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Asymptotic and monotonicity properties of some repairable systems

Part of: Special processes

Published online by Cambridge University Press:  01 July 2016

Günter Last  and
Ryszard Szekli
Günter Last*
Affiliation:
TU Braunschweig
Ryszard Szekli*
Affiliation:
Wrocław University
*
∗ Postal address: Institut für Mathematische Stochastik, TU Braunschweig, Pockelstr. 14, 38106 Braunschweig, Germany.
∗∗ Postal address: Mathematical Institute, Wrocław University, pl. Grunwaldzki 2-4, 50-384 Wrocław, Poland.
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Abstract

The paper studies a model of repairable systems which is flexible enough to incorporate the standard imperfect repair and many other models from the literature. Palm stationarity of virtual ages, inter-failure times and degrees of repair is studied. A Loynes-type scheme and Harris recurrent Markov chains combined with coupling methods are used. Results on the weak total variation and moment convergences are obtained and illustrated by examples with IFR, DFR, heavy-tailed and light-tailed lifetime distributions. Some convergences obtained are monotone and/or at a geometric rate.

Keywords

Monotonicitystationarityimperfect repairgeneral repairpoint processesstochastic intensitygeometric ergodicity

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 30 , Issue 4 , December 1998 , pp. 1089 - 1110
Copyright
Copyright © Applied Probability Trust 1998 

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Footnotes

Work done while the author visited Technische Universität Braunschweig supported by the Deutsche Forschungsgemeinschaft, in part supported by KBN Grant.

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