This article mainly analyzes the applications of importance measures in inventory systems' reliability. Previous importance measures are mostly developed based on Birnbaum importance; however, they are not applicable to the identification of weakness and optimization in inventory systems by considering the customer requirements for mechanical products. Based on the three-echelon inventory system structure, the corresponding reliability is analyzed under the Poisson distribution. Then three importance measures, namely, composite importance measure, mean absolute deviation, and differential importance measure, are extended to the three-echelon inventory systems. By calculating and comparing the importance values of various components, the key parameters in inventory systems can be identified to achieve the minimal cost and optimal inventory system. Finally, a numerical example is used to demonstrate the proposed method.

Background: In recent years, the cost is becoming one of the biggest obstacles for the effective operation of supply chain. It is increasingly urgent to minimize the cost and optimize the supply chain system. However, importance measures have been little used in it as a research focus in solving the optimization problems. Methods: With respect to the foregoing, this paper combines the reliability, importance measures and cost issues to improve the supply chain. Supply chain costs can be divided into three classes: design cost, manufacturing cost, and inventory cost. Results: Then importance measures based on the costs are given and demonstrated in a case study. Results show that the optimal system and minimal cost can be obtained by focusing on the important parts in supply chain operation. Conclusion: The importance order and the key elements identification are helpful to increase the operational efficiency of the supply chain and provide effective methods for improving the supply chain management.