Analytical Comparison of An Optimal Replacement Policy for Cold Standby with Priority in Use When Failure and Repair Rates are Uncertain

In this article, we consider the two nonidentical components and one repairman. The failure rate of component 1 is very small as compared to component 2. Hence, the priority is given to component 1. In this study we present a two replacement policies, first based on the number of down times, k of the system such that the long run expected reward per unit time is maximized and second is based on number of failures, N of component 1 such that long run expected reward per unit time is maximized. For the first policy system can be replaced when the number of down times for the system reaches k and for the second policy system can be replaced when number of failure of the component 1 reaches to N. The failure rate and repair rate are uncertain. Triangular fuzzy numbers are used to allow expert opinion, uncertainty and imprecision in information of these parameters. Using α-cuts, we get different levels of failure and repair rates. The expression for long run expected reward per unit time for renewal cycle is derived, we present the proposed policies with numerical example and simulation study. © 2018, The Indian Society for Probability and Statistics (ISPS).