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Preservation of some partial orderings under Poisson shock models

Published online by Cambridge University Press:  01 July 2016

Harshinder Singh  and
Kanchan Jain
Harshinder Singh*
Affiliation:
Panjab University
Kanchan Jain*
Affiliation:
Panjab University
*
Postal address for both authors: Department of Statistics, Panjab University, Chandigarh-160014, India.
Postal address for both authors: Department of Statistics, Panjab University, Chandigarh-160014, India.
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Abstract

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Suppose each of the two devices is subjected to shocks occurring randomly as events in a Poisson process with constant intensity λ. Let Pk denote the probability that the first device will survive the first k shocks and let denote such a probability for the second device. Let and denote the survival functions of the first and the second device respectively. In this note we show that some partial orderings, namely likelihood ratio ordering, failure rate ordering, stochastic ordering, variable ordering and mean residual-life ordering between the shock survival probabilities and are preserved by the corresponding survival functions and .

Keywords

RELIABILITYPOSITIVE AGEING CLASSES OF DISTRIBUTIONSTOTAL POSITIVITYVARIATION DIMINISHING POLICY
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 21 , Issue 3 , September 1989 , pp. 713 - 716
Copyright
Copyright © Applied Probability Trust 1989 

References

Deshpande, J. V., Singh, H., Bagai, I. and Jain, K. (1988) Some partial orders describing positive ageing. To appear.Google Scholar
Esary, J. D., Marshall, A. W. and Proschan, F. (1973) Shock models and wear processes. Ann. Prob. 1, 627–649.Google Scholar
Karlin, S. (1968) Total Positivity. Vol. I. Stanford University Press, Stanford.Google Scholar
Klefsjö, B. (1981) HNBUE survival under some shock models. Scand. J. Statist. 8, 39–47.Google Scholar
Ross, S. M. (1983) Stochastic Processes. Wiley, New York.Google Scholar
Singh, H. (1988) On partial orderings of life distributions. Naval Res. Logist. Quart. 35, 53–60.Google Scholar