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Optimal test Interval for a Monotone Safety System

Published online by Cambridge University Press:  14 July 2016

Terje Aven*
Affiliation:
University of Stavanger
*
Postal address: University of Stavanger, PB 8002 Ullandhaug, 4036 Stavanger, Norway. Email address: [email protected]
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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.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 2009 

References

Aven, T. and Bergman, B. (1986). Optimal replacement times—a general set-up. J. Appl. Prob. 23, 432442.Google Scholar
Aven, T. and Castro, I. T. (2009). A delay time model with safety constraint. Reliab. Eng. System Safety 94, 261267.Google Scholar
Aven, T. and Jensen, U. (1999). Stochastic Models in Reliability (Appl. Math. 41). Springer, New York.Google Scholar
Baker, R. D. and Christer, A. H. (1994). Review of delay-time OR modelling of engineering aspects of maintenance. Europ. J. Operat. Res. 73, 407422.Google Scholar
Christer, A. H. (1982). Modelling inspection policies for building maintenance. J. Oper. Res. Soc. 33, 723732.Google Scholar
Christer, A. H. (1999). Developments in delay time analysis for modelling plant maintenance. J. Oper. Res. Soc. 50, 11201137.Google Scholar
Christer, A. H. and Redmond, D. F. (1992). Revising models of maintenance and inspection. Internat. J. Production Econom. 24, 227234.Google Scholar
Jensen, U. (1996). Stochastic models of reliability and maintenance: an overview. In Reliability and Maintenance of Complex Systems, ed. Ozekici, S., Springer, Berlin, pp. 336.Google Scholar
Nakagawa, T. (2005). Maintenance Theory of Reliability. Springer, New York.Google Scholar
Ross, S. M. (1970). Applied Probability Models with Optimization Applications. Holden-Day, San Francisco, CA.Google Scholar
Valdez-Flores, C. and Feldman, R. M. (1989). A survey of preventive maintenance models for stochastically deteriorating single-unit systems. Naval Res. Logistics 36, 419446.3.0.CO;2-5>CrossRefGoogle Scholar
Wang, H. (2002). A survey of maintenance policies of deteriorating systems. Europ. J. Operat. Res. 139, 469489.Google Scholar
Wang, H. and Pham, H. (2006). Reliability and Optimal Maintenance. Springer, New York.Google Scholar