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Preservation of phase-type distributions under Poisson shock models

Part of: Distribution theory

Published online by Cambridge University Press:  01 July 2016

M. Manoharan ,
Harshinder Singh  and
Neeraj Misra
M. Manoharan
Affiliation:
Panjab University
Harshinder Singh
Affiliation:
Panjab University
Neeraj Misra
Affiliation:
Panjab University
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Abstract

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In this paper, we consider the life distribution H(t) of a device subject to shocks governed by a finite mixture of homogeneous Poisson processes. It will be shown that if (pk), the probabilities that the device fails on the kth shock, has a discrete phase-type (DPH) distribution, then H(t) is continuous phase-type (CPH). The relationship between the mean values of (pk) and H(t) is established.

Keywords

RELIABILITYMIXED POISSON PROCESSESSURVIVAL FUNCTION

MSC classification

Primary: 62E99: None of the above, but in this section
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 24 , Issue 1 , March 1992 , pp. 223 - 225
Copyright
Copyright © Applied Probability Trust 1992 

References

A-Hameed, M. S. and Proschan, F. (1973) Nonstationary shock models. Stoch. Proc. Appl. 1, 383–404.Google Scholar
A-Hameed, M. S. and Proschan, F. (1975) Shock models with underlying birth process. J. Appl. Prob. 12, 18–28.CrossRefGoogle Scholar
Block, H. W. and Savits, T. H. (1978) Shock models with NBUE survival. J. Appl. Prob. 15, 621–628.CrossRefGoogle Scholar
Esary, J. D., Marshall, A. W. and Proschan, F. (1973) Shock models and wear processes. Ann. Prob. 1, 627–649.Google Scholar
Klefsjö, B. (1981) HNBUE survival under some shock models. Scand. J. Statist. 8, 39–47.Google Scholar
Neuts, M. F. (1981) Matrix-Geometric Solutions in Stochastic Models—An Algorithmic Approach . The Johns Hopkins University Press, Baltimore.Google Scholar