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A probabilistic analogue of the mean value theorem and its applications to reliability theory

Part of: Special processes Operations research and management science Stochastic analysis

Published online by Cambridge University Press:  14 July 2016

Antonio Di Crescenzo
Antonio Di Crescenzo*
Affiliation:
Università della Basilicata
*
∗Postal address: Dipartimento di Matematica, Universitö degli Studi della Basilicata, Via N. Sauro, 85, 85100 Potenza, Italy. Email address: dicrescenzo@unibas.it.
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Abstract

In a similar spirit to the probabilistic generalization of Taylor's theorem by Massey and Whitt [13], we give a probabilistic analogue of the mean value theorem. The latter is shown to be useful in various contexts of reliability theory. In particular, we provide various applications to the evaluation of the mean total profits of devices having random lifetimes, to the mean total-time-on-test at an arbitrary order statistic of a random sample of lifetimes, and to the mean maintenance cost for the second room of queueing systems in steady state characterized by two serial waiting rooms.

Keywords

Renewal processesequilibrium distributionusual stochastic orderageing notionsrandom lifetimesorder statisticstotal-time-on-testqueueing systems

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 90B25: Reliability, availability, maintenance, inspection 60H25: Random operators and equations
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 3 , September 1999 , pp. 706 - 719
Copyright
Copyright © Applied Probability Trust 1999 

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Footnotes

This paper is dedicated to the memory of Gian Carlo Rota.

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