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Inspection times for stand-by units

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Giovanni Parmigiani
Giovanni Parmigiani*
Affiliation:
Duke University
*
∗Postal address: Institute of Statistics and Decision Sciences, Duke University, Box 90251, Durham, NC 27708–0251, USA.
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Abstract

This paper studies optimal timing of inspections for units in cold stand-by. The problem is approached in continuous time. The policies developed adapt optimally to information provided by failures of the main unit and by ageing of both the standby and the main unit.

Results include a general form for the optimal policy, consisting of a recursive relation between successive inspection times, and of a renewal-type integral equation to determine the value of the objective function for a given policy. Further results are derived for the case in which the failure densities describing the process are logconcave. Then the stopping rule is easily characterized. It is also shown that the interval between inspections decreases with time, and that the optimal schedule is unique. A binary search algorithm for finding the solution is outlined.

Keywords

RELIABILITYCONSTRAINED OPTIMIZATIONNON-MARKOVIAN DETERIORATION

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 31 , Issue 4 , December 1994 , pp. 1015 - 1025
Copyright
Copyright © Applied Probability Trust 1994 

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References

Barlow, R. E. and Proschan, F. (1965) Mathematical Theory of Reliability. Wiley, New York.Google Scholar
Barlow, R. E., Hunter, L. C. and Proschan, F. (1963) Optimum checking procedures. J. SIAM 4, 1078–1095.Google Scholar
Nakagawa, T. (1980) Optimum inspection policies for a standby unit. J. Operat. Res. Soc. Japan 23, 13–26.Google Scholar
Parmigiani, G. (1993a) Scheduling inspections in reliability. In Advances in Reliability , ed. Basu, A. P., pp. 303–319. Reidel, Dordrecht.Google Scholar
Parmigiani, G. (1993b) On optimal screening ages. J. Amer. Statist. Assoc. 88, 622–628.CrossRefGoogle Scholar
Parmigiani, G. (1993C) Optimal inspection and replacement policies with age-dependent failures and fallible tests. J. Operat. Res. Soc. 44, 1105–1114.Google Scholar
Sengupta, B. (1980) Inspection procedures when failure symptoms are delayed. Operat. Res. 28, 768–776.Google Scholar
Thomas, L. C., Jacobs, P. A. and Gaver, P. (1987) Optimal inspection policies for standby systems. Commun. Statist. Stoch. Models 3, 259–273.Google Scholar
Zabreyko, P. P. et al. (1975) Integral Equations – A Reference Text. Noordhoff, Leyden.CrossRefGoogle Scholar