Reliability analysis of consecutive n-out-of-nG repairable systems with a multi-state component

A consecutive n-out-of-nG repairable system is studied. It is assumed that the working time of the components in the system is exponentially distributed, that the repair time of the component in the system is continuously distributed, and that the components in the system are subject to two kinds of failure. The system is analyzed using the vector Markov process and Laplace transformation. The exact formulas for the Laplace transformation of the system reliability and the system's mean time to the first failure are obtained.