Journal of Applied Probability

Monotone Markov processes with respect to the reversed hazard rate ordering: an application to reliability

Sophie Bloch-Mercier

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Abstract

We consider a repairable system with a finite state space which evolves in time according to a Markov process as long as it is working. We assume that this system is getting worse and worse while running: if the up-states are ranked according to their degree of increasing degradation, this is expressed by the fact that the Markov process is assumed to be monotone with respect to the reversed hazard rate and to have an upper triangular generator. We study this kind of process and apply the results to derive some properties of the stationary availability of the system. Namely, we show that, if the duration of the repair is independent of its completeness degree, then the more complete the repair, the higher the stationary availability, where the completeness degree of the repair is measured with the reversed hazard rate ordering.

Article information

Source
J. Appl. Probab. Volume 38, Number 1 (2001), 195-208.

Dates
First available in Project Euclid: 5 August 2001

Permanent link to this document
http://projecteuclid.org/euclid.jap/996986653

Digital Object Identifier
doi:10.1239/jap/996986653

Mathematical Reviews number (MathSciNet)
MR1816123

Zentralblatt MATH identifier
0981.60086

Subjects
Primary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) [See also 90Bxx] 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07]
Secondary: 60E15: Inequalities; stochastic orderings

Keywords
reliability reversed hazard rate ordering monotone Markov processes stationary availability

Citation

Bloch-Mercier, Sophie. Monotone Markov processes with respect to the reversed hazard rate ordering: an application to reliability. J. Appl. Probab. 38 (2001), no. 1, 195--208. doi:10.1239/jap/996986653. http://projecteuclid.org/euclid.jap/996986653.


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