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Stationary availability of a semi‐Markov system with random maintenance
Author(s) -
BlochMercier Sophie
Publication year - 2000
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/1526-4025(200007/09)16:3<219::aid-asmb416>3.0.co;2-4
Subject(s) - limit (mathematics) , markov chain , markov process , optimal maintenance , preventive maintenance , process (computing) , computer science , markov decision process , mathematical optimization , markov model , condition based maintenance , duration (music) , stochastic process , computation , markov renewal process , failure rate , state space , mathematics , statistics , reliability engineering , markov property , algorithm , engineering , physics , mathematical analysis , acoustics , operating system
We consider a reparable system with a finite state space, evolving in time according to a semi‐Markov process. The system is stopped for it to be preventively maintained at random times for a random duration. Our aim is to find the preventive maintenance policy that optimizes the stationary availability, whenever it exists. The computation of the stationary availability is based on the fact that the above maintained system evolves according to a semi‐regenerative process. As for the optimization, we observe on numerical examples that it is possible to limit the study to the maintenance actions that begin at deterministic times. We demonstrate this result in a particular case and we study the deterministic maintenance policies in that case. In particular, we show that, if the initial system has an increasing failure rate, the maintenance actions improve the stationary availability if and only if they are not too long on the average, compared to the repairs ( a bound for the mean duration of the maintenance actions is provided). On the contrary, if the initial system has a decreasing failure rate, the maintenance policy lowers the stationary availability. A few other cases are studied. Copyright © 2000 John Wiley & Sons, Ltd.