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Mathematical Problems in Engineering
Volume 2014, Article ID 486368, 8 pages
Research Article

A Bayesian Framework for Reliability Assessment via Wiener Process and MCMC

1Department of Industrial Engineering, Southeast University, Nanjing 211189, China
2Department of Mathematics, Hubei Engineering University, Xiaogan 432100, China

Received 27 August 2013; Revised 2 March 2014; Accepted 14 March 2014; Published 9 April 2014

Academic Editor: Sarp Adali

Copyright © 2014 Huibing Hao and Chun Su. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The population and individual reliability assessment are discussed, and a Bayesian framework is proposed to integrate the population degradation information and individual degradation data. Different from fixed effect Wiener process modeling, the population degradation path is characterized by a random effect Wiener process, and the model can capture sources of uncertainty including unit to unit variation and time correlated structure. Considering that the model is so complicated and analytically intractable, Markov Chain Monte Carlo (MCMC) method is used to estimate the unknown parameters in the population model. To achieve individual reliability assessment, we exploit a Bayesian updating method, by which the unknown parameters are updated iteratively. Based on updated results, the residual use life and reliability evaluation are obtained. A lasers data example is given to demonstrate the usefulness and validity of the proposed model and method.