On a hazard (failure) rate process with delays after shocks

Nil Kamal Hazra, Maxim Finkelstein and Ji Hwan Cha

Statistics & Probability Letters, 2022, vol. 181, issue C

Abstract: Distinct from conventional shock models when a failure of a system or accumulation of the corresponding damage occurs immediately after a shock, we consider a setting when these consequences appear with a random delay. In our model, a shock acts directly upon the failure rate of a system. This, after a random time, can result either in a failure or in the increase in the failure rate by a random amount. We derive expressions for survival probability and the failure rate for a system. Asymptotic behavior of the failure rate is also studied in detail.

Keywords: Failure rate; Hazard rate process; Nonhomogeneous Poisson process; Stochastic intensity (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2021.109276

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