Approximating the Lévy-Frailty Marshall-Olkin Model for Failure Times

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In this paper we approximate the last, close-to-first, and what we call quantile failure times of a system, when the system-components' failure times are modeled according to a Levy-frailty Marshall-Olkin (LFMO) distribution. The LFMO distribution is a fairly recent model that can be used to model components failing simultaneously in groups. One of its prominent features is that the failure times of the components are conditionally iid; indeed, the failure times are iid exponential when conditioned on the path of a given Lévy subordinator process. We are motivated by further studying the order statistics of the LFMO distribution, as recently Barrera and Lagos (2020) showed an atypical behavior for the upper-order statistics. We are also motivated by approximating the system when it has an astronomically large number of components. We perform computational experiments that show significative variations in the convergence speeds of our approximations.

Original languageEnglish
Title of host publicationProceedings of the 2020 Winter Simulation Conference, WSC 2020
EditorsK.-H. Bae, B. Feng, S. Kim, S. Lazarova-Molnar, Z. Zheng, T. Roeder, R. Thiesing
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages11
ISBN (Electronic)9781728194998
StatePublished - 14 Dec 2020
Event2020 Winter Simulation Conference, WSC 2020 - Orlando, United States
Duration: 14 Dec 202018 Dec 2020

Publication series

NameProceedings - Winter Simulation Conference
ISSN (Print)0891-7736


Conference2020 Winter Simulation Conference, WSC 2020
Country/TerritoryUnited States


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