Reliability indices of multi-state repairable m-out-of-r-within-k-out-of-n system using Lz-transform method

A multi-state m-out-of-r-within-k-out-of-n system has found great importance in reliability theory because of its wide applications in engineering systems. In previous studies, usually all the components of the m-out-of-r-within-k-out-of-n system were considered to be binary and that too in a steady state, despite the fact that there are numerous complex systems where the components of this type of system can be multi-state and dynamic in nature i.e., their states change over time. To deal with this circumstance, the current research presents an algorithm, based on the Lz-transform to determine the reliability indices of the considered system in the dynamic setup. The Markov process is assumed to be followed by the components of the considered system and is mended only after they entirely fail. In the proposed research, reliability, availability, instantaneous mean expected performance and mean performance deficiency are obtained for the considered system. Finally, a case study of the photovoltaic system is studied to implement and validate the proposed method.