Reliability Evaluation of Systems With Performance Sharing Mechanism Under Semi‐Markov Process

ABSTRACT A new performance‐sharing system is proposed in this paper, in which the states of units follow the general distribution like semi‐Markov process, and the transmission of surplus performance is restricted to adjacent units for some reason. First, we establish a new system that n‐ subsystems are connected in series, and the state transition of components not only obeys exponential distribution, but also obeys Weibull distribution and normal distribution. In such a system, performance units generate performance, demand units consume performance, and performance transfer units share surplus performance between adjacent subsystems via lines, where the transmission loss of lines and the capacity limitation of performance transmission units are considered. When one or more subsystems fail, the whole system fails. Meanwhile, a semi‐Markov process is used to reflect the state probability of a system, and the universal generating function technique is applied to solve the system reliability. A high‐precision calculation method based on the Simpson formula is raised to access analytical solution of state probability, and the Monte Carlo algorithm is applied to verify the correctness and efficiency of the proposed method. Finally, a wind power system is employed to reflect the application of this model. The results show that a high‐precision state probability calculation method based on Simpson formula and semi‐Markov process can describe the complex system in practical engineering more accurately and solve the limitation that the current performance sharing model is limited to exponential distribution assumption.