Optimum estimators for the Weibull distribution of censored data. Singly-censored tests [electrical breakdown test data

Abstract

Six techniques (maximum likelihood, least squares regression and the Jacquelin, Boss, White and Bain Engelhardt estimators) have been compared in terms of their simplicity and accuracy in estimating the shape and scale parameters of the 2-parameter Weibull distribution applied to singly censored data. Monte Carlo simulations using 10000 iterations were used to find the bias of the expected values of the parameters and the 90 statistical confidence limits of their distributions. Both parameters were characterized in this way for sample sizes of 6, 10 and 20, true values of the shape parameter of 0.5, 1.0 and 10, and for 30% and 50% censored data. At a 30/spl deg/ level of censoring, the modified Jacquelin and Boss techniques are satisfactory but they may become unsatisfactory at 50% censoring. The maximum-likelihood and least-squares regression techniques are not to be recommended on censored data sets. The sophisticated White or Bain-Engelhardt estimators work very well even at 50% censoring. In most cases, the 90/spl deg/ confidence limits of the estimates increase by approximately 1.4 as the censoring level is increased from 30% to 50%.