Bayesian reliability assessment and degradation modeling with calibrations and random failure threshold

A degradation model with a random failure threshold is presented for the assessment of reliability by the Bayesian approach. This model is different from others in that the degradation process is proceeding under pre-specified periodical calibrations. And here a random threshold distribution instead of a constant threshold which is difficult to determine in practice is used. The system reliability is defined as the probability that the degradation signals do not exceed the random threshold. Based on the posterior distribution estimates of degradation performance, two models for Bayesian reliability assessments are presented in terms of the degradation performance and the distribution of random failure threshold. The methods proposed in this paper are very useful and practical for multi-stage system with uncertain failure threshold. This study perfects the degradation modeling approaches and plays an important role in the remaining useful life estimation and maintenance decision making.