A note on 'curable' shock processes

Ji Hwan Cha; Maxim Finkelstein

doi:10.1016/j.jspi.2012.06.020

A note on 'curable' shock processes

Ji Hwan Cha, Maxim Finkelstein

Department of Statistics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	3146-3151
Number of pages	6
Journal	Journal of Statistical Planning and Inference
Volume	142
Issue number	12
DOIs	https://doi.org/10.1016/j.jspi.2012.06.020
State	Published - Dec 2012

Bibliographical note

Funding Information:
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2011-0017338 ). The work of the second author was supported by the NRF (National Research Foundation of South Africa) grant FA2006040700002 .

Keywords

Cumulative shock model
Cure models
Delayed failure
Nonhomogeneous Poisson process
Shock model

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10.1016/j.jspi.2012.06.020

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title = "A note on 'curable' shock processes",

abstract = "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.",

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AU - Finkelstein, Maxim

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AB - 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.

KW - Cumulative shock model

KW - Cure models

KW - Delayed failure

KW - Nonhomogeneous Poisson process

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JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

IS - 12

ER -

A note on 'curable' shock processes

Abstract

Bibliographical note

Keywords

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