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Partial orderings under cumulative damage shock models
- Part of
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- Journal:
- Advances in Applied Probability / Volume 25 / Issue 4 / December 1993
- Published online by Cambridge University Press:
- 01 July 2016, pp. 939-946
- Print publication:
- December 1993
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- Article
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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.
and 
denote the probability of surviving 
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.