Estimation Of Parameter In The Case Of Zero-failure Data In The Extreme-value Distribution

With the development of science and technology, the quality of production is better and better. So in the type-â… life testing, the situation of zero-failure data often occurs, especially in high reliability and small sampling tests. Therefore the problem of zero-failure data becomes a new research aspect in the reliability engineering.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 extreme-value distribution.First, the reliability estimate for extreme-value distribution is discussed. On the basis of the failure probability and reliability, the paper gets the Bayesian estimate by means of the hierarchical prior distribution. Then, by a least square method parameters and the important reliability indexes Bayesian estimate are given out. Besides, after introducing failure information, Bayesian synthesis estimates are given out.Secondly, Bayesian confidence bounds are studied for the two cases. One is that the scale parameter is known and the location parameter is unknown, the other is that both are unknown. The paper gives out the two-sided confidence interval and one-sided confidence interval of the parameter and the reliability indexes through the Bayesian method.At last, the reliability demonstration test for extreme-value 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.