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Reliability analysis of complex repairable systems by means of marked point processes

Published online by Cambridge University Press:  14 July 2016

Peter Franken  and
Arnfried Streller
Peter Franken*
Affiliation:
Humboldt-Universität, Berlin
Arnfried Streller*
Affiliation:
Humboldt-Universität, Berlin
*
∗Postal address: Sektion Mathematik, Humboldt-Universität, 1086 Berlin PSF 1297, German Democratic Republic.
∗Postal address: Sektion Mathematik, Humboldt-Universität, 1086 Berlin PSF 1297, German Democratic Republic.
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Abstract

Starting from the theory of point processes the concept of a process with an embedded marked point process is defined. It is shown that the known formula expressing the relation between the stationary and synchronous version of a regenerative process remains valid without the assumption of independence of cycles. General formulae for stationary availability and interval reliability of complex systems with repair are also obtained. In this way generalizations of Keilson's results for Markovian systems and Ross's results for systems with separately maintained elements are presented. The formulae are applied to a two-unit parallel system with a single repair facility.

Keywords

COMPLEX SYSTEMS WITH REPAIRAVAILABILITYINTERVAL RELIABILITYSTEADY STATESTOCHASTIC POINT PROCESSPROCESS WITH AN EMBEDDED MARKED POINT PROCESSSOJOURN TIMEEXIT TIME
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 1 , March 1980 , pp. 154 - 167
Copyright
Copyright © Applied Probability Trust 1980 

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