Bias Reduction of MLEs for Weibull Distributions under Grouped Lifetime Data

ABSTRACT

Accelerated life tests (ALTs) usually contain subsampling because of the cost-effective evaluation. The two-stage method can deal with grouped data with subsampling, but the bias of maximum likelihood estimates (MLEs) can be alarmingly high. In this article, we propose reducing the bias of MLEs for grouped data via an unbiasing factor method. We introduce the procedures and give the unbiasing factor values. The proposed method is studied and compared with the modified maximum likelihood method for relative bias (RB) and mean square error (MSE) in Monte Carlo simulations. The results show that the unbiasing factor method is better in most cases.

KEYWORDS:

• censoring
• grouped data
• MLEs
• unbiasing factor
• Weibull distribution

FUNDING

This research was supported in part by grants 71401123, 70931004, 71071107, and 71225006 from the National Natural Science Foundation of China.

ABOUT THE AUTHORS

Guodong Wang is a Ph.D. candidate in the College of Management and Economics at Tianjin University, China. He received his B.S. degree in applied mathematics from Nanchang Hangkong University, Nanchang, China, and an M.S. degree in reliability engineering from Beihang University, Beijing, China. His research interests focus on quality engineering and reliability improvement.

Zhanwen Niu is a professor in the College of Management and Economics at Tianjin University, China. He received his Ph.D. degree from Tianjin University in 1993. His research interests include quality engineering, lean production, and industrial engineering.

Zhen He is a distinguished professor in the College of Management and Economics at Tianjin University, China. He received B.S., M.S., and Ph.D. degrees from Tianjin University, Tianjin, China, in 1988, 1991, and 2000, respectively. His current research interests include statistical process controls, design of experiments, response surface methodology, and Six Sigma.