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Bounds for the availabilities in a fixed time interval for multistate monotone systems

Published online by Cambridge University Press:  01 July 2016

Espen Funnemark  and
Bent Natvig
Espen Funnemark*
Affiliation:
National Mass Radiography Service
Bent Natvig*
Affiliation:
University of Oslo
*
∗Postal address: P.O. Box 8155, Dep., Oslo 1, Norway.
∗∗Postal address: Institute of Mathematics, University of Oslo, P.O. Box 1053, Blindem, Oslo 3, Norway.
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Abstract

In this paper upper and lower bounds for the availability and unavailability, to any level, in a fixed time interval are arrived at for multistate monotone systems based on corresponding information on the multistate components. These are assumed to be maintained and interdependent. Such bounds are of great interest when trying to predict the performance process of the system, noting that exact expressions are obtainable just for trivial systems. The bounds given generalize the existing bounds known in traditional binary theory, and represent improvements of the ones now being developed in multistate theory.

Keywords

UNAVAILABILITIES: MAINTENANCEINTERDEPENDENT COMPONENTS
Type
Research Article
Information
Advances in Applied Probability , Volume 17 , Issue 3 , September 1985 , pp. 638 - 665
Copyright
Copyright © Applied Probability Trust 1985 

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References

Agrawal, A. and Barlow, R. E. (1984) A survey of network reliability and domination theory. Operat. Res. 32, 478–492.Google Scholar
Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing. Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
Block, H. W. and Savits, T. H. (1982) A decomposition for multistate monotone systems. J. Appl. Prob. 19, 391–402.CrossRefGoogle Scholar
Bodin, L. D. (1970) Approximations to system reliability using a modular decomposition. Technometrics 12, 335–344.CrossRefGoogle Scholar
Butler, D. A. (1982) Bounding the reliability of multistate systems. Operat. Res. 30, 530–544.Google Scholar
El-Neweihi, E., Proschan, F. and Sethuraman, J. (1978) Multistate coherent systems. J. Appl. Prob. 15, 675–688.Google Scholar
Esary, J. D. and Proschan, F. (1970) A reliability bound for systems of maintained, interdependent components. J. Amer. Statist. Assoc. 65, 329–338.CrossRefGoogle Scholar
Funnemark, E. (1982) Bounds for the availability and unavailability in a fixed time interval for multistate systems of multistate, maintained, interdependent components. Unpublished cand. real. thesis (in Norwegian), Institute of Mathematics, University of Oslo.Google Scholar
Griffith, W. (1980) Multistate reliability models. J. Appl. Prob. 17, 735–744.Google Scholar
Hjort, N. L., Natvig, B. and Funnemark, E. (1985) The association in time of a Markov process with application to multistate reliability theory. J. Appl. Prob. 22, 474–480.CrossRefGoogle Scholar
Natvig, B. (1980) Improved bounds for the availability and unavailability in a fixed time interval for systems of maintained, interdependent components. Adv. Appl. Prob. 12, 200–211.Google Scholar
Natvig, B. (1982) Two suggestions of how to define a multistate coherent system. Adv. Appl. Prob. 14, 434–455.Google Scholar
Natvig, B. (1985) Multistate coherent systems. In Encyclopedia of Statistical Sciences , Vol. 5, ed. Johnson, N. L. and Kotz, S.. Wiley, New York, 732–735.Google Scholar
Sverdrup, E. (1965) Estimates and test procedures in connection with stochastic models for deaths, recoveries and transfers between different states of health. Scand. Actuar. J. 48, 184–211.CrossRefGoogle Scholar