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Preservation of unimodality under shock models

✍ Scribed by Mini N. Balu; S.V. Sabnis

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
299 KB
Volume
46
Category
Article
ISSN
0894-069X

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✦ Synopsis

A number of results pertaining to preservation of aging properties (IFR, IFRA etc.) under various shock models are available in the literature. Our aim in this paper is to examine in the same spirit, the preservation of unimodality under various shock models. For example, it is proved that in a non-homogeneous Poisson shock model if {p k } kβ‰₯0 , the sequence of probabilities with which the device fails on the kth shock, is unimodal then under some suitable conditions on the mean value function Ξ›(t), the corresponding survival function is also unimodal. The other shock models under which the preservation of unimodality is considered in this paper are pure birth shock model and a more general shock model in which shocks occur according to a general counting process.

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