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A class of correlated cumulative shock models

Published online by Cambridge University Press:  01 July 2016

Ushio Sumita  and
J. George Shanthikumar
Ushio Sumita*
Affiliation:
University of Rochester
J. George Shanthikumar*
Affiliation:
University of Arizona
*
∗Postal address: Graduate School of Management, University of Rochester, Rochester, NY 14627, USA.
†Postal address: Systems and Industrial Engineering Department, University of Arizona, Tucson, AZ 85721, USA.
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Abstract

In this paper we define and analyze a class of cumulative shock models associated with a bivariate sequence {Xn, Yn}∞n=0 of correlated random variables. The {Xn} denote the sizes of the shocks and the {Yn} denote the times between successive shocks. The system fails when the cumulative magnitude of the shocks exceeds a prespecified level z. Two models, depending on whether the size of the nth shock is correlated with the length of the interval since the last shock or with the length of the succeeding interval until the next shock, are considered. Various transform results and asymptotic properties of the system failure time are obtained. Further, sufficient conditions are established under which system failure time is new better than used, new better than used in expectation, and harmonic new better than used in expectation.

Keywords

FIRST-PASSAGE TIMESNEW BETTER THAN USEDNEW BETTER THAN USED IN EXPECTATIONHARMONIC NEW BETTER THAN USED IN EXPECTATION: CUMULATIVE DAMAGE
Type
Research Article
Information
Advances in Applied Probability , Volume 17 , Issue 2 , June 1985 , pp. 347 - 366
Copyright
Copyright © Applied Probability Trust 1985 

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