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General shock models associated with correlated renewal sequences

Published online by Cambridge University Press:  14 July 2016

J. G. Shanthikumar  and
U. Sumita
J. G. Shanthikumar*
Affiliation:
University of Arizona
U. Sumita*
Affiliation:
University of Rochester
*
∗ Postal address: Systems and Industrial Engineering, University of Arizona, Tucson, AZ 85721, U.S.A.
∗∗ Postal address: The Graduate School of Management, The University of Rochester, Rochester, NY 14627, U.S.A.
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Abstract

In this paper we define and analyze a general shock model associated with a correlated pair (Xn, Yn) of renewal sequences, where the system fails when the magnitude of a shock exceeds (or falls below) a prespecified threshold level. Two models, depending on whether the nth shock Xn is correlated to the length Yn of the interval since the last shock, or to the length Yn of the subsequent interval until the next shock, are considered. The transform results, an exponential limit theorem, and properties of the associated renewal process of the failure times are obtained. An application in a stochastic clearing system with numerical results is also given.

Keywords

SHOCK MODELSCORRELATED RENEWAL PROCESSEXPONENTIAL LIMIT THEOREMSTOCHASTIC CLEARING SYSTEM
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 3 , September 1983 , pp. 600 - 614
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

This research was done while the authors were at Syracuse University and was published as Working Paper No. 82–006.

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