Dynamic Reliability Measures of Multi-state k-out-of-n Systems Using Lz-transform

In system engineering, k-out-of-n multi-state system is one of the important systems as it finds wide application in many complex engineering structures. In earlier studies, k-out-of-n multi-state systems were usually thought to be operated in non dynamic state. However, in reality, these systems can have components whose states change over time, making them dynamic in nature. To tackle this, we propose a method utilizing the Lz-transform to obtain the dynamic reliability measures of such systems. The system’s components are presumptively Markov-process compliant and are only repaired after a total failure. In the proposed research work the reliability, availability, instantaneous performance expected, and deficiency in performance are found for the system under consideration. Lastly, a real-life example of the oil supply system is investigated to authenticate the proposed approach. It was observed that the reliability and availability of the oil supply system decline as the minimum number of required components in different states increases.