Some Applications Of Bayes Method In The Study For The Reliability Of Zero-Failure Data

Bayesian reliability analysis method is a parameter estimation method which applies Bayesian method to the reliability models in order to solve parameter estimation. With the extensive application of high technology in real life and the continuous development of science and technology,the data which we obtained in the censored tests may be the zero-failure data. That is to say,within the time prescribed test,there is no product failure. There is a certain degree of difficulty that using data analysis for failure to establish the basis of the existing reliability theory to analyze the issues of the zero-failure data. So,now we are finding out a way that can analysis data scientifically and effectively under the condition of no failure data has became a very important and a new research direction in reliability investigation.This paper is mainly composed of three parts:Part One: For the exponential distribution of the products,the use of the convexity and non-memory property of exponential distribution,the Bayesian estimation of the product reliability is given in the case of the zero-failure data, and further to get the weighted least squares estimations of the average life expectancy of the product.Part Two: When the zero-failure data was got in the time curtailed test of the product of exponential distribution,the hierarchical Bayesian estimation and the expected Bayesian estimation of the product reliability were given by the convexity and the non-memory property of the exponential distribution,the numerical example illustrate the relationship between them. The weighted least squares estimations of parameterθunder the two cases were obtained.Part Three :after introducing failure information by two kinds of method, When prior distribution of failure-rate is in form of the Gamma distribution, the synthesize expected Bayesian estimation of the failure-rate in exponential distribution has come from zero-failure data under two cases. Then the synthesize estimation of reliability of zero-failure data is given.