Bayesian inference of multi-stage reliability for degradation systems with calibrations

The importance of degradation analysis as a method of reliability assessment has been increasing because the products become more and more reliable. Bayesian updating is important in the dynamic analysis of few degradation data collected in multiple stages. A problem of assessing the reliability of a degradation system, wherein calibration of a development program is carried out, within a multi-stage, by Bayesian inference, is proposed in this article. Two types of posterior distribution are obtained in each testing stage under an assumption that degradation performance follows a normal distribution for two cases. Then, two Bayesian models are presented to evaluate the system reliability. A conclusion is also derived, that is, the variance of a key random variable decreases as the number of testing stage grows. Finally, a numerical example illustrates the model, process and the analysis results.