A Bayesian Predictive Analysis of Step-Stress Accelerated Tests in Gamma Degradation-Based Processes

Degradation modeling might be an alternative to the conventional life test in reliability assessment for high quality products. This paper develops a Bayesian approach to the step-stress accelerated degradation test. Reliability inference of the population is made based on the posterior distribution of the underlying parameters with the aid of Markov chain Monte Carlo method. Further sequential reliability inference on individual product under normal condition is also proposed. Simulation study and an illustrative example are presented to show the appropriateness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.

[1]  Narayanaswamy Balakrishnan,et al.  Optimal Step-Stress Accelerated Degradation Test Plan for Gamma Degradation Processes , 2009, IEEE Transactions on Reliability.

[2]  B. Yum,et al.  Optimal design of accelerated degradation tests based on Wiener process models , 2011 .

[3]  Suk Joo Bae,et al.  Generalized Linear Mixed Models for Reliability Analysis of Multi-Copy Repairable Systems , 2007, IEEE Transactions on Reliability.

[4]  Nagi Gebraeel,et al.  An adaptive functional regression-based prognostic model for applications with missing data , 2015, Reliab. Eng. Syst. Saf..

[5]  W. J. Padgett,et al.  Accelerated Degradation Models for Failure Based on Geometric Brownian Motion and Gamma Processes , 2005, Lifetime data analysis.

[6]  Jan M. van Noortwijk,et al.  A survey of the application of gamma processes in maintenance , 2009, Reliab. Eng. Syst. Saf..

[7]  Alaa Elwany,et al.  Residual Life Predictions in the Absence of Prior Degradation Knowledge , 2009, IEEE Transactions on Reliability.

[8]  Rong Li,et al.  Residual-life distributions from component degradation signals: A Bayesian approach , 2005 .

[9]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[10]  M. Nikulin,et al.  Estimation in Degradation Models with Explanatory Variables , 2001, Lifetime data analysis.

[11]  Tongmin Jiang,et al.  A Bayesian reliability evaluation method with integrated accelerated degradation testing and field information , 2013, Reliab. Eng. Syst. Saf..

[12]  Sheng-Tsaing Tseng,et al.  Optimal design for step-stress accelerated degradation tests , 2006, IEEE Trans. Reliab..

[13]  Alyson G. Wilson,et al.  A fully Bayesian approach for combining multilevel failure information in fault tree quantification and optimal follow-on resource allocation , 2004, Reliab. Eng. Syst. Saf..

[14]  W. J. Padgett,et al.  Inference from Accelerated Degradation and Failure Data Based on Gaussian Process Models , 2004, Lifetime data analysis.

[15]  G A Whitmore,et al.  Estimating degradation by a wiener diffusion process subject to measurement error , 1995, Lifetime data analysis.

[16]  L. Pettit,et al.  Bayesian analysis for inverse gaussian lifetime data with measures of degradation , 1999 .

[17]  M. Crowder,et al.  Covariates and Random Effects in a Gamma Process Model with Application to Degradation and Failure , 2004, Lifetime data analysis.

[18]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  Huan Wang,et al.  Planning of step-stress accelerated degradation test based on the inverse Gaussian process , 2016, Reliab. Eng. Syst. Saf..

[20]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[21]  Z. Birnbaum,et al.  A new family of life distributions , 1969 .