使用管制圖追蹤品質特性在製造過程中的變異前，使用者應先決定管制圖

的設計參數值 (Design Parameters) ， 如樣本大小、抽樣時間間隔，及

管制界限寬度等。當已知每次抽樣的樣本大小大於 10 ，且非隨機因素

(Assignable Causes) 的發生只會使製程變異增大時，則 S 管制圖應被

選用來追蹤製程是否穩定。 S 管制圖的經濟設計，首由 Collani 及

Sheil(1989) 提出，文中他們只考慮單一非隨機因素的情形。唯實務上，

製程常同時受多重非隨機困素的影響。為使製程模式假設更合理，使用更

有彈性，我們先將多重非隨機因素製程表示為更新過程 (Renewal

Processes) ， 其中每個更新循環 (Renewal Cycles) 則表示為馬可夫過

程 (Markov Process) 。 接著，以 S 管制圖追蹤的製程平均循環時間

(The Expected Cycle Time) 及平均循環成本 (The Expected Cycle

Cost)應用馬可夫性質可容易的推導出。最後，目標函數可利用更新報酬

過程 (Renewal Reward Processes) 性質獲得。 由於目標函數是設計參

數之函數， 因此藉著最佳化目標函數， S管制圖之最適設計參數值可被

決定。由針對一個特例所做的變異數分析及回應圖分析結果，我們可決定

重要製程與成本參數，這些參數的了解可做為決策者決策上的參考。另外

， S 經濟管制圖所發生的品質成本遠比傳統 S 管制圖的小,而在製程失

控下， S 經濟管制圖的偵測力也比傳統 S 管制圖的強。 是以 S 經濟管

制圖優於傳統的 S 管制圖。本研究所推導出的製程模式及 S 管制圖設

計方法可應用於各種分配的製程變數 (Process Variable) 及其他類型管

制圖的設計上。

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