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The association in time of a Markov process with application to multistate reliability theory

Published online by Cambridge University Press:  14 July 2016

Nils Lid Hjort ,
Bent Natvig  and
Espen Funnemark
Nils Lid Hjort*
Affiliation:
Norwegian Computing Center
Bent Natvig*
Affiliation:
University of Oslo
Espen Funnemark*
Affiliation:
National Mass Radiography Service
*
∗Postal address: Forskningsveien 1 B, 0371 Oslo 3, Norway.
∗∗Postal address: Institute of Mathematics, University of Oslo, P.O. Box 1053, Blindern, Oslo 3, Norway.
∗∗∗Postal address: P.O. Box 8155, Dep., Oslo 1, Norway.
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Abstract

A series of bounds for the availability and unavailability in a fixed time interval, I, for a system of maintained, interdependent components are given in Natvig (1980) in the traditional binary case, and in Funnemark and Natvig (1985) in the multistate case. For the special case of independent components the only assumption needed to arrive at these bounds is that the marginal performance process of each component is associated in I. When these processes are Markovian and binary, a sufficient condition for this to hold is given by Esary and Proschan (1970). In the present paper we generalize this condition to the multistate case, and give an equivalent and much more convenient condition in terms of the transition intensities.

Keywords

RELIABILITY THEORY
Type
Short Communications
Information
Journal of Applied Probability , Volume 22 , Issue 2 , June 1985 , pp. 473 - 479
Copyright
Copyright © Applied Probability Trust 1985 

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References

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