管制圖為統計製程管制(SPC)中經常被使用的品質管制方法，管制圖透過統計概念來監控製程，能夠偵測到製程的異常，以便監控者在品質發生嚴重問題之前，就能夠先一步找出製程異常的原因。然而在品質特性的量測上，許多製程以外的不確定性會發生，例如量測工具的誤差、作業員主觀判定的過程等，這些不確定性的資訊透過模糊理論，可以使用模糊數來表示品質特性，此表示方法更能夠包含這些模糊現象與資訊的存在。過去已有許多學者以模糊數的計量值品質特性為對象來發展模糊管制圖，但目前確尚未有文獻以區分隨機性與模糊性的概念來建構管制圖，因此，本研究參考過去文獻中模糊管制圖的方法，來發展能夠區分隨機性與模糊性的模糊管制圖。

本研究首先以解模糊化的概念，對模糊品質特性計算代表隨機性之值；在研究中提出重心法與平均最可能值法做為計算代表隨機性之值的方法，而這些代表隨機性之值透過使傳統管制圖的使用，用來監控製程的隨機性是否異常。接著再修正以往模糊數的左、右展幅計算方法，並將修正過後的左、右展幅的值做整合，以整合後的值代表模糊數之值，而這些代表模糊性之值透過使傳統管制圖的使用，用來監控製程的模糊性是否異常。透過二種對於不同的不確定性來源的管制圖，使得監控者可以在製程發生異常時，區分造成異常的來源是來自於製程中的機遇原因，或是品質量測上的人為主觀因素等不確定性的原因。

The control chart approach is a frequently used method for Statistical Process Control (SPC). By monitoring the manufacturing process using statistical concepts, the control chart is capable of detecting abnormalities during the process, allowing the supervisor to react and locate the causes of these before severe quality defects occur. However, with regard to the measuring of quality characteristics, there remain many uncertainties beyond the manufacturing process, such as the accuracy of the measurement tools or the subjective judgment of the operator. These uncertainties may be solved through the application of fuzzy theory, which represents quality characteristics using fuzzy numbers. This representation can include the information and phenomenon of fuzziness. In the past, many scholars have used fuzzy numbers derived from quantitative quality characteristics to develop fuzzy control charts, but no control charts that separate randomness and fuzziness have been documented in the literature. Therefore, this study takes uses various methods of developing fuzzy control charts from the literature and designs a randomness-fuzziness separated fuzzy control chart.

This study begins by calculating the random values of fuzzy quality characteristics using the concept of defuzzification, and specifically uses the center of gravity and mean of maxima methods to calculate the representational values of randomness. Through the use of traditional control charts, these values are applied to monitor the randomness of the manufacturing process. The method used to calculate method the left and right spreads is improved, and then the revised values of the left and right spreads are combined to represent a fuzzy number. Again, using traditional control charts, the fuzzy numbers are used monitor the fuzziness of the manufacturing process. By using these two control charts to identify two different sources of uncertainties, the supervisor is able to distinguish between abnormalities in the manufacturing process that come from chance causes or the bias of quality measurements.

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