Reliability evaluation of multi-state series-parallel systems with multi-state performance sharing mechanism

Reliability is the probability that a system will perform properly over a period of time under specified operating conditions. A Performance-sharing system has been proposed by researchers to increase and improve the reliability of a system. Recently, a new procedure for sharing surplus performance has been introduced. In this procedure, the surplus performance of each unit is shared with its adjacent unit. This mechanism is investigated in a simple series structure. But in reality, the system can have different components and more complex structures. Therefore, it is necessary to investigate this procedure in other structures such as series-parallel structures with different components. Classical reliability theory in the basic state is considered binary, in which a system or a component has only two possible states, that is, it either works or breaks down. However, many real-world systems have multiple operational performance levels. Therefore, the study of multi-state systems is of particular importance. The problem of transmission loss can be considered in various dimensions such as power systems, mechanical tools, etc. If transmission loss is not considered in performance-sharing systems, system reliability is overestimated. Therefore, it is important to consider the transmission loss between lines of this system. In this study, a series-parallel multi-state system with a performance-sharing mechanism is provided. In this system, the surplus performance of each subsystem is shared with adjacent subsystems through multi-state transmission lines. Due to transmission loss, the lines lose some of their performance during transmission. The mathematical model is presented for the proposed system and the universal generating function method is used to evaluate it. To solve the proposed model using a genetic algorithm, a numerical example is defined. In this example, two issues are examined.1) The effect of the performance-sharing mechanism on system reliability 2) The effect of transmission loss on system reliability. The results show an increase in reliability in the proposed system.