Empirical Bayes estimates in exponential reliability model

Abstract

This paper is devoted to the estimation of the reliability measures in an exponential reliability model using empirical Bayes procedure. The nonparametric polynomial density estimate of the unknown prior probability density function of the value of the exponential reliability function is considered. Monte Carlo simulation method is used in order to (i) investigate how the number of the available past experiments and the sample size of each experiment are reflected on the accuracy of the estimate, (ii) study whether a nonparametric polynomial density estimation of the prior density function with a higher degree gives a significantly better estimate, and (iii) make a comparison between the obtained empirical Bayes estimate and Bayes estimate when a gamma prior distribution of the failure rate parameter is considered.