Researches On The Small Sample Statistical Inference And Fusion Theory And Its Application To The Assessment Of Weapon System

According to the dominant characteristics of test analysis and assessment of weapon system in small sample circumstance, the Baysian method in small sample statistical inference and fusion theory is adopted as an important and suitable approach. Some general theoretical problems in Baysian approach's engineering application have been studied in this dissertation, and what is more, the dissertation conducted further application researches in respect of weapon system accuracy and reliability assessment.First, some general theoretical problems in a prior information processing are studied in this dissertation, such as calassification, acquirment, expression, consistency test and credibility analysis of a prior information and fusion of a prior information from multiple sources and so on. A new method of calculating a prior information creditability is especially presented by using the concept of information likelihood rate .Secondly, some general problems concerned with the engineering application of Bayesian statistical inference are studied in this dissertation. The dissertation introduced the concepts of a prior cost and test cost into loss function for the first time and analyzed the relation among the sample size, a prior information and Bayesian statistical decsion adventure. It deduced the inequality formula between a prior information credibility and sample size, which proposed a theoretic criterion for finding the guarantee lower limit of a prior information credibility in the case of given small sample size. It proposed a new concept, sub-optimal sample size, and therefore obtained an optimizing stratage to determine the test sample size. Considering that the problem of "different probability distribution" exists in test analysis and assessment, the dissertation also studied the modeling and Bayesian estimation for dynamic distribution parameters.Thirdly, the Bootstrap method is applied to the small-sample statistical inference and fusion theory. On the basis of engineering application, the following problems are studied in detail, they are the acquisition of a prior distribution based on Bootstrap method or random weighted method, and the comparison of the above two methods under circumstance of small-sample, and the self-help fusion estimation on a prior distribution, and so on.At last, the dissertation completed two application researches in respect of weapon system accuracy and reliability assessment. First, based on the accuracy assessment of X X - X X C type cluster warhead, the Baysian assessment method of Circular Error Probability ( CEP ) in small sample circumstance has been studied. Second, the Baysian reliability assessment method of a large complex system in small sample circumstance has been studied in the advanced research project of "Tenth-Five-Year-Plan" of weapon system and it is innovatory to develop a system Baysian reliability assessment (SBRA) software in order to advance the ability of a large complex system reliability assessment.