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Partial Orderings under Cumulative Damage Shock Models

Franco Pellerey
Advances in Applied Probability
Vol. 25, No. 4 (Dec., 1993), pp. 939-946
DOI: 10.2307/1427800
Stable URL: http://www.jstor.org/stable/1427800
Page Count: 8
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Partial Orderings under Cumulative Damage Shock Models
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Abstract

Two devices are subjected to common shocks arriving according to two identical counting processes. Let P̄k and Q̄k denote the probability of surviving k shocks for the first and the second device, respectively. We find conditions on the discrete distributions {P̄k, k=0,1,⋯ } and {Q̄k, k=0,1,⋯ } 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.

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