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Optimal test Interval for a Monotone Safety System

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

Terje Aven
Terje Aven*
Affiliation:
University of Stavanger
*
∗Postal address: University of Stavanger, PB 8002 Ullandhaug, 4036 Stavanger, Norway. Email address: terje.aven@uis.no
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Abstract

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We consider a safety system represented by a monotone (coherent) structure function of n components. The state of the components and the system is only revealed through inspection, which is carried out at intervals of length T. If the inspection shows that the system is in a critical state or has failed, it is overhauled and all components are restored to a good-as-new condition. Costs are associated with tests, system downtime, and repairs. The problem is to find an optimal T minimizing the expected long-run cost per unit of time. The purpose of this paper is to present a formal set-up for this problem and to show how an optimal T can be determined. A special case where the components have three states is given particular attention. It corresponds to a ‘delay time type system’, where the presence of a fault in a component does not lead to an immediate failure—there will be a ‘delay time’ between the occurrence of the fault and the failure of the component.

Keywords

Monotone systemtest intervaldelay time modelexpected costs

MSC classification

Secondary: 90B25: Reliability, availability, maintenance, inspection 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 2 , June 2009 , pp. 330 - 341
Copyright
Copyright © Applied Probability Trust 2009 

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