Bayesian Degradation Tests with Random Effects and Time Scaling(1/2)

In this proposal, we are interested in the reliability analysis of the product based on degradation data.Degradation analysis is more efficient than the conventional life test in drawing reliability assessment forhigh quality products. This research aims on applying Bayesian approach to degradation data of differentproducts collected via degradation paths. Due to the heterogeneity of the test products, there may existpossible random effects among the test products and yet the degradation process may not be linear in time.The main purpose of this research is to develop a Bayesian degradation analysis based on stochasticdegradation processes in power function time scale with random effects. We shall first construct Bayesianformulation with random effects for commonly used stochastic processes, such as Wiener process, inverseGaussian process or gamma process. We will also consider using mixture priors of a point mass and acontinuous distribution to find the appropriate time scale transformation in the degradation model. How toconstruct a mixture prior to identity the existence of random effects so that both time scale and randomeffects can be clarified simultaneously is of particular interest in the first year. In the second year, in additionto extending the above Bayesian degradation models to accelerated degradation tests, we will also discusshow to utilize the information analyzed from the accelerated tests to sequential degradation tests undernormal use condition of a similar but new product. Both constant stress and step stress accelerateddegradation tests will be considered in this project. By updating the prior information in the degradation test,it can substantially reduce the experimental time. When random effects and time scaling are taken intoaccount, the challenge raised by the complicated likelihood function is computation of the global maximumlikelihood estimates. Bayesian approach, however, provides an alternative by introducing latent variables intothe model. A unified approach to selecting an ultimate model combining all the above aspects is to bedeveloped based on the structure of the prior as well as the posterior sample provided by the MCMCprocedure.