Renewal process and operation strategies in the theory of reliability of technical systems under prefailure lives distributed as a mixture of two exponential distributions

Abstract

A number of problems in the reliability theory as applied to technical systems is considered for the case when the time-to-failure values are distributed as a mixture of two exponential distributions. This consists of finding a renewal function for a simple restorative (renewal) process, a comparison of three operating strategies according to the criterion of minimal cost intensity and using the method of moments to find point estimates for the parameters involved in the mixture. The choice of the mixture is caused by the fact that its failure rate has a running-in period that is characteristic within the initial operation period of technical systems, whereas afterwards, the failure rate is almost constant. This distinguishes the considered mixture from the exponential distribution with a constant failure rate widely used in the reliability theory.