RENEWAL PROCESS IN QUEUING PROBLEM AND REPLACEMENT OF MACHINE

The paper is studying the renewal process. There are many fields in which it’s used for example: the renewable energy (solar energy, wind energy), maintenance and replacement decision models, queuing system and other field in electronics. In this study our objective is to find the probability density function related to a renewal at a given time. Also to drive the renewal equation, how to find the current lifetime and residual life time. We obtain that as expected value of a renewal process which is the renewal function or mean-value function of the renewal process. Also we use the renewal equation and renewal reward processes in the applications. The solutions of these applications show a real answers due to reality conditions within a given accuracy.