Lz‐transform approach to evaluate reliability indices of multi‐state repairable weighted K‐out‐of‐n systems

A multi‐state weightedK‐out‐of‐nsystem is of great importance in system engineering due to its generalized nature. In earlier studies, usually all the components of the multi‐state weightedK‐out‐of‐nsystem were considered to be in a steady state though we can encounter engineering systems where the components of this type of system can be dynamic in nature, that is, the states of components change over time. To deal with this situation, in the current study an algorithm, based on ‐transform is presented to determine the reliability indices of multi‐state weightedK‐out‐of‐nsystem in dynamic setup. The components of the system are assumed to follow Markov process and are repaired only when they are completely failed. In this proposed study reliability, availability, instantaneous mean expected performance, and performance deficiency are obtained for the considered system. Finally, a case study of the power system of warship is considered to apply and validate the proposed approach.