自Duncan在1956年提出管制圖的經濟設計以來,陸續有許多學者提出各種不同型態管制圖的經濟設計,但是在這些文章中,尚無將描點的連串檢定列入考慮者,然而在管制圖中加入描點的連串檢定實有其必要性,加入描點的連串檢定可增加管制圖的偵測能力,但是這種作法頗為麻煩,因此Jaehn(1987)提出了區域管制圖來取代傳統管制圖加上連串檢定的不便,本研究提出X Bar-S Square 區域管制圖的經濟設計以改善一般經濟管制圖未將描點的連串檢定列入考慮的缺點.我們以製程中各項製程和成本資料為因子,對經濟區域管制圖的最佳設計參數值做敏感度分析,以找出製程中的關鍵參數.另外我們應用Saniga(1989)經濟統計管制圖的觀念設計經濟統計區域管制圖.雖然經濟統計區域管制圖所計算出的成本會比經濟區域管制圖稍大,但是在統計表現上卻符合我們的要求.

管制圖之經濟模型首由Duncan(1956)提出，自此之後陸續有學者致力研究經濟管制圖，包括X-bar管制圖、S管制圖等。但R管制圖之經濟設計目前尚無人提出。而在實務上，部份產業可能由於產品過於昂貴，或者產品的製造時間所需甚長，而使得品檢時所抽取的樣本數無法達到25個，這時若採用傳統的管制圖來分析製程，將無法顯示製程真正的狀態。因此本研究首先探討少量連串下X-bar和R管制圖之製作原理，並計算及整理出較完整的少量連串下X-bar和R的管制係數表。接著假設非機遇因素只影響製程運用Banerjee和Rahim(1987)的更新理論方法，建立少量連串情形下的R經濟管制圖。再利用最佳化方法，即可求得最適設計參數值。於是，少量連串情形下的R經濟管制圖得以建立。最後，我們將舉一個例子來說明如何獲得最適設計參數值、決定關鍵參數，以及少量連串情形下R經濟管制圖之建立與應用。

管制圖設計的經濟模式在最近三十年已經被廣泛的研究。本研究利用更新 理論方法(Renewal Theory Approach) 解出兩個非隨機因素下之S 經濟管 制圖。與其它的多重非隨機因素製程模式相比較，我們的模式不僅假設更 合理且以此方法表示平均循環時間(The Expected Cycle Time) 及平均循 環成本(The Expected Cycle Cost)會比擴展Duncan的方法或其它的方法 簡單容易。文中以數值例子說明建立 S 經濟管制圖的過程，並比較 S經 濟管制圖與Shewhart S 管制圖成本的大小及偵錯能力。另外，當製程上 有多重非隨機因素發生時，其成本模式也可容易的以更新理論方法擴展而 得。在實務上，若業者希望以最小成本維持製程之穩定，則可依本文所提 出的方法建立經濟管制圖。

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。

量測誤差是工業製程中影響產品值常見的因素。大的量測誤差會使得產品的量測值偏離實際值，並引導監控者至錯誤的結論。本文提出一種新的捲積管制圖。提出指數分配形式的時間間隔型資料，並加上量測誤差的考量，應用在指數加權移動平均管制圖上。此外，假設量測誤差為常態或是指數分配。研究顯示出，在兩種不同分配的量測誤差之下，管制圖的表現都會顯著的受到影響。 / Measurement error is an important factor in industry that influences the outcome of a process. Large measurement error would cause the observation measure deviate from the true value and consequently lead to a wrong decision. In this project, we propose a convolution control chart. We then design the EWMA ‘time between events’ (TBE) control chart with the measurement error, with the assumption that the observations are exponentially distributed. In addition, we assumed the measurement error follows a normal distribution or an exponential distribution. We showed that, in two cases of the measurement error, the performance of the proposed chart monitoring the process mean is greatly affected.

本論文針對防丟器的剖面進行追蹤分析。防丟器包含發射器及接收器，發射器會發射訊號，接收器會記錄RSSI (Receive Signal Strength Index)與發射點數，其中RSSI表示訊號的強度。在工程理論上，RSSI與距離具有函數關係；然而環境中的干擾及事件發生都會影響此函數關係，特別是事件發生會嚴重地改變此函數關係，因此論文主要目的在於區別事件是否發生。 　　所謂的剖面指的是變數之間的函數關係，而論文中的剖面追蹤是利用管制圖的概念，用管制圖來監控剖面的參數估計值。如果管制圖上的點子出界，則表示事件發生而導致失控。 　　本論文以腳踏車是否被偷為例，嘗試一些實驗後找出顯著影響的因子設計實驗，包含17種腳踏車未被偷之情境與18種腳踏車被偷情境；欲利用未被偷的實驗建立試驗管制圖，而以被偷之情境來追蹤，用以驗證管制圖之有效性。 　　論文中主要透過分析防丟器產生的RSSI與距離的剖面、距離與發射點數的剖面來探討事件是否發生。另外剖面追蹤其實是種事後追蹤的方法，為了能即時追蹤，本論文亦採用預測區間的方式，來追蹤事件是否發生。 　　本論文建議監控距離與發射點數的剖面，因該方法的表現最好，另外建議增加防丟器上能紀錄距離的功能，此方法會更加合適。 　　本論文提出的即時追蹤方式並沒有特別好，因此一個比較好的即時追蹤方法是未來值得研究的方向。 / The device of Babyfinder is designed to detect if an event occurs. The Babyfinder includes transceiver and receiver. The signal strength, Received Signal Strength Indicator (RSSI), generates once there are distances between transceiver and receiver. In wireless communication theory, the relationship between RSSI and distance should be expressed by the model that RSSI = a + b ln (distance) Nevertheless, some circumstance noises and user noises (or common causes), and/or events (special causes) may affect the variation of RSSI. Since the occurrence of events may change the functional relationship of RSSI and distance, to distinguish if the functional relationship is changed by the occurred events is the subject of this study. This study designs some events and noises experiments based on the real noise factors and special events. Two monitoring schemes are proposed to distinguish the occurred events and noise circumstance. One is the profile monitoring scheme, the other is the real time monitoring scheme. The two proposed approaches of profile monitoring scheme are considered to monitor the profile of RSSI and distance and that of distance and the number of transmitting points, respectively. The profile monitoring approach for distance and the number of transmitting points shows better performance. However, the profile monitoring is an after-event tracing approach. It cannot detect the occurred events in time. A better approach of real-time monitoring approach is worth to be proposed in the future study.

To determine the economic design of control charts and the specification limits with minimum cost are two separate issues in previous research areas. In this study, we proposed a method to determine the optimal design parameters of X control charts and the specification limits simultaneously from an economic viewpoint. We also consider two types of X control charts: one is the economic X control chart and the other is the economic statistical X control chart. We obtain the optimal results by minimizing the expected cost per unit time for the-larger-the-better quality characteristic with a Weibull distribution. We consider the asymmetric control limits because of the asymmetric feature of theWeibull distribution. Also, we are considering the difference between monitoring the process by using an economic statistical X control chart and conducting a complete inspection plan. Which way is better, process control or inspection plan? In our data analysis of the two types of X control chart, we find that the optimal expected cost per unit time with complete inspection is lower than without complete inspection. This is because the coefficient of Taguchi’s quadratic loss function we set is too small. And the analysis shows us the significant parameters for the optimal expected cost per unit time and design parameters. At last, in our numerical examples for two different types of X control chart, we find that the performance of the economic X control chart is as good as the economic statistical one. However, we suggest the producer use the economic statistical X control chart with a complete inspection plan to obtain a lower expected cost per unit time and larger power of the control chart.

由近期的研究中發現變動所有參數的管制圖在偵測小幅度偏移時的速度比起傳統的舒華特管制圖來的快，許多文獻也討論到利用調適性管制技術同時監控製程的平均數和變異數。而在這份研究中，為了改善現有管制圖的偵測效率，依序提出了U-V管制圖以及Max-M管制圖來偵測單一製程與兩相依製程的平均數和變異數。採用AATS及ANOS來衡量管制圖的偵測績效，並利用馬可夫鏈推導計算得之。透過兩階段的範例來介紹所提出的管制圖的應用方法並將VP U-V管制圖、VP Max-M管制圖與FP Z(X-bar)-Z(Sx^2)管制圖加以比較。從所研究的數值分析中發現VP Max-M管制圖比另兩種管制圖的表現來的好，再加上只需要單一管制圖在使用上對工程師來說也較為簡便，因此建議Max-M管制圖値得在實務上被使用。 / Recent studies have shown that the variable parameters (VP) charts detect small process shifts faster than the traditional Shewhart charts. There have been many papers discussed adaptive control schemes to monitor process mean and variance simultaneously. In the study, to improve the efficiency and performance of the existing control charts, the U-V control charts and Max-M control charts are respectively proposed to monitor the process mean and variance for a single process and two dependent process steps. The performance of the proposed control charts is measured by using adjusted average time to signal (AATS) and average number of observations to signal (ANOS). The calculation of AATS and ANOS is derived by Markov chain approach. The application of the proposed control charts is illustrated by a numerical example for two dependent process steps, and the performance of VP U-V control charts, VP Max-M control charts and FP Z(X-bar)-Z(Sx^2) control charts is compared. From the results of data analyses, it shows that the VP Max-M control charts have better performance than VP U-V control charts and FP Z(X-bar)-Z(Sx^2) control charts. Furthermore, using a single chart to monitor a process is easier than using two charts for engineers. Hence, Max-M control charts are recommended in real industrial process.

當我們利用Shewhart管制圖(Shewhart control chart)或累積和管制圖(Cumulative-sum chart. CUSUM chart)來偵測製程時,通常假設製品係獨立取自一個服從均數μ和標準差為σ的獨立常態分配的管制下進行。但是若產品特性值呈現自相關時,這類管制圖就可能發生誤導的結果。本文利用時間序列模式來解決具相關變數的管制圖問題。並考慮利用非線性時間序列模式及特別原因管制圖(special-cause control chart)來檢視台灣經濟景氣指標是否處於控制中的狀態。並討論特別原因管制圖的連串長度分佈(run length distribution)。在最後的實例分析中,介紹自動控制的觀念。 / Traditionally, in the quality control process, such as: Shewhart control chart or CUSUM chart, it is assumed that the observation process follows an i.i.d normal distribution. If the assumption for independence fails, that is when the process exhibits type of autocorrelation, we need to find a more reliable decision method. In this paper, we will apply the time series analysis and structure changed concept to slove the serial correlation problem. The idea of automatic control can be applied in the explanation of this nonlinear process. Finally, a time series about the monitoring indicators of Taiwan is discussed in detail as an example.

近年來有許多研究發現，適應性管制圖在偵測製程或產品幅度偏移時的速度比傳統的舒華特管制圖來的快，許多文獻也討論到利用適應性管制技術同時監控製程的平均數和變異數。隨著科技的發達，許多產品在製造上更加精密，現今普遍使用的固定參數管制圖並無法有效率的偵測出製程失控，導致巨大的成本損失。為了改善現有管制圖的偵測效率與有效控制製程失控下的損失，我們提出了三種適應性加權損失管制圖，包括變動抽樣間隔(VSI)、變動樣本數與抽樣間隔(VSI)、變動管制參數(VP)來偵測單一製程與兩相依製程的平均數和變異數。採用製程發生變動後到管制圖偵測出異常訊息所需的平均時間(AATS)與所需的總觀測數(ANOS)來衡量管制圖的偵測績效，並利用馬可夫鏈推導計算得之。從數值分析中發現，適應性加權損失管制圖在「偵測小偏移幅度時的偵測效率」與「成本的控制」明顯比傳統管制圖表現的更好，再加上每一個製程僅需採用單一管制圖，對使用者也較為簡便並且容易理解，因此適應性加權損失管制圖在實務上是值得被推薦使用的。 / Recent research has shown that control charts with adaptive features detect process shifts faster than traditional Shewhart charts. In this article, we propose three kinds of adaptive weighted loss (WL) control charts, variable sampling intervals (VSI) WL control charts , variable sample sizes and sampling intervals (VSSI) WL control charts and variable parameters (VP) WL control charts, to monitor the target and variance on a single process step and two dependent process steps simultaneously. These adaptive WL control charts may effectively distinguish which process step is out-of-control. We use the Markov chain approach to calculate the adjusted average time to signal (AATS) and average number of observations to signal (ANOS) in order to measure the performance of the proposed control charts. From the numerical examples and data analyses, we find the adaptive WL control charts have better detection abilities and performance than fixed parameters (FP) WL control charts and FP Z(X-bar)-Z(Sx^2) and Z(e-bar)-Z(Se^2) control charts. We also proposed the optimal adaptive WL control charts using an optimization technique to minimize AATS when users cannot specify the values of the variable parameters. In addition, we discuss the impact of misusing weighted loss of outgoing quality control chart. In conclusion, using a single chart to monitor a process is inherently easier than using two charts. The WL control charts are easy to understand for the users, and have better performance and detection abilities than the other charts, thus, we recommend the use of WL control charts in the real industrial process.