Duncan首先將成本的概念加入管制圖的設計，並於1956年發表 經濟設計管制圖，此後許多學者分別針對不同類型的管制圖提出經濟設計模型。Wu et al.於2006年首先將人力配置的議題加入管制圖的經濟設計，藉由事前優化監控管制圖所需的人力，達到成本的降低。然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，且過去經濟設計的相關研究主要為監控單張管制圖的情況，實際工廠營運時通常為多條生產線同時運作，也就是同時監控多張管制圖的情況。
本研究建構一套管制界限的設定方法，當短期內監控管制圖的人力資源有限，又要同時監控多張管制圖的情況下，該如何針對管制界限調整。損失成本函數參考Duncan的經濟設計模型，包括(1)製程在可歸屬變異發生後繼續運作的額外成本(2)製程處於穩定狀態時搜尋錯誤警告的成本(3)製程處於失控狀態時搜尋可歸屬原因的成本(4)維護管制圖的成本；透過總成本對管制界限做一階微分並令其為零的方式求得能夠使總成本最小化之管制界限值。另外，由於工程師在處理發出異常警訊之管制圖時式採取先進先處理的策略，因此發出異常警訊之管制圖的等候時間以M/M/c queue模型建構。研究結果顯示，透過管制界限的調整可以避免成本的上升，達到品質管制與成本控制的目的。根據敏感度分析可以發現抽樣間隔時間、工程師單位時間可以處理的管制圖數量及處理發出異常警訊之管制圖一單位時間產生的成本有較大之影響，因此未來應用此模型於工廠實際運作之企業可以更加注意此部分之變化。

The economic design of control charts have received considerable attention since Duncan first proposed the economic design of control charts in 1956. Wu et al. proposed a methodology for deploying manpower to a statistical process control scheme in order to minimize the expected total cost. The concept of economic design is to construct control charts from a long-term perspective; however, changing control chart parameters may cause cost rising in the short term. In this thesis, we develop a methodology for setting control limits of control charts, subject to short-term human resources for monitoring multiple control charts. The objective of this design is to minimize the total cost per production cycle, as a result, we use Duncan cost function for economic design as well as M/M/C queue model for human resources construction. Results of numerical studies show that cost can be reduced by setting appropriate control limits. Finally, a sensitivity analysis has been performed to evaluate how the parameters influence the total cost per unit time.

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