指數加權移動平均與修華特單一觀測值合併管制圖偵測製程平均數與標準差

Design of Single-Featured EWMA-X (SFEWMA-X) Control Chart Using Individual Observations for Detecting Process Mean Shifts and Standard Deviation Changes

劉季旋(Chi-Shuan Liu)

指導教授 ： 田方治

國立臺北科技大學/管理學院/工商管理研究所/博士(2011年)

https://doi.org/10.6841/NTUT.2011.00492

摘要

管制圖是一個重要的製程監控與品質改善的工具。過去已經提出幾種能夠偵測製程參數的大變動與小變動的混合型管制圖，但是這些管制圖需要計算與偵測二個統計量，並且在管制圖上需使用二組管制界限。這篇研究提出一個使用單一觀測值的管制圖，稱作指數加權移動平均與修華特單一觀測值合併管制圖，用來偵測製程平均數的大小變動與標準差變動（簡稱SFEWMA-X管制圖）。這篇研究提出的方法是透過簡單的參數轉換，使指數加權平均數與觀測值有相同的管制界限，並且在SFEWMA-X管制圖中只使用一個統計量。這篇研究示範SFEWMA-X管制圖的使用，也提出使用流程與參數表，方便使用者查詢。管制圖偵測力的比較顯示提出的方法在偵測製程參數大小變動時，SFEWMA-X管制圖比單一管制圖強。這篇研究延伸SFEWMA-X管制圖的使用成為SFEWMA-X診斷圖，並且以範例說明SFEWMA-X 診斷圖的使用方式。

關鍵字

修華特管制圖 ； 製程變動 ； 指數加權移動平均 ； 偵測力 ； 診斷圖

並列摘要

Quality control chart is an important tool for process monitoring and quality improvement. Several combined control charts have been proposed to enhance the detection ability in detecting small and large process parameter changes simultaneously. However, these control charts require calculating and monitoring two statistics along with two sets of control limits. This study propose a new control chart using individual observations, called a single featured EWMA-X (SFEWMA-X) control chart, to monitor both small and large process mean shifts and process standard deviation changes. The SFEWMA-X control chart is designed by a simple variable transformation that rescales the statistic of EWMA into the range of Shewhart-X so that only one statistic is required to be monitored. A pilot experiment demonstrates the detection ability of the proposed scheme. To facilitate the use of the proposed method on the shop floor, this study proposed the algorithm for deriving optimal chart design tables and implementing procedures. A comparison of the detection ability shows that the proposed control chart is superior to individual control chart when monitoring both small and large process parameter change. A SFEWMA-X diagnosis chart was extended from SFEWMA-X control chart. An example was given to show the application of the proposed diagnosis chart.

並列關鍵字

Shewhart control chart ； process shifts ； EWMA ； detection power ； diagnosis chart

參考文獻

1. S. L. Albin, L. Kang, and G. Shea, “An X and EWMA chart for individual observations,” Journal of Quality Technology, vol. 29, 1997. pp.41-48.

2. R. W. Amin, and R. A. Ethridge, “A note on individual and moving range control charts,” Journal of Quality Technology, vol. 30, 1998, pp.70–74.

3. R. W. Amin, H. Wolff, W. Besenfelder and R. Baxley Jr. “EWMA control charts for the smallest and largest observations,” Journal of Quality Technology, vol. 31, 1999, pp. 189-206.

4. F. Aparisi, and J. C. Garc-.a-D-.az, “Optimization of univariate and multivariate exponentially weighted moving-average control charts using genetic algorithms,” Computers & Operations Research, vol. 31, 2004, pp.1437-1454.

5. A. F. Bissel, "CUSUM techniques for quality control," Applied Statistics, vol. 18, 1969, pp.1-30.