Baysian Analysis For Weibull Distribution

The reliability estimate and the reliability demonstration test are important in the reliability engineering. The reliability estimate is the problem how to estimate the products' reliability based on the known distribution and data and the reliability demonstration is the problem how long the test is based on the known distribution and some reliability index meeting the expectation. In the paper, Bayesian method is used to study the problems of the reliability estimate and the reliability demonstration test for Weibull distribution.First, the reliability estimate for Weibull distribution is discussed. On the basis of the failure probability and reliability, the paper proves the prior distribution is reasonable and gets their Bayesian estimate by means of the hierarchical priordistribution. Then, by a least square method parameters and the important reliability indexes Bayesian estimates are given out. Besides, after introducing failure information, Bayesian synthesis estimates are given out.Secondly, Bayesian confidence bounds is studied for the two cases. One is that the scale parameter is known and the characteristic life is unknown, the other is that both are unknown. After introducing the concept of the shortest Bayesian confidence interval, the paper given out the bilateral and single interval estimates of the parameters and the important reliability indexes .At last, the reliability demonstration test for Weibull distribution is discussed. The reliability demonstration testing procedure is given for each of the two cases which is the same as the confidence interval estimate. The procedure not only thinks over the employers' interests but also guarantees the producers' by means of the unconditional probability.