# On the Use of Importance Measures in the Reliability of Inventory Systems, Considering the Cost  
[PERSON]  
1 School of Electrical Engineering, Zhengzhou University, Zhengzhou 450001, Henan, China 1,* 1,  
of inventory systems and extended the importance measure to the three-echelon inventory systems. [PERSON] et al. (2017) studied the cascading failure in an inventory network from the perspective of the payoffs of nodes in a multi-strategy evolutionary game. [PERSON] et al. (2018) proposed opportunistic maintenance decision rules based on the criticality level of components and the availability of spare parts. [PERSON] and [PERSON] (2019) developed a cost-effective ordering inventory model where the increase in reliability of the item lead to a rise in demand and decreases the rate of deterioration. [PERSON] et al. (2020) found the optimal number of transportation cycles and components, which can maximize the total business profit and system reliability with volume, weight, and cost of the system as constraints. [PERSON] (2018) studied the system reliability of a stochastic delivery-flow distribution network with an inventory. [PERSON] et al. (2020) studied an imperfect production inventory model with production system reliability under two-layer supply chain management. [PERSON] et al. (2020) proposed an optimal solution of the reliability model by a generalized reduced gradient algorithm. Currently, the competitive environment is drastically changing, which will lead to the adaptation of system resilience design and maintenance in dynamic environments ([PERSON] et al., 2018; [PERSON] et al., 2018). There are too many uncertainty factors involved in inventory models. With the interference of various uncertainties, the problem of stock shortage occurs frequently. In situations where enterprises operate normally and minimize inventory, how to realize the optimization of inventory models out of stock, has become a hot topic for scholars from all circles ([PERSON] et al., 2018). [PERSON] and [PERSON] (2018) proposed an economic order quantity inventory model of multi-items in a two-layer supply chain where demand was sensitive to promotional effort, and they compared collaborative and non-collaborative systems in terms of their average profits. [PERSON] et al. (2018) developed a reverse inventory model where the recoverable manufacturing process was affected by the learning theory. [PERSON] et al. (2019) characterized the optimal policies that simultaneously determine the optimal ordering and pricing decisions in each period over a finite planning horizon. Meanwhile, the impacts of supply source diversification and supplier reliability on the firm and on its customers are studied. [PERSON] et al. (2020) considered the optimal production, pricing, and substitution policies of a continuous-review production-inventory system with two products: a high-end product and a low-end product. [PERSON] et al. (2020) examined vendor-managed inventory systems with stockout-cost sharing between a supplier and a customer with shortages allowed under limited storage capacity, where a stockout penalty was charged to the supplier when stockouts occurred with the customer. [PERSON] and [PERSON] (2020) analyzed the reliability of supply chain systems by using copulas. [PERSON] et al. (2020) developed a theoretical conceptualization of supply chain uncertainty and reliability. [PERSON] et al. (2020) built a logistics service supply chain model under the stochastic demand to consider the feature of non-storage and reliability. [PERSON] et al. (2020) evaluated the supply chain reliability and resilience for the complexity of supply chain structures. The inventory models provide an effective means for companies to carry out inventory management and reduce inventory costs. Scholars have continuously improved and optimized the models from various perspectives and fields, however, have neglected the application of importance measures to effectively identify and optimize systems in this field.