Markov Repairable Systems with History-Dependent Up and Down States

Abstract

This paper introduces a Markov model for a multi-state repairable system in which some states are changeable in the sense that whether those physical states are up or down depends on the immediately preceding state of the system evolution process. Several reliability indexes, such as availability, mean up time, and steady-state reliability are calculated using the matrix method. A sufficient condition under which the availabilities of the stochastically monotone repairable systems with history-dependent states can be compared is also obtained. Some examples are presented to illustrate the results in the paper.

Keywords:

• Availability
• Down time
• History-dependent state
• Markov repairable system
• Multi-state maintenance model
• Reliability
• Up time

Mathematics Subject Classification:

• 60K10

ACKNOWLEDGMENTS

We thank two referees and an editor for their detailed comments and suggestions that led to an improvement of the content and of the presentation of this paper. Lirong Cui was supported by the NSF of China Grants 70371048 and 70671009.