Experimental Comparison of some of the Classical and Bayesian Nonparametric Estimators for some Reliability Systems

Abstract

In this paper, the classical nonparametric estimations are used to estimate reliability function for k-out of-n system, series system, and parallel system by using three different methods: Kernel estimator method, Kaplan-Meier estimator method, and product limit estimator method. These functions are compared to Bayesian nonparametric reliability estimator which is proposed by Ferguson in 1973 and dubbed the “Prior Dirichlet Processes”. To choose a better method for estimation, it has been used a simulation procedure for different sample sizes of size (14, 30, 60, and100) using Integral Mean Square Error (IMSE) for comparison. The results indicate that it is better to use the classical method with k-out of-n system and parallel system, whereas for series system it is better to use Bayesian method for small samples of size (14, and 30) and the classical method for big samples size of (60,and100)