Reliability assessment of multi-state weighted k-out-of-n man-machine systems considering dependent machine deterioration and human fatigue

Multi-state weighted k-out-of-n systems have been extensively investigated while previous studies have only focused on machine systems. In practice, the systems with n man-machine units (MMUs) are common, especially in manufacturing areas. In this paper, we first investigate the reliability of multi-state weighted k-out-of-n man-machine systems. Furthermore, the machine deterioration process, human fatigue process, and their mutual dependence are incorporated into the reliability model. The machine deterioration and human fatigue both degrade MMUs’ performance such as production capacity. Moreover, the mutual dependence facilitates MMUs’ transitions to lower performance states: (i) machine deterioration accelerates fatigue accumulation through increasing fatigue inducing conditions, and (ii) high fatigue causes more human errors considered as shocks on machine and accelerates machine deterioration recursively. To model the state probability of MMUs with the mutual dependence, a piecewise-deterministic Markov process model is proposed, where multi-state machine deterioration is described by a semi-Markov process and the evolutions of fatigue and human error rate are piecewise-deterministic during each machine state. After that, a mathematical daily output model and a universal generating function are proposed to evaluate MMUs’ state performance and system reliability, respectively. Numerical examples are presented to illustrate the effectiveness of the proposed model.