Probability plots are popular graphical tools used by reliability engineers and other practitioners for assessing parametric distributional assumptions. When used for data from (log)location-scale families, the location and scale parameters can be estimated by fitting a line through the plot. This method is quick-and-easy especially when used for censored data. The commonly known problem of this graphical estimation is its bias. In this study, we approximate the bias through the bootstrap method, and then make adjustment to the graphical estimators. The properties of the bootstrap-based bias corrected graphical estimators are studied through simulation for selected distributions with complete and right-censored data. We find that with bootstrap-based bias correction, the efficiency of the graphical estimators is improved especially for small sample size. The effect from the censoring rate on the improvement of the estimators and the relationship between true bias from a sample and its approximated bias are also studied and discussed.

References:

Genschel, U. and Meeker, W. Q. (2010) “A Comparison of Maximum Likelihood and Median-Rank Regression for Weibull Estimation,” Quality Engineering, 22(4).

Nair, V. and Somboonsavatdee, A. (2010) “Comments,”Quality Engineering, 22(4).

Somboonsavatdee, A., Nair, V., and Sen A. (2007), “Graphical estimator with right-censored data,” Technometrics, 49(4): 420-429

Zhang, L. F., Xie, M. and Tang, L.C. “Bias correction for the least squares estimators of Weibull shape parameter with complete and censored data,” Reliability Engineering and System Safety, 91:930-939

Keywords: Bootstrap; Bias correction; Probability plot; Censored data

Biography: Dr. Anupap Somboonsavatdee is a lecturer at Department of Statistics, Faculty of Commerce and Accountancy, Chulalongkorn University, Thailand. He recieved Ph.D. degree in Statistics at University of Michigan, USA. His research interests are reliabiliy, competing risks, and nonparametric statistics.