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Partial orderings under cumulative damage shock models

Part of: Operations research and management science

Published online by Cambridge University Press:  01 July 2016

Franco Pellerey
Franco Pellerey*
Affiliation:
Universitá di Milano
*
* Postal address: Universitá di Milano, Dipartimento di Matematica, Via L. Cicognara 7, 20129 Milano, Italy.
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Abstract

Two devices are subjected to common shocks arriving according to two identical counting processes. Let and denote the probability of surviving k shocks for the first and the second device, respectively. We find conditions on the discrete distributions and in order to obtain the failure rate order (FR), the likelihood ratio order (LR) and the mean residual order (MR) between the random lifetimes of the two devices. We also obtain sufficient conditions under which the above mentioned relations between the discrete distributions are verified in some cumulative damage shock models.

Keywords

STOCHASTIC ORDERINGSSHOCK MODELSIFRPF2 DENSITYDMRLDRFRTP2 PROPERTY

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Type
Research Article
Information
Advances in Applied Probability , Volume 25 , Issue 4 , December 1993 , pp. 939 - 946
Copyright
Copyright © Applied Probability Trust 1993 

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Footnotes

Research carried out while the author was visiting the University of Arizona, Tucson, Arizona.

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