Bayesian analysis for inverse Gaussian lifetime data with measures of degradation

There are many models for lifetime data. In this paper we consider a situation where in addition to data on lifetimes we also have data on a measure of degradation for surviving items. The assumption is that when an item degrades to a certain level it fails. By modelling the degradation process as a Wiener process for which the first passage time to a boundary has an inverse Gaussian distribution we can model the lifetime data and degradation data together in a natural way. We make inferences about the parameters of the degradation process and predictions about future items using a Bayesian approach. Gibbs sampling is used as it enables posterior distribution and predictive distributions to be found. We illustrate the methods using a simulated data set which has previously been analysed using maximum likelihood methods. We compare the results with the analysis of the data treating the surviving items as censored observations. Using the simulated data we show that inferences are much sharper if we take account of the degradation information rather than treating the surviving items as censored observations.