Analyzing step-stress accelerated life testing data using generalized linear models

Abstract

In this article the parameter estimation method of Step-Stress Accelerated Life Testing (SSALT) model is discussed by utilizing techniques of Generalized Linear Model (GLM). A multiple progressive SSALT with exponential failure data and right censoring is analyzed. The likelihood function of the SSALT is treated as being a censoring variate with Poisson distribution and the life-stress relationship is defined by a log link function of a GLM. Both the maximum likelihood estimation and the Bayesian estimation of GLM parameters are discussed. The iteratively weighted least squares method is implemented to obtain the maximum likelihood estimation solution. The Bayesian estimation is derived by applying Jeffreys' non-informative prior and the Markov chain Monte Carlo method. Finally, a real industrial example is presented to demonstrate these estimation methods.

Keywords:

• Accelerated life testing
• Bayesian statistics
• inference
• reliability engineering

Acknowledgement

We sincerely thank one anonymous referee for a stimulating discussion on data diagnosis and Bayesian analysis, and we thank Dr. Wayne Nelson for providing us the experimental context of the example used in this article. The research is partially supported by the NSF grant DMI-0654417.

Notes

*The number inside the parenthesis is the thickness (mm) of cable, and + indicates the censoring time.