A New Rank Estimator for Least Squares Estimation of Weibull Modulus

Abstract

The Weibull distribution is widely used in reliability analysis to evaluate the failure behavior and lifetime characteristics of various systems and components. One of the most commonly used methods for estimating the parameters of the Weibull distribution is the ordinary least squares (OLS) technique, which is based on fitting a linear regression model to the transformed data. This paper proposes a new rank estimator for ordinary least squares estimation of Weibull modulus, a key parameter used as a measure of variability in the data. The new rank estimator is a quadratic function of the ranks of order statistics, with three parameters that are optimized by Monte Carlo simulations. Using relative efficiency as a criterion, the performance of the new rank estimator is compared with three commonly used rank estimators, mean, median and Hazen rank estimators, which are linear functions of the ranks of order statistics. The results show that the new rank estimator has a significant advantage over the other rank estimators for any sample size between 3 and 150. The findings also imply that other nonlinear functions, such as cubic polynomials, could be applied to further improve the efficiency of the parameter estimators of the ordinary least squares method.