Planning accelerated life tests with multiple sources of random effects

Abstract

Accelerated life testing (ALT) is a commonly used experiment in industries for assessing a product’s lifetime. Planning a proper test with consideration of possible constraints on randomization is important because the prediction accuracy highly depends on the test plan. In this article, an optimal ALT test plan with multiple sources of random effects is demonstrated. Specifically, we consider two types of random effects caused by subsampling and blocking, and the experimental design consists of a crossed experimental factor – supplier, as well as a nested experimental factor – test chamber. The D-optimal ALT test plan is derived via a quasi-likelihood approach. An optimization algorithm with three iterative steps is developed to determine testing stress conditions, chamber assignments, and the number of test units for each testing condition and their supplier sources. The resulting test plans assign test units to chambers such that the effect of stress factor will not confound with the effect of test chamber and a similar number of test units from different suppliers will be required for each test condition.

Keywords:

• accelerated life tests
• D-optimal design
• nested and crossed experiments
• quasi-likelihood
• random effects

Acknowledgments

The authors are very grateful to the editor and the anonymous referees. Their constructive and detailed comments have contributed to substantial improvements of this article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Kangwon Seo

Kangwon Seo is an Assistant Professor in the departments of Industrial and Manufacturing Systems Engineering and Statistics at the University of Missouri-Columbia. His research interests include applied statistics, quality and reliability engineering, and optimal experimental designs.

Rong Pan

Rong Pan received B.S. Materials Science and Engineering from Shanghai Jiao Tong University, Shanghai, China, in 1995. He received M.S. Industrial Engineering from Florida A&M University in 1999 and his Ph.D. degree industrial engineering from the Pennsylvania State University in 2002. He is currently an Associate Professor in the School of Computing, Informatics, and Decision Systems Engineering at Arizona State University. His research interests include quality and reliability engineering, design of experiments, time series analysis, and statistical learning theory. He is a senior member of IEEE, ASQ and IISE, and a lifetime member of SRE.