A simple procedure for analyzing reliability data from double-stage accelerated life tests

ABSTRACT

This paper proposes a simple statistical approach for analyzing reliability data arising from double-stage Accelerated Life Tests (ALT). The main motivation is to develop a workable solution, which can be easily understood and implemented by quality and reliability engineers, for incorporating existing engineering knowledge on life-stress relationship into ALT data analysis. We focus on the most general scenario where the lifetime follows the log-location-scale distribution and the life-stress relationship is log-linear. The proposed approach, which is based on the shrinkage estimation technique, utilizes the prior knowledge on the slope parameter in the form of an initial estimate or guessed value. The risk of incorporating such knowledge is investigated in terms of the bias, variance, and mean squared error of the estimator of a certain life quantile at use condition. The applications of the proposed method are illustrated by numerical examples. Comprehensive comparison study between the proposed method and Maximum Likelihood estimation is performed based on three real-life ALT examples. The proposed approach can be easily implemented in any statistical packages. In particular, the computer program, both in the MATLAB Graphical User Interface Design Environment (GUIDE) and R, is available on GitHub.

KEYWORDS:

• Accelerated life test
• shrinkage estimator
• least squares
• maximum likelihood estimation

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Notes on contributors

Xiao Liu

Dr. Xiao Liu is an Assistant Professor at the Department of Industrial Engineering, University of Arkansas. Before that, he was a Research Staff Member (RSM) at IBM Thomas J. Watson Research Center, New York (2015~2017), and IBM Smarter Cities Research Collaboratory Singapore (2012~2015).His research focuses on the integration of engineering domain knowledge and data-driven methodologies for spatio-temporal modeling, reliability, etc.