EM algorithms for ordered and censored system lifetime data under a proportional hazard rate model

Abstract

In this paper, we consider maximum likelihood estimation of the proportional parameter in a proportional hazard rate (PHR) model based on single and multiply censored order statistics, and progressively Type-II censored order statistics from lifetimes that follow the PHR model. The expectation-maximization (EM) algorithm is proposed for computing the maximum likelihood estimate (MLE) by utilizing the relationship between order statistics and lifetimes of components in a system. The existence and uniqueness of the MLE under different data structures are discussed. We also propose a reliable initial value for the iterative algorithm based on approximating the likelihood function using Taylor series expansion. Monte Carlo simulation studies are used to study the performance of the proposed EM algorithms and the proposed initial value. The proposed EM approach is shown to be a good alternative to the Newton-Raphson method in terms of computational efficient and robustness to the initial value. We also show that the proposed initial value works well with the EM algorithm in obtaining the MLE.