Data analysis of step-stress accelerated life tests with heterogeneous group effects

ABSTRACT

Step-Stress Accelerated Life Testing (SSALT) is a special type of experiment that tests a product′s lifetime with time-varying stress levels. Typical testing protocols deployed in SSALTs cannot implement complete randomization of experiments; instead, they often result in grouped structures of experimental units and, thus, correlated observations. In this article, we propose a Generalized Linear Mixed Model (GLMM) approach to take into account the random group effect in SSALT. Failure times are assumed to be exponentially distributed under any stress level. Two parameter estimation methods, Adaptive Gaussian Quadrature (AGQ) and Integrated Nested Laplace Approximation (INLA), are introduced. A simulation study is conducted to compare the proposed random effect model with the traditional model, which pools data groups together, and with the fixed effect model. We also compare AGQ and INLA with different priors for parameter estimation. Results show that the proposed model can validate the existence of group-to-group variation. Lastly, the GLMM model is applied to a real data and it shows that disregarding experimental protocols in SSALT may result in large bias in the estimation of the effect of stress variable.

KEYWORDS:

• Step-stress accelerated life test
• constrained randomization
• generalized linear mixed model
• adaptive Gaussian quadrature
• integrated nested Laplace approximation

Acknowledgements

The authors would like to thank the Editor and three referees for their valuable comments and suggestions that greatly improved the quality of this article.

Additional information

Notes on contributors

Kangwon Seo

Kangwon Seo is a Ph.D. candidate in industrial engineering at Arizona State University. He received his M.S. degree in industrial engineering from Arizona State University in 2014 and a B.E. in industrial systems engineering from Hongik University, South Korea, in 2004. His research interests include statistical modeling and data analysis, experimental designs for reliability improvement, and large-scale data analysis for social media and healthcare applications.

Rong Pan

Rong Pan is an associate professor of industrial engineering in the School of Computing, Informatics, and Decision Systems Engineering at Arizona State University. He received his Ph.D. degree in industrial engineering from Penn State University in 2002. His research interests include failure time data analysis, system reliability, design of experiments, multivariate statistical process control, time series analysis, and computational Bayesian methods.