Some sensitive industries with precise specifications in their manufacturing process, such as aircraft engine parts, impose 100% inspection processes in their inventory-manufacturing system. In some cases, a lot of small dimensions are measured and compared with strict acceptable tolerances during these inspection processes, causing manufacturing process times (machine time speed) to be less than inspection times. This study is relevant to manufacturing enterprises that implement comprehensive 100% inspection protocols within their production procedures, encompassing sectors such as pharmaceuticals, aerospace, electronics, medical devices, and textiles. In this paper, such a phenomenon is investigated, as an inventory system with a strict inspection model is deployed under three conditions: a) an inventory-manufacturing system with scrapped items without shortage, b) an inventory-manufacturing system with reworked items without shortage, and c) an inventory-manufacturing system with scrapped and reworkable items with backorder. The aim is to minimize total cost by considering strict inspection during production process. These proposed models are suitable for managing systems where quality control is a bottleneck due to its speed such as high-precision manufacturing systems. The optimal solutions for each model are obtained as a closed-form expression. In models 1 and 2, where the shortage is not allowed, the closed-form expression is focused on determining the economic production quantity. However, in model 3, there are two expressions of significance. First, it addresses the economic production quantity, like models 1 and 2. Additionally, it provides an optimal value for the shortage in each cycle, as it considers a scenario where shortages are permitted within the inventory-manufacturing system. This study has included a numerical example to illustrate the practical applicability of each model. Based on the optimal solutions obtained, it is evident that Model 3 stands out as the superior choice. This outcome aligns with expectations, as Model 3 encompasses and comprehensively addresses the scenarios presented in the two other models. Finally, a sensitivity analysis is performed to investigate the effects of key parameters on the optimal solutions of each model, and the results are summarized to present a comparison between them.

中文翻译：

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严格检验的不完善制造系统的经济生产数量模型

一些在制造过程中具有精确规范的敏感行业，例如飞机发动机零部件，在其库存制造系统中实行 100% 的检验过程。在某些情况下，在这些检查过程中，需要测量大量小尺寸并将其与严格可接受的公差进行比较，从而导致制造过程时间（机器时间速度）小于检查时间。本研究适用于在生产过程中实施全面 100% 检验协议的制造企业，涵盖制药、航空航天、电子、医疗器械和纺织等行业。本文对这种现象进行了研究，在三种情况下部署具有严格检验模型的库存系统：a）无短缺报废品的库存制造系统，b）无短缺返工品的库存制造系统，以及 c) 一个库存制造系统，其中包含有缺货的报废和可返工物品。目的是通过在生产过程中考虑严格的检查来最小化总成本。这些提出的模型适用于管理质量控制因其速度而成为瓶颈的系统，例如高精度制造系统。每个模型的最优解以封闭形式表达式的形式获得。在模型1和2中，不允许短缺，封闭式表达式的重点是确定经济生产数量。然而，在模型3中，有两个重要的表达方式。首先，它解决了经济生产数量，如模型 1 和 2。此外，它为每个周期中的短缺提供了最佳值，因为它考虑了库存制造系统内允许短缺的情况。本研究包括一个数值示例来说明每个模型的实际适用性。根据获得的最佳解决方案，Model 3 显然是最佳选择。这一结果符合预期，因为模型 3 包含并全面解决了其他两个模型中提出的场景。最后，进行敏感性分析，研究关键参数对每个模型最优解的影响，并对结果进行总结以进行比较。