Shock and wear models under policy N using phase-type distributions

A device submitted to shocks and wear is considered. The shocks occur with inter-arrival times phase-type distributed, and can induce the device failure. The device also can fail due to ageing, and the lifetime follows a phase-type distribution. The inter-arrival times between shocks and the lifetime depend on the number of cumulated shocks. The number of shocks that the device can support is limited. For this model, the survival probability is calculated. Other models are considered under these assumptions, and the survival functions are determined and expressed in a well-structured form. A numerical application illustrates the methods introduced in the paper.