Journal of Applied & Computational Mathematics

Reliability Analysis for Monte Carlo Simulation Using the Expectation- Maximization Algorithm for a Weibull Mixture Distribution Model

Abstract

Emad E. Elmahdy

This paper presents a simulation study of a finite Weibull mixture distribution (WMD) for modelling life data related to system components with different failure modes. The main aim of this study is to compare two analytical methods for estimating the parameters of WMD models, the maximum likelihood estimation (MLE) method using the expectation-maximization (EM) algorithm, [A1] and the non-linear median rank regression (NLMRR) method with the Levenberg-Marquardt algorithm. To perform this comparison, the Monte Carlo simulation technique is implemented to generate several replicates for complete failure data and censored data based on samples of different sizes that follow a two-component WMD. This study showed that MLE using the EM algorithm yields more accurate parameter estimates than the NLMRR method for small or moderate complete failure data samples. This method also converges faster than the NLMRR method for large samples that include censored data.