On the coherent systems subject to Marshall-Olkin type shocks

Year 2020, Volume: 8 Issue: 1, 185 - 192, 20.03.2020

Murat Ozkut , Cihangir Kan

https://doi.org/10.36753/mathenot.621901

Abstract

Coherent systems and Marshall-Olkin run shock models are combined. Coherent systems consisting of n components receive some kind of shocks from n+1 different sources similar to Marshall-Olkin type. More precisely, when the component j receives k consecutive fatal shocks from the source j or k consecutive fatal shocks from the source n+1, it fails, j = 1, …,n. When the interarrival time of shocks has phase-type distribution, reliability, mean time to failure (MTTF) and mean residual life (MRL) function of the coherent systems are studied. Numerical examples and graphical representations are provided.

Keywords

Phase-type distributions, Coherent system, Marshall-Olkin distribution, Reliability, Mean residual lifetime

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