輪胎產業因應各種車廠車型開發需求，開發出配合各式車型、尺寸花紋輪胎以符合不同性能與磨耗需求調配出多種配方與樣式需求，例如電動車節能出需要低滾動阻力的節能配方，性能車款需要高抓地力的性能配方。因規格花紋的多樣性導致龐大數量的驗證計畫，即是導致檢驗成本高居不下的主要原因。為了降低抽檢造成之成本，本研究將從成本的角度下探討在符合經濟效益的前提下能夠及時反應出製程發生變異的抽檢方法，Duncan首先將成本的概念加入管制圖的設計，發表X經濟設計管制圖，經濟設計的基本概念為調整管制圖中的抽樣間隔長度、樣本大小、管制界限，三個重要決策變數以獲得最低之總成本。適應性管制圖是將這些決策變數由定值調整為隨著前一次製程觀測資料進行變動微調。而經濟設計是在長期的架構下重新設計管制圖，短期內若對管制圖的設計做大幅度的改變可能會導致成本的提升。
本研究建構一套可調整抽樣間隔的設定方法，當短期內監控管制圖的人力資源有限，同時監控多張管制圖的情況下，該如何針對抽樣間隔長度做調整。損失成本函數除參考Bai 和 Lee 學者的經濟設計，本研究加入工廠實際運作流程，將成本分為五項(1)製程因警報響起而產生之等待處理的單位時間成本 (2)製程等待處理及消除可歸屬原因之單位時間成本 (3)製程在失控狀態下之單位時間生產成本 (4)預防與鑑定之成本 (5)外部失敗成本
透過適應性與經濟設計方式建構數學模型，期望能降低總成本並維持製程偵測變異的效率，成本函數進行二次微分，證明此模型為凸函數具有極小值。並在總成本最小化的目標下，找出最適抽樣間隔長度，最後透過實際案例驗證，針對重要的參數進行敏感度分析，了解不同參數對成本函數的影響程度。

The tire industry usually cooperates with various car manufacturers, to meet different performance and size requirement. Such as electric vehicles require low rolling resistance and energy saving solutions. High-performance racecars require high-grip performance solutions. Because of the diversity of specifications and patterns, a huge number of verification projects are the main reason for the high cost of inspection. In order to reduce the cost caused by sampling inspection, this dissertation will explore the sampling inspection method that can reflect the variation of the process in time under the premise of economic benefit from the perspective of cost.

In order to reduce the cost of sampling without affecting the sensitivity of detecting process. This dissertation use adaptive economic design control chart to construct the sampling interval length of the control chart. This model will combine the concepts of economic design and adaptive design, and add labor cost considerations to minimize the expected total cost of the statistical process control program. The conclusion of the dissertation show that by appropriately adjusting the combination of the length of the sampling interval, the expected total cost per unit time can be reduced. Sensitivity analysis is used to evaluate how parameters affect the total cost per unit time.

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