Weibull Parameter Estimation for Small Censored Data Sets

Comparison of the maximum likelihood method and generalised least squares method in the estimation of Weibull parameters

Bachelor thesis (2024)

Authors

S.W. van Leuven Electrical Engineering, Mathematics and Computer Science

Contributors

L.E. Meester Applied Probability - EEMCS (mentor)
Faculty
Electrical Engineering, Mathematics and Computer Science
More Info
expand_more

Published Date

24-07-2024

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

The Weibull distribution is one of the most widely used distributions in reliability analysis. The ability to accurately estimate the parameters of Weibull distributed data can be very useful, and particularly important when dealing with small data sets and high degrees of censoring. This project aims to compare the performance of the maximum likelihood (ML) method and a generalised least squares (GLS) method in estimating the parameters of small, censored Weibull distributed data. The study involves a simulation of type II censored Weibull data to estimate the log-Weibull parameters and predict the quantiles of the next failure. Simulations were performed across a broad range of sample sizes and number of observed failures. We evaluated the efficiency and accuracy of both estimation methods. The simulation results demonstrated that the unbiased versions of the ML estimators consistently outperform the GLS estimators in terms of efficiency. The root mean squared error (RMSE) of the ML estimator were lower, indicating a higher accuracy in parameter estimation.