Spare parts management is one of the most important aspects in industrial systems where a large number of spare parts are stocked to replace with failed parts and reduce the system's downtime. In this study, it is supposed that the quality of spare parts can differ from the quality of the original parts since they might be supplied from different suppliers. This problem is modeled by using the probability tree and Markov chains approach to determine the optimal number of spare parts, their supplier, and appropriate quality, leading to minimization of the system's total cost and or system's total availability. Meanwhile, highly expensive parts cause large investment. In this study, a k-out-of-N redundant system is modeled in which by failing each part it is replaced by a stocked spare part if exists. Otherwise, in case of spare parts lacking the system continues to its operation with failed part(s) which reduces system performance. If the number of failed parts reaches a predetermined threshold level (N-k+1) it leads to system shutdown. All suggesting models are applied on numerical samples for to show the representation of the state and determine optimal spare parts supply strategies and inventory policies in large-scale industrial systems.
