Applying Hierarchical Bayesian Method in Reliability Prediction Based on Degradation Measurements

摘要

The reliability for some devices with few or no failures in their life tests becomes very hard to access if a traditional life test which records only time-to-failure was utilized. To solve this problem, the analysis of the over time degradation measurements is always considered in the practical cases. The realization of the degradation processes is expected to be represented by the constructed degradation model. Based on the developed models, the failure times for devices and the time-to-failure distribution can be estimated. In this paper, a hierarchical Bayesian model (HBM) with autocorrelated residuals is proposed to construct a broad class of degradation models for dealing with degradation measures. For finding the appropriate estimates of model's parameters, the Markov Chain Monte Carlo (MCMC) algorithms are applied. A fatigue crack growth data is used as an example for illustrated the modeling procedure of HBM. By specifying the coefficients in the HBM, the heterogeneity varying across individual products can be successfully identified. In additions, the prediction intervals of future degradation measures for evaluated the prediction efficiency are provided.