本篇研究的目的為建立Optimal DS AL管制圖，並以ARL為績效的衡量指標，接著以R軟體的基因演算法決定使失控ARL最小化的管制界線。接著建立DSVSI EWMA AL管制圖，並以ATS為績效的衡量指標。當EWMA的權重 時，DSVSI EWMA AL管制圖則簡化為DSVSI AL管制圖，當固定抽樣間隔時，DSVSI EWMA AL管制圖則簡化為DS EWMA AL管制圖，當EWMA的權重 且抽樣間隔固定時，DSVSI EWMA AL管制圖則簡化為DS AL管制圖。最後以資料分析比較 DSVSI EWMA AL管制圖、DSVSI AL管制圖 、DS EWMA AL管制圖、Optimal DS AL管制圖、 DS AL管制圖 、 Optimal VSI AL管制圖(Yang 2013a) 、AL管制圖(Yang 2013)和DS X-bar and S管制圖(He and Grigoryan 2004)之失控的偵測績效。

國內近年來工商企業發展極為蓬勃，各企為對產品品質均相當重視，在製程品管中使用管制圖管制產品品質工廠亦非常普遍，惟各廠在設計品質管制圖時均未從經濟觀點加以考慮。本文即從經濟觀點探討製程品管中最重要的品質管制圖之設計，應如何參酌本身各項品質管制成本來建立管制圖，以降低成本，達到經濟有效控制產品品質之目的。 根據本文之研究分析結果，在考慮經濟觀點之下設計管制圖時，其最適參數設計值應視檢驗成本、非機遇原因所造成製程之偏移量、品質失靈損失、非機遇原因之發生頻率以及追查異常原因所需成本之高低等之不同而異： 1.檢驗成本較低時，採樣本數大、抽樣時距短之方案較合乎經濟原則；反之如檢驗成本較高時，樣本數則應小，抽樣時間間隔應長始較為經濟。 2.非機遇原因所造成制程之偏移量較大時，樣本數可以較小，抽樣時距亦應短些；反之如非機遇原因所造成製程之偏移量小時，樣本數應取大些，抽樣時距亦應長些。 3.製程在偏移狀態下生產所導致企業之損失較大時，應採較短之抽樣時距；反之如損失額不大，則抽樣時間間隔可較長些。 4.非機遇原因造成製程偏移之發生頻率低時，所設計之抽樣時距可較長；反之當發生頻率高時，抽樣時距應較短。 5.追查異常原因所需之成本對管制幅度之設計值影響較大。當追查原因成本較高時，管制幅度應較寬些；反之追查原因成本較低時，管制幅度可較狹。 6.從經濟觀點設計品質管制圖，必需運用生產製程之實況資料以及各項品質成本資料，如果對各項資料缺乏記錄或者記載不確實，則所設計出來的管制圖計劃必定收效極微，因此，對各項生產狀況資料及品質成本資料隨時記錄並定期分析整理實為建立經濟有效品質管制圖之要件。

利用單一二元損失管制圖來偵測製程平均數向量及共變異數矩陣同時偏移。不同於已存在的多元管制圖，本文所提出的管制圖是以二元平均損失函數建構而成的，因此，在監控製程時，我們同時能獲得產品平均損失的資訊。平均連串長度分析結果指出二元損失管制圖在偵測製程小幅度偏移上有不錯的其偵測能力。本文將與現存的多元方法做績效表現的比較，例如：二元管制圖、多元的累積管制圖和多元的指數加權平均管制圖等。結果顯示，二元損失管制圖在偵測程平均數向量及共變異數矩陣同時偏移的情況下有較好的偵測能力。

The CUSUM control charts have been widely used in detecting small process shifts since it was first introduced by Page (1954). And recent studies have shown that adaptive charts can improve the efficiency and performance of traditional Shewhart charts. To monitor the process mean and variance in a single chart, the loss function is used as a measure statistic in this article. The loss function can measure the process quality loss while the process mean and/or variance has shifted. This study combines the three features: adaption, CUSUM and the loss function, and proposes the optimal VSSI, VSI, and FP CUSUM Loss chart. The performance of the proposed charts is measured by using Average Time to Signal (ATS) and Average Number of Observations to Signal (ANOS). The ATS and ANOS calculations are based on Markov chain approach. The performance comparisons between the proposed charts and some existing charts, such as X-bar+S^2 charts and CUSUM X-bar+S^2 charts, are illustrated by numerical analyses and some examples. From the results of the numerical analyses, it shows that the optimal VSSI CUSUM Loss chart has better performance than the optimal VSI CUSUM Loss chart, optimal FP CUSUM Loss chart, CUSUM X-bar+S^2 charts and X-bar+S^2 charts. Furthermore, using a single chart to monitor a process is not only easier but more efficient than using two charts simultaneously. Hence, the adaptive CUSUM Loss charts are recommended in real process. / The CUSUM control charts have been widely used in detecting small process shifts since it was first introduced by Page (1954). And recent studies have shown that adaptive charts can improve the efficiency and performance of traditional Shewhart charts. To monitor the process mean and variance in a single chart, the loss function is used as a measure statistic in this article. The loss function can measure the process quality loss while the process mean and/or variance has shifted. This study combines the three features: adaption, CUSUM and the loss function, and proposes the optimal VSSI, VSI, and FP CUSUM Loss chart. The performance of the proposed charts is measured by using Average Time to Signal (ATS) and Average Number of Observations to Signal (ANOS). The ATS and ANOS calculations are based on Markov chain approach. The performance comparisons between the proposed charts and some existing charts, such as X-bar+S^2 charts and CUSUM X-bar+S^2 charts, are illustrated by numerical analyses and some examples. From the results of the numerical analyses, it shows that the optimal VSSI CUSUM Loss chart has better performance than the optimal VSI CUSUM Loss chart, optimal FP CUSUM Loss chart, CUSUM X-bar+S^2 charts and X-bar+S^2 charts. Furthermore, using a single chart to monitor a process is not only easier but more efficient than using two charts simultaneously. Hence, the adaptive CUSUM Loss charts are recommended in real process.

在全球競爭的環境中，服務或產品品質是非常重要的。好的服務或產品品質將導致顧客的高度滿意和企業的持續利潤與永續經營。 目前兩階流程管理的觀念與方法只應用在製造業品質的管制上，而本研究將此觀念與方法推廣並應用在個案公司的採購與銷售作業流程管理上。經由收集個案公司的採購成本和銷售額的資料，再分別據以建立兩階流程的個別管制圖和選控圖以管制採購成本和利潤變異情形。分析結果顯示採購成本和利潤變異並不穩定，而造成的原因經由分析發現後，分別提出適當的改善策略。預期未來實施後應能達到有效的改善作業流程、降低成本並提昇市場之競爭力。

In this article, a renewal theory approach is used to derive an expression for the expected cost per unit production time of adaptive sampling interval economic control chart. First, we derive the expected cycle time E(T) and expected cycle cost E(C). Then the expected cost per unit production time is E(V)=E(C)/E(T). The optimal design parameters can be determined by minimizing the expected cost per unit production time E(V). In this paper, minimizing the cost function, the optimal design parameters can be determined by using Fortran program and IMSL library. Furthermore, the sensitivity analysis illustrates the effects of cost and process input parameters on the optimal design parameters and the minimal expected cost per unit production time for the proposed control chart.

Control charts are used to effectively monitor and determine whether a process is in-control or out-of-control. The properties of EWMA control charts on a single process have been discussed by many researchers. They have proved that EWMA control charts detect small shifts in means or variances more quickly than the traditional Shewhart control charts. However, many products are currently produced in several dependent process steps. In this article, (1) we propose three kinds of EWMA control charts, - , - , and a combined control charts, to monitor the process mean and variance for a single process step, and (2) extend the three kinds of EWMA control charts in (1) to control two dependent steps. The performance of the proposed control charts is measured by using the Markov chain approach. The application of the proposed control charts is illustrated by using some numerical examples, and the performance of the proposed charts is compared by using some numerical examples. The adjusted average time to signal (AATS) and the adjusted average samples to signal (ANOS) are calculated to measure the performance of the proposed EWMA control charts by Markov chain approach. A data set consisting of the measurements of the inside diameter of the cylinder bores in an engine block example illustrates the applications of the three kinds of EWMA control charts for a single step and a empirical automobile braking system example illustrates the applications of the three kinds of EWMA control charts for two dependent steps. Moreover, their performances are compared by some numerical analysis results.

本研究針對兩個相依製程下兩個等級產品之製程管制提出以統計方法管制製程和以經濟觀點管制製程。在統計製程管制方面，本研究在製程的第一階段建立個別等級的EWMA管制圖和合併的EWMA管制圖以快速地偵測出影響個別等級產品品質特性之非機遇因素是否發生及同時影響所有等級產品品質特性之非機遇因素是否發生；在第二階段建立個別等級的選控圖和合併的選控圖以快速地偵測出影響個別等級產品品質特性之非機遇因素是否發生及同時影響所有等級產品品質特性之非機遇因素是否發生。利用這些管制圖不但考慮到前後製程的關係，在製程失控時更可明確地劃分各個子製程的責任歸屬。本研究並以資料分析比較EWMA管制圖和選控圖、Shewhart Individual管制圖與Hotelling 管制圖的診斷效果。在經濟設計方面，本研究發展經濟設計的EWMA管制圖和選控圖以分別監控生產兩個等級產品之兩階段製程。文中將製程表示為更新過程，而更新過程中每一個循環又被表示為馬可夫過程，於是利用馬可夫鏈方法及更新過程性質可導出成本函數。由於導出的單位時間成本是管制圖設計參數的函數，故用最佳解技巧即可決定設計參數的最佳值。文中並以數值分析與例子說明經濟設計的EWMA管制圖和選控圖的設立及應用。

自從1956年Duncan首先提出X管制圖的經濟模式以來，各類管制圖的經濟設計即被廣泛的研究，但有關S管制圖經濟設計卻非常少。最早是由Collani and Sheil於1989年提出，他們假設製程中只存在一個非機遇因素，且其發生時間服從指數分配，但實務上製程中經常存在二種或以上的非機遇因素，而且故障率並不一定為固定的，所以本研究係探討製程中存在二個非機遇因素的情況下，擴展其發生時間之分配至範圍較廣的韋伯分配，並藉由Banerjee and Rahim(1987)的更新方程式方法建立S管制圖之最適設計。 在資料分析方面，本研究分別對連續性及非連續性製程，利用最佳化技巧，求出不同成木和製程參數組合下的最適設計參數值及最適單位時間成本。再利用變異數分析、回應圖分析及敏威度分析，決定影響設計參數的重要製程及成本參數。以供管理者決策之參考。關鍵字：管制圖、韋伯分配、經濟設計、更新理論。

隨著經濟的發展和人民生活水準的提昇，罐裝食品或日用品的市場需求日益增加。罐裝產業為因應廣大的市場需求，加速生產已為必然。為加速生產效率，業者多會採用多注頭的製程生產產品。 到目前為止，可用於追蹤多注頭製程是否穩定的方法很多，但大部分都只是用於注頭間產品品質特性是互相獨立的情形。本研究乃針對注頭製程間產品品質特性相關的情形，探討失控注頭對其它製程的影響情況並分別提出變數變換法及Gram-Schmidt垂直化方法建立管制圖，以期望能偵測出多注頭製程的第一類非機遇因素或會干擾單一注頭製程的第二類非機遇因素所造成。 在資料分析方面，本研究分別模擬當注頭間產品品質特性相關且失控的注頭製程不會影響其它注頭製程，及當注頭間產品品質特性具函數關係且失控的注頭製程會影響其它注頭製程等兩種情形下的資料分別建立變數變換法管制圖、Gram-Schmidt垂直化方法管制圖、X-R管制圖及Hotelling’s T2管制圖以比較其偵測效果。資料顯示我們設計的管制圖偵測力較有效。