Research On Small-Sample Fuzzy Reliability Based On BMC Method

Because fuzzy reliability can deal with the fuzzy problems which the traditional reliability can't resolve, recently it becomes a hotspot in the research area of reliability. In order to solve problems such as the difficulty of data statistics for large sample, the high cost of the Fuzzy Reliability and so on, this thesis presents BMC method for the small-sample Fuzzy Reliability evaluation to minish the prior subjective and posterior complexity efficiently.The main works are as the following:1. Study the Bayes method and propose the weakness of it. To improve Bayes method, present BMC method and establish the whole framework of it for the small-sample Fuzzy Reliability evaluation.2. To resolve the three key problems of BMC framework, which are prior distribution deduce, one-dimension posterior evaluation and multi-dimension posterior evaluation, propose the methods of weighted prior distribution based on information entropy, one-dimension posterior evaluation based on multi-weighted sample and multi-dimension posterior evalution based on the sample of Markov Chains Monte Carlo respectively.3. Using BMC method, Establish the BMC evalution models of exponential life distribution and Weibull life distribution, evaluate the small-sample Fuzzy Reliability for the two distributions. At the same time, design simulation experiment for the two distributions based on Matlab. Show the applicability and rationality of BMC method from the views of application and experiment respectively.