Reliability analysis of a two-dissimilar-unit warm standby repairable system with priority in use

Abstract

In this paper, a warm standby repairable system consisting of two dissimilar units and one repairman is studied. There are two failure modes, i.e. hardware failure and human error failure, for each unit. Once one of the units failed, it is sent to the repairman for repair immediately. Assume that working time distributions of the two units are exponential and the repair time distributions are arbitrarily general. After repair, both unit 1 and unit 2 are as good as new. Suppose that the switch is reliable and the switching time (if any) is instantaneous. Unit 1 has priority in use. By using Markov renewal method, some reliability measures such as the first failure time distribution, the mean time to the first failure, the system’s steady-state availability, and the expectation of system failure numbers in the interval $(0,t]$ are obtained.

Keywords:

• Availability
• semi-Markov process
• Markov renewal equation
• warm standby system
• priority in use

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China (Nos. 71871008 and 71571014).