The Determination Of Prior Distribution And Bayesian Reliability Evaluation In The Case Of Dynamic Collectivity

According to the characteristics of multi-stage in weapon tests, this paper studies the theories and the methods of Bayesian dynamic statistics. Exactly speaking, this paper does research on the determination of prior distribution and Baysian reliability evaluation in dynamic collectivity, driven by application of evaluation in reliability growth tests of weapons.Prior information is imperative in determining prior distribution. In order to use the prior information thoroughly and soundly, this paper firstly summarizes and concludes the basic methods of dealing with prior information, including acquisition, classification and denotion of the prior information; inspection of coincidence of prior information; analysis of credibility of prior information. It places emphasis on the discussion of credibility of prior information and describes the determination of relative parameters of credibility in details.Then this paper researches the determination of prior distribution in dynamic collectivity and Bayesian evaluation of reliability growth tests based on exponential distribution. It summarizes the general methods of determining prior distribution, places value on the conversion methods and presents the dynamic modeling method of conversion factor based on AMSAA model at the end of every stage. Relative formulas are deduced and an example is presented to illustrate this method. Besides, a method of regarding the conversion factor as a random variable is provided when considering the characteristic in statistics of the conversion factor. The method is more effective by comparison with traditional methods.Furthermore, this paper studies the determination of prior distribution in dynamic collectivity and Bayesian evaluation of reliability growth tests based on Weibull process. It summarizes the current methods and compares them by an example. A method of test analysis based on order model of multi-stage Weibull process is provided, which determines the prior distribution of failure rate by orderly constrainting relation of failure rate and by supposing and inspecting the shape parameter. It uses the test information of multi-stage fully and reduces the confidence span of failure rate.A new flow chart is presented to analyze multi-stage reliability growth tests of correct-delay model. Transforming available prior information to number of expectant failure and prior distribution of shape parameter, the method applies conversion factor to confuse test information of every stage. Some deduction is done to select variable accurately and the reasonable value range is given. A reasonable method to deal with dynamic statistics of multi-stage reliability grow tests is formed by time adjust, prior distribution transformation and conversion factor.The robustness analysis is an important aspect in Bayesian statistics and inference. At last, the paper researches the robustness of prior distribution and posterior distribution, providing the basic theories and methods in analysis. Some research is done to apply the relative theory of exponential distribution to the determination of confidence level of conversion factor. An idea that the general form of conversion factor is determined by prior information and the conversion factor is amended by spot information is presented, which lowers the subjectivity to some extent and improves the accuracy of evaluation.