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On reliability prediction and semi-renewal processes

Part of: Operations research and management science Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Michael Tortorella
Michael Tortorella*
Affiliation:
Rutgers University
*
∗Current address: RUTCOR 148, Rutgers University, 640 Bartholomew Road, Piscataway, NJ 08854, USA. Email address: mtortore@rci.rutgers.edu
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Abstract

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We analyze the notion of ‘reliability prediction’ by studying in detail a key property that is tacitly assumed to make reliability prediction possible. The analysis leads in turn to a special type of point process for which the connection of future to past can be explicitly displayed. In this type of process, the semi-renewal process, all finite-dimensional distributions are completely determined by the distribution of the time to the first event in the process. The theory provides a heretofore unappreciated unification of the two most commonly used reliability prediction models for maintained systems, namely, the renewal and revival processes. We show that familiar results from renewal theory extend and generalize to semi-renewal processes.

Keywords

Renewalrelevationbad-as-oldrecord value processsemigroup

MSC classification

Secondary: 60G55: Point processes 90B25: Reliability, availability, maintenance, inspection
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 2 , June 2010 , pp. 394 - 406
Copyright
Copyright © Applied Probability Trust 2010 

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