A Bayesian approach for estimating survival probabilities

Attribute life testing is one way assessing the reliability of a device, in which only the information of survival or nonsurvival of each test item is recorded. To optimize and accelerate the reliability estimation procedures for the survival probability p prior knowledge will be incorporated into the statistical analyses. Different sources of information like human expert's experience, field data or knowledge from similar designs can supply such prior information. The integration of this additional knowledge can be achieved with the aid of Bayesian inference. Since efficient algorithms like Markov Chain Monte Carlo (MCMC) have been developed over the past two decades, with which even complex integrals can be solved, Bayesian methods became popular in practical applications. This paper focuses on deriving characteristic reliability measures like the credibility interval, the mean value etc. from a posterior probability distribution reflecting both a sample of test data as well as the additional available knowledge.