Bayesian Estimation for Failure Probability Through Bogey Test Data

The increase of high-cost and high precision manufacturing process underlines the importance of the reliability estimation of Bogey test data. To estimate the failure probability of Bogey test, Bayesian approaches often focus on the choice of the prior distribution. However, this paper develops a new method, which making use of the concavity of lifetime's distribution function to construct a non informative prior for the failure probability. By integrating all the test information, not only the number of effective samples but also previous test information, we explore a new form of the likelihood function for failure probability. Through updating the boundaries of the prior in each step by previous steps' estimations, we obtain the failure probability progressively. In the case study, we construct sensitivity analysis to show that our method is more robust to different lifetime distribution assumptions than other existed methods.