【正文】 1W e i b u l lA n d e r s o n D a r l i n g ( a d j )9 99 59 08 07 06 05 04 03 02 01 0 5 3 2 11 0 0 0 0 01 0 0 0 0W e i b u l lPercent9 99 58 07 06 05 04 03 02 01 0 5 11 0 0 0 0 01 0 0 0 0L o g n o r m a l b a s e ePercent9 99 89 79 59 08 07 06 05 03 01 03 0 0 0 0 02 0 0 0 0 01 0 0 0 0 00E x p o n e n t i a lPercent9 99 58 07 06 05 04 03 02 01 0 5 11 0 0 0 0 05 0 0 0 00N o r m a lPercentF o u r w a y P r o b a b i l i t y P l o t f o r T o n g u e I n s e rM L E s t i m a t e s C o m p l e t e D a t a27 Minitab Follow along: Parametric Reliability Analysis, cont. 2. Get an overview of the reliability of the buckle heads. StatReliability/SurvivalDistribution Overview PlotRight Cens… Enter the distribution you’ve found here 28 Minitab Follow along: Parametric Reliability Analysis, cont. At 35,000 Plug Ins the rate of failure is about % The probability of a buckle head surviving 35,000 tongue insertions is about 85% 29 Minitab Follow along: Parametric Reliability Analysis, cont. 3. Analyze the reliability further more to find out after how many plugins 1% of the heads fail and how many percent survive 35,000 plugins StatReliability/SurvivalParametric Dist AnalysisRight Cens… 30 Minitab Follow along: Parametric Reliability Analysis, cont. Use your notebook to follow along. 31 Minitab Follow along: Parametric Reliability Analysis, cont. As seen in the Overview Plot Plus confidence bands 1000005000000 .0 0 0 1 00 .0 0 0 0 50 .0 0 0 0 0T i m e t o F a i l u r eRatePara m et ric H az ard Plot f or T on gu e I ns ert ionW e ib u ll D ist ri b u t io n M L E st im a t e sC o m p le t e D a t aS h a p eS c a l eM T T FS tD e vM e d i a nIQ R 2 .8 6 4 1 6 6 6 1 5 5 9 3 7 0 2 2 4 9 3 5 8 6 1 4 3 1 5 4 50 50000 1000000 .00 .10 .20 .30 .40 .50 .60 .70 .80 .91 .0T i m e t o F a i l u r eProbabilityPara m et ric Surv iv al Plot f or T on gu e I ns ert ionW e ib u ll D ist ri b u t io n M L E st im a t e s 9 5 . 0 % C IC o m p le t e D a t aS h a p eS c a l eM T T FS tD e vM e d i a nIQ R 2 .8 6 4 1 6 6 6 1 5 5 9 3 7 0 2 2 4 9 3 5 8 6 1 4 3 1 5 4 532 Minitab Follow along: Parametric Reliability Analysis, cont. ? Reliability is more usually stated with a single sided confidence limt, . ―99% Reliability at 90% Confidence‖, meaning there is only a 10% chance that the Reliability is less than 99%. To use a single sided limit: Reedit the last dialog (ctl E) Or repeat StatReliability/SurvivalParametric Dist AnalysisRight Cens… EstimateType ―90‖ for Confidence Level amp。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。 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。 C ? In the second sample, you test 40 windings at 100 17