On the coherent systems subject to Marshall-Olkin type shocks

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 receive 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.