An adaptive two-stage Bayesian model averaging approach to planning and analyzing accelerated life tests under model uncertainty

Abstract

Accelerated life testing (ALT) is commonly used to predict the lifetime of a product at its use stress by subjecting test units to elevated stress conditions that accelerate the occurrence of failures. For new products, the selection of an acceleration model for planning optimal ALT plans is challenging due to the absence of historical lifetime data. The misspecification of an ALT model can lead to considerable errors when it is used to predict the product’s life quantiles. This article proposes a two-stage Bayesian approach to constructing ALT plans and predicting lifetime quantiles. At the first stage, the ALT plan is optimized based on the prior information of candidate models under a modified V-optimality criterion that incorporates both asymptotic prediction variance and squared bias. A Bayesian model averaging (BMA) framework is used to derive the posterior model and the posterior distribution for the life quantile of interest under use stress. If the obtained test data cannot provide satisfactory model selection results, an adaptive second-stage test is conducted based on the posterior information from the first stage. A revisited numerical example demonstrates the efficiency and robustness of the resulting Bayesian ALT plans by comparing with the plans derived from previous methods.

Keywords:

• design of experiments
• lognormal distribution
• reliability assessment
• robust design
• Weibull distribution

Acknowledgment

We are grateful to the editor and two referees for their insightful comments to earlier versions of the article.

Additional information

Funding

Xie and Zhao were supported in part by the Research Grants Council of Hong Kong under Grant T32-101/15-R and CityU 11203815, and in part by the National Natural Science Foundation of China (71532008). Pan was partially supported by National Science Foundation CMMI 1726445.

Notes on contributors

Xiujie Zhao

Mr. Zhao received his PhD degree from the Department of Systems Engineering and Engineering Management. He is the corresponding author. His email address is [email protected]

Rong Pan

Dr. Pan is associate professor in the School of Computing, Informatics & Decision Systems Engineering. His email address is [email protected]

Enrique del Castillo

Dr. del Castillo is distinguished professor of Industrial and Manufacturing Engineering and professor of Statistics. His email address is [email protected]

Min Xie

Dr. Xie is chair professor in the Department of Systems Engineering and Engineering Management. His email address is [email protected]