Dynamic reliability and sensitivity analysis of weighted (k, r)-out-of-n cold standby system with multi-performance multi-state components

The standby multi-performance multi-state (MPMS) systems represent a significant advancement in reliability engineering, incorporating the diversity of multi-states and standby configurations. Unlike traditional binary systems, which classify the states as operational or failed, standby MPMS models consider multiple performance levels and states, capturing real-world scenarios where systems can operate at reduced capacities. This paper develops a comprehensive approach based on the $L_z$-transform to evaluate the dynamic reliability measures of a weighted (k, r)-out-of-n cold standby system incorporating maintenance and inspection techniques that emphasize MPMS components and their dynamic interconnections. The failed components are queued under the (M|M|1):(∞|FCFS) model to undergo repair or replacement following the inspection. In case of minor, semi-minor and semi-major failures, the components are repaired according to Erlang distributions, while major failures require replacement, which follows Weibull distributions. In the considered model, standby components take over their respective places when primary components fail, ensuring the system continues operating even after component failures. The reliability measures for the system, including reliability, availability, sensitivity, instantaneous mean expected performance and cost analysis have been determined. A case study on a solar thermal power (STP) system is presented to validate the proposed methodology, illustrating its practical implementation and effectiveness.