Multiple-Steps Step-Stress Accelerated Degradation Modeling Based on Wiener and Gamma Processes

Abstract

During the step-stress accelerated degradation test (SSADT) experiment, the operator usually elevates the stress level at a predetermined time-point for all tested products that had not failed. This time-point is determined by the experience of the operator and the test is carried on until the performance degradation value of the product crosses the threshold value. In fact, this mode only works when a lot of products have been used in the experiment. But in the SSADT experiment, the number of products is relatively few, and so the test control to the products should be done more carefully. Considering the differences in products, we think the time-point of elevating stress level varies randomly from product-to-product. We consider a situation in which when the degradation value crosses a pre-specified value, the stress level is elevated. Under the circumstances, the time at which the degradation path crosses the pre-specified value is uncertain, and so we may regard it as a random variable. We discuss multiple-steps step-stress accelerated degradation models based on Wiener and gamma processes, respectively, and we apply the Bayesian Markov chain Monte Carlo (MCMC) method for such analytically intractable models to obtain the maximum likelihood estimates (MLEs) efficiently and present some computational results obtained from our implementation.

Keywords:

• Bayesian MCMC method
• Gamma process
• Maximum likelihood estimation
• Step-stress accelerated degradation modeling
• Wiener process

Mathematics Subject Classification:

• 62P30
• 60G51
• 62F15

Acknowledgment

This research was supported by the National Science Foundation of China under agreement 60701006 through a visit of the first author to McMaster University, Canada, for carrying out collaborative research with the second author.

Notes

*Visiting professor at King Saud University, Riyadh, Saudi Arabia, and the National Central University, Taiwan.