A note on ‘curable’ shock processes

In most conventional shock models, the events caused by an external shock are initiated at the moments of its occurrence. Recently, Cha and Finkelstein (2012) had considered the case when each shock from a nonhomogeneous Poisson processes can trigger a failure of a system not immediately, as in the...

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Bibliographic Details
Published inJournal of statistical planning and inference Vol. 142; no. 12; pp. 3146 - 3151
Main Authors Cha, Ji Hwan, Finkelstein, Maxim
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2012
Subjects
Cumulative shock model
Cure models
Delayed failure
Nonhomogeneous Poisson process
Shock model
Cumulative shock model
Delayed failure
Nonhomogeneous Poisson process
Cure models
Shock model
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Summary:In most conventional shock models, the events caused by an external shock are initiated at the moments of its occurrence. Recently, Cha and Finkelstein (2012) had considered the case when each shock from a nonhomogeneous Poisson processes can trigger a failure of a system not immediately, as in the classical shock models, but with delay of some random time. In this paper, we suggest the new type of shock models, where each delayed failure can be cured (repaired) with certain probabilities. These shock processes have not been considered in the literature before. We derive and analyze the corresponding survival and failure rate functions and consider a meaningful reliability example of the stress–strength model.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2012.06.020