 1/ ? Cumulative Failures / Reliability F(t) = 1 exp ( t/?) R(t) = exp ( t/ ?) Where Mean Time to Failure MTTF = ? Probability Density Function f(t) = 1/ ? * exp ( t/ ?) Exponential Hazard Rate h(t) = 1/ ? (constant), often denoted as ? Same proportion fail in any time period no infant mortality or wear out Sometimes applies. Many parts have infant mortality amp。 wear out Hazard Function is then the “Bathtub” Curve. Reliability Exponential Model 7 Breakin, infant mortality, manufacturing defects, insufficient burnin Useful life Wearout Degradation Fatigue Corrosion Hazard Rate time Components / units may have all or some or a bination of the three “failure modes” Common hazard function: The “Bathtub” Curve 8 ?Exponential ?Normal ?Lognormal ?Weibull R(t) = exp [ (t/?)**?] ?Extreme Value “the weakest link” of identical parts ?Logistic ?Loglogistic ?Nonparametric In Minitab: We will find which of these models fits the data best and estimate percentiles. Other Reliability Models 9 Weibull R(t) = exp [ (t/?)**?] ?Shape (?) amp。 Scale (?) Factor for “one size fits all” ?Exponential is Weibull with Shape 1 ?Normal is Weibull with Shape 4 (approx.) ?63% failed at time t = ? Weibull Model 210T i m eWEI BULL FA MI LY OF CURV ESw eibull1. m gfB=5B=3B=2B=1 . 5B=1B=0 . 5B=0 . 210 T i m eFailure RateRELI A BI LI T Y BA T HT UB CURV EI n f a n t M o rt a l i t y R a n d o m (c o n s t a n t ) W e a ro u tt rng9. m gfR a n d o m F a i l u r e sIn f a n tM o r t a l i t yW e a r o u tU s e f u l L i f eYou recall the bathtub curve we discussed earlier. Degreasing steep failure rate at first, followed by constant failure rate, then a sharp increase in failure rate. The Weibull can take on each of these shapes depending on ? (Beta) (though not at the same time, of course !). Weibull Model amp。 Bathtub Curve 11 Who’s in charge of reliability? Concept and Product Definition Design and Product Engineering Procurement Process Engineering Production Planning and Manufacturing Distribution and Service QFD FMEA Reliability Planning, Testing, Improving DOE Process Qualification SPC 12 Reliability Roadmap Concept and Product Definition Design and Product Engineering Procurement Process Engineering Production Planning and Manufacturing Distribution and Service Identify reliability requirements, Set reliability targets Prognosis of reliability, Maximize robustness with DOE and reliability tests, determine redundancy Ensure reliable capabilities Control reliable process Analyze field data, Plan spare part contingents 13 Hours of operation 0 20xx F = 30% R = 70% Failures Basic Concepts Definitions ? Reliability is the probability of a product (or system) performing its purpose satisfactorily for a specified time period given specified operating conditions. ? Probability ranges from 0 (or 0%) plete unreliability to 1 (or 100%) plete reliability. ? . if we say that a unit is 70% reliable at 20xx hours, (in shorthand。 R (20xx) = ) we mean that 70% of units will last at least 20xx hours before failure. ? Failure percentage F is (100 R) , where R is the Reliability percentage (eg 30% of units will fail before 20xx hours.) 14 Hours of operation 0 20xx F = 30% R = 70% Failures Basic Concepts, cont. ? Knowing the underlying failure distribution (. Weibull form illustrated here see Appendix), we can estimate the reliability (or failure percentage) at any age. ? At 0 hours the reliability is 100%. ? At 20xx hours (after a cumulative 30% failures), the reliability is 70%. ? Note that the reliability statement is x% reliability at xx hours. ? We can also determine: ? the Survival Function or Lifetime to Failure ? the Hazard Function or Hazard Rate (Mortality Rate) 15 Reliability A B C D EL if e ( in 1 0 , 0 0 0 H o u r s )N o . F a ilu r e s s u r v iv o r s a t s t a r t o f p e r io dS u r v iv a l F u n c t io n ( = C / t o t a l )H a z a r d R a t e ( = B / C )0 1 6 100 1 . 0 0 0 . 0 6 01 2 50 94 0 . 9 4 0 . 5 3 22 3 20 44 0 . 4 4 0 . 4 5 53 4 10 24 0 . 2 4 0 . 4 1 74 5 5 14 0 . 1 4 0 . 3 5 75 6 4 9 0 . 0 9 0 . 4 4 46 7 1 5 0 . 0 5 0 . 2 0 07 8 1 4 0 . 0 4 0 . 2 5 08 9 1 3 0 . 0 3 0 . 3 3 39 1 0 1 2 0 .