Linear regression parameter estimation methods for the weibull distribution

Abstract

The least squares estimation (LSE) method is a simple parameter estimation method for the Weibull distribution. It is frequently used with Weibull probability plot and such a method is preferred by practitioners. This thesis explores various refinements of the ordinary LSE method. Firstly, suggestions are given on the selection of failure probability estimators and the regression direction. Secondly, simple bias correcting formulas for the OLS shape parameter estimator are proposed. Third, weighted least squares estimation methods and robust regression estimation methods are proposed and their improvement of estimation efficiency is justified by simulation experiments. Application instructions are provided for the proposed methods together with numerical examples. This thesis focuses on small samples, multiply censored samples, and samples with outliers. The proposed methods are good for dealing with one or several of these data types. These methods are based on linear regression techniques and hence can be easily applied and understood.