A Comparison of Maximum Likelihood and Median-Rank Regression for Weibull Estimation

ABSTRACT

The Weibull distribution is frequently used in reliability applications. Many different methods of estimating the parameters and important functions of the parameters (e.g., quantiles and failure probabilities) have been suggested. Maximum likelihood and median-rank regression methods are most commonly used today. Largely because of conflicting results from different studies that have been conducted to investigate the properties of these estimators, there are sharp differences of opinion on which method should be used. The purpose of this article is to report on the results of our simulation study, to provide insight into the differences between the competing methods, and to resolve the differences among the previous studies.

KEYWORDS:

• censored data
• least squares
• ML
• MRR
• reliability

ACKNOWLEDGMENTS

We thank Bob Abernethy for providing copies of The New Weibull Handbook to us and Paul Barringer for providing copies of Liu (1997) and results of his research to reduce bias in ML estimates. We also benefited from correspondence with Bob Abernethy, Luis Escobar, and Wes Fulton. We thank Chuck Annis, Senin Banga, Luis Escobar, Yili Hong, Shuen-Lin Jeng, Ed Kram, Chris Gotwalt, John McCool, Katherine Meeker, Dan Nordman, Joseph Lu, and Fritz Scholz for providing helpful comments on an earlier version of this article.