Reliability of non-repairable systems with cyclic-mission switching and multimode failure components

This paper considers a mission-based non-repairable system which has multiple and cyclic mission sequences, and whose components have multimode failures. For example, the valve system with two failure modes cannot only fail to close when required to close but can also fail to open when required to open. A discrete-time semi-Markov chain within the time evolution framework is constructed, which is more properly to model the realistic problems because the sojourn times between the successive missions may be not satisfied Markov property. Using the aggregated stochastic theory and Z-transform, the explicit form of the solution of system reliability is obtained, which can simplify calculations and get some distributions of some sojourn times that the readers relish, including perfect and imperfect operations. In addition, two special valve systems with two-mission and three-mission switching are provided respectively. Finally, numerical examples are presented to illustrate the proposed model and the method.