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Cluster shock models

Published online by Cambridge University Press:  14 July 2016

Peter F. Thall
Peter F. Thall*
Affiliation:
George Washington University
*
∗ Postal address: Department of Statistics, Bldg. C, Room 304, George Washington University, Washington, D.C. 20052, U.S.A.
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Abstract

The survival distribution of a device subject to a sequence of shocks occurring randomly over time is studied by Esary, Marshall and Proschan (1973) and by A-Hameed and Proschan (1973), (1975). The present note treats the case in which shocks occur according to a homogeneous Poisson cluster process. It is shown that if [the device survives k shocks] = zk , 0 < z < 1, then the device exhibits a decreasing failure rate. A DFR preservation theorem is proved for completely monotonic . A counterexample to the IFR preservation theorem is given in which is strictly IFR while the failure rate is initially decreasing and then increasing.

Keywords

RELIABILITYFAILURE RATEPRESERVATION THEOREMPOINT PROCESS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981, pp. 104 - 111
Copyright
Copyright © Applied Probability Trust 

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