【正文】 C ? In the second sample, you test 40 windings at 100 176。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。 C Some of the units drop out of the test for unrelated reasons. In the Minitab worksheet, you use a column of censoring indicators to designate which times are actual failures (1) and which are censored units removed from the test before failure (0). Note: For Minitab analysis you need to specify the column containing the censoring information in all the dialogue windows at the ―censor‖ button. Data: C:/BoosterData/ Time: 30 min. 36 Exercise: Answers Find an appropriate distribution ? The distribution ID plots suggest to either use the lognormal or the loglogistic distribution. We selected the loglogistic for continued analysis. ? Note: You must specify the Censor columns L o g n o r m a l b a s e e6 7 . 2 2 , 1 6 . 5 0L o g n o r m a l b a s e 1 06 7 . 2 2 , 1 6 . 5 0E x t r e m e v a lu e6 8 . 5 1 , 1 7 . 8 3L o g lo g i s t i c6 7 . 1 4 , 1 6 . 4 5A n d e r s o n D a r l i n g ( a d j )T e m p 8 0T e m p 1 0 0 1 51 02 03 04 05 06 07 08 09 59 91 0 1 0 0L o g n o r m a l b a s e ePercent 1 51 02 03 04 05 06 07 08 09 59 91 0 1 0 0L o g n o r m a l b a s e 1 0Percent 1 2 3 51 02 03 04 05 06 07 08 09 09 59 9 1 0 0 0 1 0 0E x t r e m e v a l u ePercent 1 51 02 03 04 05 06 07 08 09 59 91 0 1 0 0L o g l o g i s t i cPercentF 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 e m p 8 0 T e m p 1 0 0M L E s t i m a t e s C e n s o r i n g C o l u m n i n C e n s 8 0 . . . C e n s 1 0 037 Exercise: Answers, cont. Create the Overview plot. 3 4 / 63 7 / 1 3F / C1 6 . 4 56 7 . 1 4A D *0 . 4 1 6 40 . 2 8 1 4S ca l e3 . 6 3 5 94 . 0 7 0 9L o ca t i o nT e m p 1 0 0T e m p 8 0T e m p 8 0T e m p 1 0 0100109995908070605040302010 5 1Log log istic Pro bab ilityPercent25020xx501005001 . 00 . 90 . 80 . 70 . 60 . 50 . 40 . 30 . 20 . 10 . 0Su rviva l Fu nct ionProbability25020xx501005000 . 0 30 . 0 20 . 0 10 . 0 0Haz ard Fu nct ionRate25020xx501005000 . 0 20 . 0 10 . 0 0Pro bab ility D ens ity F unc tionOv erv iew P lot f or T em p80T em p100M L E s t i m a t e s C e n s o r i n g C o l u m n i n C e n s 8 0 . . . C e n s 1 0 038 Exercise: Answers, cont. T e m p 8 0 T e m p 1 0 0 25020xx501005001 . 00 . 90 . 80 . 70 . 60 . 50 . 40 . 30 . 20 . 10 . 0T i m e t o F a i lu r eProbabilityPa ra me t ri c Su rv i v a l Pl o t f o r T e mp 8 0 T e mp 1 0 0L o g lo g i s t i c D i s t r i b u t i o n M L E s t i m a t e s 9 5 . 0 % C IC e n s o r i n g C o lu m n i n C e n s 8 0 C e n s 1 0 0L o c a t i o n Sc a l e4 . 0 7 0 9 0 . 2 8 1 43 . 6 3 5 9 0 . 4 1 6 4T e m p 8 0 T e m p 1 0 0 100010010 9 9 9 5 9 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 5 1T i m e t o F a i lu r ePercentPro b a b i l i t y Pl o t f o r T e mp 8 0 T e mp 1 0 0L o g lo g i s t i c D i s t r i b u t i o n M L E s t i m a t e s 9 5 . 0 % C IC e n s o r i n g C o lu m n i n C e n s 8 0 C e n s 1 0 0L o c a t i o n Sc a l e A D * F/C4 . 0 7 0 9 0 . 2 8 1 4 6 7 . 1 3 7 / 1 33 . 6 3 5 9 0 . 4 1 6 4 1 6 . 4 3 4 / 6T e m p 8 0 T e m p 1 0 0 25020xx501005000 . 0 30 . 0 20 . 0 10 . 0 0T i m e t o F a i lu r eRatePa ra me t ri c H a za rd Pl o t f o r T e mp 8 0 T e mp 1 0 0L o g lo g i s t i c D i s t r i b u t i o n M L E s t i m a t e sC e n s o r i n g C o lu m n i n C e n s 8 0 C e n s 1 0 0L o c a t i o n Sc a l e4 . 0 7 0 9 0 . 2 8 1 43 . 6 3 5 9 0 . 4 1 6 439 Exercise: Answers, cont. From the Session Window answer the questions: At 80176。 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