Weibull分布幻灯片.ppt

Introductions to Weibull Distribution Useful website : Motivation - Example) Testing 40 capacitors at 85C, 105C, and 125C(totally 120 capacitors) How long can we guarantee a capacitor’s life @ 25C ??? Or How many cells will fail in 10000 hours @ 25C ??? Reliability - Definition product Alive? : P(t) Dead? : 1-P(t) After t(time) - Reliability Test or Reliability Analysis Population Sample : failure rate f(t) : probability density function ? modeling Reliability functions PDF(Probability Density Function) = probability of failure between t and t+dt CDF(Cumulative Distribution Function) = probability of failure between 0 and t = Reliability function R(t) probability of pass between 0 and t Hazard function h(t) : failure rate h(t)dt = probability of failure between t and t+dt in survivors Cumulative hazard function H(t) Bathtub curve for failure rate Types of data X X X X X X X X X X X X X X X X t t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 T Exact times-Censored type I kth failure Exact times-Censored type II t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 1 fail 1 fail 1 fail 2 fail 1 fail 2 fail 1 fail 1 fail 1 fail 3 fail T Readout time data multicensored data : readout time data with non-uniform interval Most commonly used Distribution functions 1. Exponential distribution : modeling the constant failure rate Most commonly used Distribution functions(Cont’d) 2. Weibull distribution : model for many product failure mechanisms : shape parameter ?: scale parameter Most commonly used Distribution functions(Cont’d) 2. Weibull distributions : model for many product failure mechanisms : shape parameter ?: scale parameter Cumulative hazard function Hazard function CDF Reliability function Mean Variance where Most commonly used Distribution functions(Cont’d) 3. Normal distribution (Gaussian distribution) : most widely-used general purpose distribution Most commonly used Distribution functions(Cont’d) 4. Log-Normal