 On the occurrence time of an extreme damage in a general shock modelMohsen Bohlooli-Zefreh, Afshin Parvardeh and Majid Asadi Journal of Risk and Reliability, 2023, vol. 237, issue 6, 1100-1113 Abstract: In the literature of system reliability and other fields related to the time to occurrence of an event, shock models play an important role. In this paper, we assume that a system is subject to shocks that occur according to a counting process describing the number of shocks that arrive during a specified time interval. As the magnitude of the damage imposed to the system by each shock is a crucial parameter to the system’s survival, we investigate some important random variables related to this parameter. A random variable of interest associated with this process is the first time, after a pre-specified time s , at which the amount of a shock damage to the system gets greater than the maximum of damages imposed to the system until time s . We obtain the reliability function of this random variable and investigate various properties of it and some other related random variables. In order to explore further the results, we examine two commonly used processes in the literature, that is, the non-homogeneous Poisson process and the Pólya process. Keywords: Reliability; shock models; nonhomogeneous Poisson process; Pólya process; extreme damage (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:sae:risrel:v:237:y:2023:i:6:p:1100-1113 DOI: 10.1177/1748006X221119549 Access Statistics for this article More articles in Journal of Risk and Reliability |
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