Real-time reliability evaluation based on independent increment process with random effect

Degradation data provide useful information about the reliability assessment for highly reliable and long lifetime products. Motivated by laser degradation data, a new degradation modelling approach is proposed, in which degradation path has linear mean and linear standard deviation functions. In this article, the population degradation modelling and individual real time reliability assessment are discussed, and a Bayesian framework is proposed to integrate population degradation information and individual degradation data. The population degradation path is characterized by a random effect independent increment process where random effect captures unit to unit variation, and the Markov Chain Monte Carlo (MCMC) method is used to estimate the unknown parameters. To obtain individual real time reliability assessment, the parameters are updated iteratively using Bayesian theory. Based on updated results, the residual use life and individual real-time reliability evaluation are obtained. For an illustration of the usefulness and validity of the proposed model and method, a numerical example about laser data is given.