【文章內(nèi)容簡介】 sembles buckles for safety belt systems and you want to find out the reliability of the buckles. You are interested, for warranty purposes, after how many tongue insertions will 1% of the buckle heads fail and what percentage of buckle heads will survive 35,000 tongue insertions. Data: C:/BoosterData/ 25 Minitab Follow along: Parametric Reliability Analysis, cont. 1. Identify a distribution that fits your data StatReliability/SurvivalDistribution ID PlotRight Cens… Choose from 8 distributions here 26 Minitab Follow along: Parametric Reliability Analysis, cont. The distribution where the data points can be fitted best with the straight line is the most appropriate distribution – in our case the Weibull distribution (you can also test the other 4 distributions Minitab offers) 0 , 6 1 5N o r m a l9 , 0 9 9E x p o n e n t i a l0 , 6 4 6L o g n o r m a l b a s e e0 , 5 0 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。 Select ―Lower‖ for Confidence Intervals. Then click ―OK‖ ―OK‖ 33 Minitab Follow along: Parametric Reliability Analysis, cont. Use your notebook to follow along. 34 Minitab Follow along: Parametric Reliability Analysis, cont. Note the Probability Plot amp。 Parametric Survival Plot now have only one confidence limit line. 0 5 0 0 0 0 1 0 0 0 0 00 , 00 , 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 91 , 0T i m e t o F a i lu r eProbabilityP a r a m e t r i c S u r v i v a l P l o t f o r T o n g u e I n s e r t i o nW e i b u l l D i s t r i b u t i o n M L E s t i m a t e s 9 0 , 0 % L o w e r B o u n dC o m p l e t e D a t aS h a p eS c a leM T T FS t D 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 51 0 0 0 0 1 0 0 0 0 0 1 2 3 5 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 9 5 9 9T i m e t o F a i lu r ePercentP 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 r t i o nW e i b u l l D i s t r i b u t i o n M L E s t i m a t e s 9 0 , 0 % L o w e r B o u n dC o m p l e t e D a t aS h a p eS c a leM T T FS t D e vM e d i a nIQ RF a i lu r eC e n s o rA D * 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 5 5 0 0 0 , 5 0 0 80 5 0 0 0 0 1 0 0 0 0 00 , 0 0 0 0 00 , 0 0 0 0 50 , 0 0 0 1 0T i m e t o F a i lu r eRateP a r a m e t r i c H a z a r d P l o t f o r T o n g u e I n s e r t i o nW e i b u l l D i s t r i b u t i o n M L E s t i m a t e sC o m p l e t e D a t aS h a p eS c a leM T T FS t D 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 4 535 Exercise: Parametric Reliability Analysis Background: At an Aerospace pany which manufactures engine windings for turbine assemblies Engine windings may depose at an