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Improved availability bounds for binary and multistate monotone systems with independent component processes

Part of: Survival analysis and censored data Operations research and management science

Published online by Cambridge University Press:  15 September 2017

Jørund Gåsemyr  and
Bent Natvig
Jørund Gåsemyr*
Affiliation:
University of Oslo
Bent Natvig*
Affiliation:
University of Oslo
*
* Postal address: Department of Mathematics, University of Oslo, PO Box 1053 Blindern, 0316 Oslo, Norway.
* Postal address: Department of Mathematics, University of Oslo, PO Box 1053 Blindern, 0316 Oslo, Norway.
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Abstract

Multistate monotone systems are used to describe technological or biological systems when the system itself and its components can perform at different operationally meaningful levels. This generalizes the binary monotone systems used in standard reliability theory. In this paper we consider the availabilities of the system in an interval, i.e. the probabilities that the system performs above the different levels throughout the whole interval. In complex systems it is often impossible to calculate these availabilities exactly, but if the component performance processes are independent, it is possible to construct lower bounds based on the component availabilities to the different levels over the interval. In this paper we show that by treating the component availabilities over the interval as if they were availabilities at a single time point, we obtain an improved lower bound. Unlike previously given bounds, the new bound does not require the identification of all minimal path or cut vectors.

Keywords

Availability boundbinary monotone systemflow network systemminimal cut vectorminimal path vectormultistate monotone system

MSC classification

Primary: 62N05: Reliability and life testing 90B25: Reliability, availability, maintenance, inspection
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 3 , September 2017 , pp. 750 - 762
Copyright
Copyright © Applied Probability Trust 2017 

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