Uniqueness of the Maximum Likelihood Estimate of the Weibull Distribution Tampered Failure Rate Model

Abstract

Bhattacharyya and Soejoeti (Bhattacharyya, G. K., Soejoeti, Z. A. (1989). Tampered failure rate model for step-stress accelerated life test. Commun. Statist.—Theory Meth. 18(5):1627–1643.) pro- posed the TFR model for step-stress accelerated life tests. Under the TFR model, this article proves that the maximum likelihood estimate of the shape parameters is unique for the Weibull distribution in a multiple step-stress accelerated life test, and investigates the accuracy of the maximum likelihood estimate using the Monte-Carlo simulation.

Keywords:

• Weibull distribution
• TFR model
• Maximum likelihood estimate
• Monte-Carlo simulation
• Multiple step-stress

Acknowledgments

This project was supported by NSF of China (69971016, 10271079), the science and Technology Development Foundation of Shanghai (00JC14057), the Foundation of Ministry of Education for core Teachers of Higher Education and the Shanghai Higher Learning science and Technology Development Foundation of Shanghai (98D13). The authors are also grateful to the referees for their valuable comments and suggestions. I would like to thank the referees for the invaluable suggestions. They did provide us some proposals improvement.