Probabilistic Evaluation of Industrial Systems Under Daily Operational Cycles with Constraints on Maximum Repair Time

Abstract This article focuses on the performance of a single-active-unit repairable industrial system with three different states of unit: active unit (N), partial failure unit (P), and complete failure unit (F). The system operates continuously, 24 hours a day, without interruption, except for two cases: a complete failure of the active unit or maintenance at partial failure (P). The system always has one service available, which is kept for maintenance and repair. In the case of complete failure, the faulty unit is replaced with a new one if the repair duration exceeds the maximum allowed time predefined. However, the nighttime replacement operations have a lot of challenges that may include limited availability of spare part suppliers or replacement must be performed at a higher cost since options are limited. In this paper, it is assumed that all the times in the system are negative exponentially distributed. The supplementary variable technique and Markov process theory have been employed to evaluate the reliability of the system. Further sensitivity and relative sensitivity analyses are performed on some system parameters in order to study the effect of these parameters on the proposed system. These results are presented with numerical examples that provide useful insights contributing to the enhancement of the systems efficiency and operational reliability.