Bayesian models and ageing indicators for analysing random changes in failure occurrence

The paper introduces ageing models of repairable components based on Bayesian approach. Models for the development of both failure rate and the probability of failure on demand are presented. The models are based on the assumption that the failure probability or rate has random changes at certain time points. This is modelled by assuming that the successive transformed failure probabilities (or rates) follow a Gaussian random walk. The model is compared with a constant increment model, in which the possible ageing trend is monotone. Monte-Carlo Markov Chain sampling is applied in the determination of the posterior distributions. Ageing indicators based on the model parameters are introduced, and the application of these models is illustrated with case studies.