- Mathematical Sciences and Applications E-Notes
- Vol: 8 Issue: 1
- On the coherent systems subject to Marshall-Olkin type shocks
On the coherent systems subject to Marshall-Olkin type shocks
Authors : Murat Ozkut, Cihangir Kan
Pages : 185-192
Doi:10.36753/mathenot.621901
View : 9 | Download : 3
Publication Date : 2020-03-20
Article Type : Research
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