Reliability-oriented extended importance measures in uncertain inventory systems for mechanical products

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.