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Distribution properties of the system failure time in a general shock model

Published online by Cambridge University Press:  01 July 2016

J. G. Shanthikumar  and
Ushio Sumita
J. G. Shanthikumar*
Affiliation:
University of Arizona
Ushio Sumita*
Affiliation:
University of Rochester
*
∗Postal address: Systems and Industrial Engineering Department, 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 study some distribution properties of the system failure time in general shock models associated with correlated renewal sequences (Xn, Yn) . Two models, depending on whether the magnitude of the nth shock Xn is correlated to the length Yn of the interval since the last shock, or to the length of the subsequent interval to the next shock, are considered. Sufficient conditions under which the system failure time is completely monotone, new better than used, new better than used in expectation, and harmonic new better than used in expectation are given for these two models.

Keywords

CORRELATED RENEWAL PROCESSCOMPLETE MONOTONICITYNEW BETTER THAN USEDNEW BETTER THAN USED IN EXPECTATIONHARMONIC NEW BETTER THAN USED IN EXPECTATION
Type
Research Article
Information
Advances in Applied Probability , Volume 16 , Issue 2 , June 1984 , pp. 363 - 377
Copyright
Copyright © Applied Probability Trust 1984 

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