Comparison of Maximum Likelihood Estimation and Median Rank Regression Methods in Weibull Distribution Parameter Estimation

Abstract

The Weibull distribution is widely used in reliability analysis and risk management due to its flexibility in modeling failure patterns. This study aims to compare two methods for estimating Weibull distribution parameters, namely Maximum Likelihood Estimation (MLE) from Median Rank Regression (MRR). The data used consists of simulation data with varying parameters and sample sizes, as well as case study data.shock absorber dataset from the library weibulltools containing failure time and censored data. Parameter estimation with MLE is performed using the Newton–Raphson algorithm, while MRR is performed through linear transformation and regression. Performance evaluation is performed using bias measures and Mean Squared Error (MSE) on simulated data, as well as Kolmogorov–Smirnov and Anderson–Darling tests on case study data.