Reliability modeling for systems subject to dependent competing failure processes with set of random shocks affect specific components

We present a reliability model for system subject to dependent competing failure processes with set of shocks affect specific components. Traditional reliability method involving competing failure modes have only dealt with hard failure which occurs when the shock load is larger than the corresponding threshold level. However, soft failure analysis is also necessary for systems, which are caused by continuous degradation and shock processes. In this case, hard and soft failure processes are competing. Analysis of the reliability model of system is developed in relation to the competing failure processes. In fact, each component of system may experience different shocks. In our model, three types of random shocks are considered: every component of system experiences shock III, and shock I only affects some specific components of system, shock II affects the rest. Each component of system is independent. Every arrival of random shocks follows Poisson process.