Optimum Design for Type-I Step-stress Accelerated Life Tests of Two-parameter Weibull Distributions

Abstract

In this article, we focus on the general k-step step-stress accelerated life tests with Type-I censoring for two-parameter Weibull distributions based on the tampered failure rate (TFR) model. We get the optimum design for the tests under the criterion of the minimization of the asymptotic variance of the maximum likelihood estimate of the pth percentile of the lifetime under the normal operating conditions. Optimum test plans for the simple step-stress accelerated life tests under Type-I censoring are developed for the Weibull distribution and the exponential distribution in particular. Finally, an example is provided to illustrate the proposed design and a sensitivity analysis is conducted to investigate the robustness of the design.

Keywords:

• k-step step-stress accelerated life test
• Maximum likelihood estimation
• TFR model
• Type-I censoring
• Weibull distribution

Mathematics Subject Classification:

• 62N05

Acknowledgments

This research is supported by the Natural Science Foundation of China (10571057, 11271136). The authors wish to thank the two anonymous referees for their very constructive suggestions that have helped to improve the content of the article.