A Bayesian Framework for Reliability Assessment via Wiener Process and MCMC

The population and individual reliability assessment are discussed, and a Bayesian framework is proposed to integrate the population degradation information and individual degradation data. Different from fixed effect Wiener process modeling, the population degradation path is characterized by a random effect Wiener process, and the model can capture sources of uncertainty including unit to unit variation and time correlated structure. Considering that the model is so complicated and analytically intractable, Markov Chain Monte Carlo (MCMC) method is used to estimate the unknown parameters in the population model. To achieve individual reliability assessment, we exploit a Bayesian updating method, by which the unknown parameters are updated iteratively. Based on updated results, the residual use life and reliability evaluation are obtained. A lasers data example is given to demonstrate the usefulness and validity of the proposed model and method