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New better than used in expectation processes

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

C. Y. Teresa Lam
C. Y. Teresa Lam*
Affiliation:
University of Michigan, Ann Arbor
*
∗ Postal address: Department of Industrial and Operations Engineering, The University of Michigan, Ann Arbor, MI 48109, USA.
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Abstract

In this paper, we study the new better than used in expectation (NBUE) and new worse than used in expectation (NWUE) properties of Markov renewal processes. We show that a Markov renewal process belongs to a more general class of stochastic processes encountered in reliability or maintenance applications. We present sufficient conditions such that the first-passage times of these processes are new better than used in expectation. The results are applied to the study of shock and repair models, random repair time processes, inventory, and queueing models.

Keywords

NBUE AND NWUE PROCESSESINCREASING MARKOV RENEWAL PROCESSESFIRST-PASSAGE TIMESQUEUEINGRANDOM REPAIR TIME PROCESSESSHOCK AND REPAIR MODELSINVENTORY

MSC classification

Primary: 60K15: Markov renewal processes, semi-Markov processes
Secondary: 60K10: Applications (reliability, demand theory, etc.) 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 1 , March 1992 , pp. 116 - 128
Copyright
Copyright © Applied Probability Trust 1992 

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