Generating Antithetic Random Variates in Simulation of a Replacement Process by Rejection Method

Abstract

Analysis of a replacement process provides the needed insight into prediction of the replacement requirements of a system. Accurate prediction of such requirements can lead to cost savings as well as improved system performance. When the component lives are not exponentially distributed, simulation becomes a potentially suitable method of analysis. This paper deals with Gamma distributed component lives whose deviates are generated through the so-called Rejection Method. It will be shown that antithetic random deviates can be generated through the rejection method to estimate the renewal function in a single component replacement process. A theorem proved by George is modified and extended to the case at hand. Finally, an algorithm is developed, and along with the experimental results, will be presented. A replacement process is chosen as an example through which to verify the merits of the proposed algorithm.