Two-parameter Exponential, Weibull Distribution Parameters Bayesian Estimation And Reliability Analysis

Bayes estimation is to estimate total parameter from the prior experiment information and sample information, with fine quality. Reliability analysis is critical in reliable projects while the research on zero-failure data is more important in today emphasizing high-reliability products.This essay will discuss Two-Parameter Exponential Weibull Distribution from three aspects based on the prior research on Bayes estimation, the admissibility of parameters and the reliable analysis with zero-failure data:First and foremost, under type-II censored, we will discuss square loss function, Entropy loss function and LINEX loss function. We will choose their Gama conjugated distribution as prior experiment distribution on the condition that we have one of the parameters in two-parameter exponential Weibull distribution and give the Bayes estimation of the unknown parameter. Take Entropy loss function for example, we give the multi-layer Bayes estimation on the assumption that Gama distribution and uniform distribution are prior experiment distributions.Secondly, in the case of complete sample, we will discuss the Bayes estimation of three loss functions above and explain its admissibility. Last but not the least, in the reliable analysis of two-parameter exponential Weibull with zero-failure data, we assure that the choice of loss-probability prior experiment distribution is reasonable by proof. In addition, we obtain loss-probability estimation and reliable estimation using multiple layer prior experiment Bayes method and Virence algorithm and nonlinear regression least square method fitting failure probability and reliability. we also explain its validity by data.