E-Bayes Statistical Analysis And Modification Of Reliability Parameters In The Case Of Zero-Failure Data

With the development of science and technology, the reliability of production has been paid to more and more attention. Reliability theory mainly considers the life characteristics of products in a wide range of practice areas. Because the life of the production is a random phenomenon, it comes to a random inference problem that we try to determine the reliability indexes of the production. Therefore, it is a very significant research of applying Bayes experience and Bayes theory to a reliable field. Basing on the fruit of the predecessors, this paper makes some researches on the above-mentioned question, the main works including:Firstly, the paper discusses the problem of double hyper parameters under zero failure data. If the prior distribution be Beta function, we construct a decreasing function, give E-Bayes estimation of it failure probability, and on the above bases, we examine its reliability target. At last we give theoretical justification. The result indicates: When the total number of the test sample is sufficient, reliability target is almost equivalency which by this method and the hierarchical Bayes estimation method. The result shows that the method adopted here is feasible and reasonable.Secondly, this chapter develops a new method, to introduce into failure information in the case of zero-failure data, and then E-Bayes estimation of its failure probability is given. The estimation of reliability parameters is further amended. Finally, by the E-Bayesian estimation method applied to the simulation example, as can be seen, it is both efficient and easy to operate.At last, we take prior distribution of failure probability be itsconjugated distribution-Beta(p_i-1, 1,1, b) and hyper parameter b as the uniform distribution in(1,c). With quadratic loss function, when p_i∈(p_i-1,1), the E-Bayesian estimation of p_i is given, and discussed the relationship of p_i in different integral interval. At the same time, the examples of simulation graph are compared.