Iteration Bayes Analysis Of The Grouped Timing Terminated Data

Because of the outstanding realistic background and extensive application, many researchers committed themselves to the Bayes estimate constantly after the English scholar Bayes published–An Essay Towards Solving a Problem in Doctrine of Chances in the Royal Society transaction in 1763. The research's purpose of this paper is to apply iterative method to solve the problem of the grouped timing zero-failure data and only one failure data. The main works are as follows.In the chapter one, we introduce the background and theory of Bayes analysis as well as the developmental status of domestic.The procreant background and math model of the grouped timing zero-failure data and only one failure data were introduced. And then, we make a summary of the two problem's researchful actuality. The least squares method was recommended, which make the preparation for solving the questions of Bayes estimate in the grouped timing data.In the chaper two, aiming at the grouped timing zero-failure data, to obtain the estimates of failure probability, we introduce two used methods- Bayes method and iterative hierarchical Bayes method, and put forward the estimates of function parameters and riliability by three methods. Random simulating results indicate that HB methed is the best.In the chapter three, aiming at the grouped timing zero-failure data, to enhance the estimates precision of failure probability, we introduce IB method of amending p_i's transcendant step by step, consequently get one kind of iterative Bayes methed and IHB methed to estimate probability of failure for the grouped,timing truncated and zero-failure data. Examples prove that the methods are feasible. At the end, the choice of value ofλ_m and the difference between two iterative methods were discussed. In the chapter four, we apply the iterative method into the study of only one-failure data. For grouped, timing terminated and only-one-failure data, this chapter will obey to Weibull distribution situation at assume of the production life, discuss how to get IHB method by using life distributing function and information of only-one-failure data. Characters of IHB estimate of p_i are discussed. (λ_k , c) in IHB method, minmax Mahalanobis square distance principle is proposed in the bearing data example in this paper. The random simulating results indicate that the mothed is reasonable feasible.