The Reliability of Coherent Systems Subjected to Marshall–Olkin Type Shocks

In the classical Marshall-Olkin model, the system is subjected to two types of shocks coming at random times, and destroying components of the system. In statistics and reliability engineering literature, there are numerous papers dealing with various extensions of this model. However, none of these works takes into account the system structure, i.e., in existing shock models usually the system structure is not considered. In this work, we consider a new shock model involving the system structure. More precisely, we consider a coherent system which is subjected to Marshall-Olkin type shocks. We investigate the reliability, and mean time to failure (MTTF) of such systems subjected to shocks coming at random times. Numerical examples and graphs are provided, and an extension to a general model is discussed.