A general method of prior elicitation in bayesian reliability analysis

The primary motivation of using Bayesian statistics in reliability analysis is the ability to incorporate prior knowledge with limited testing results in a formal procedure. This idea is particularly suitable for high reliable systems, which cannot afford enough samples to meet the confidence requirement in reliability demonstration test. The problem of appropriate choice of prior distribution is the central one confronting the reliability users of Bayesian methods. In this paper, a general prior elicitation method is proposed through which analyst could communicate with experts or engineers easily. This method changes traditional approach of dealing with moments or quantiles of the parameters but translates the information from failure time into parameters in different distribution models. The best and worst estimation of the mean and variance of the failure time which reflect people´s prior knowledge are required and then the analysis could proceed automatically. The method is applied with commonly used two-parameter reliability models using normal-gamma distribution as a prior distribution family. We analyzed the goodness of the elicited prior through prior predictive distribution and found it could effectively keep the information we presumed.