掌控圖與製程績效的關聯之研究

Pre-control Chart and Process Performance Measurement

陳文魁(Wen-Kuei Chen) ； 黃耀琮(Yao-Tsung Huang)

《品質學報》 14卷1期 (2007/03) Pp. 45-56

摘要

除了以製程能力界定品管績效之短期指標和長期性指標之外，本文尚將它們連結至六標準差式的衡量基準。六標準差制度應用到實務方面時，可以系統性協助挖掘出作業過程中的各種可能差池，導引製造業者或提供服務者追求「零失誤」的境界。製程能力是從製造或過程根源來量化品管效能的主要指標，所以它能夠具體導引零失誤的追求，使企業的過程或工程績效因獲量化而得以恰當的全面經營。
(平均值)X-R管制圖是最為常用的SPC工具，惟當製程能力甚高時，製程標準差會是相對的微小，可是在管制圖上的表現卻未必展現比較穩定。顯然，製程能力業已達臻卓越境界時，使用(平均值)X-R管制圖監視製程會有畫蛇添足之憾。因此，以符合工程規格程度來掌控製程的圖形工具，的確能夠迎合現代工業界的統計品管需求。以維持高製程能力為宗旨，製程掌控圖(Pre-control chart)正是這樣的圖形技術，它即時揭露樣本圖點之色訊，以便製造現場掌控其製程的能力。
對照於六標準差制度的績效衡量，本文闡釋製程能力的長期指標與短期指標之內涵。爲便利掌控圖之軟體開發，本文特別將規格上界和規格下界固定為±3刻度，提供公式由製程能力將標準差轉換成為刻度數，以建立上紅、上黃、上綠、下綠、下黃和下紅等六區域的制式化機率公式；進一步，本文再建立色訊的α風險和β風險的制式化公式。特別的，本文使用微軟公司EXCEL之內建函數和自訂函數以便逕自計算機率數值，譬如全距數之累積機率、期望值等。

關鍵字

管制圖 ； 掌控圖 ； 製程能力 ； 製程績效 ； 長期指標 ； 短期指標

並列摘要

The employment of six-sigma system can thoroughly support error mining in operations, which may lead the product manufacturer or service provider to the way toward pursuing for zero defects. As separating process performance to precision and accuracy, we acquire a clear quantification way to manage both effectiveness and efficiency of the quality management system.
Xbar-R chart has been widely used in manufacturing industries. Once process becomes steadier, its standard deviation goes smaller. However, at the same time, the performance in Xbar-R chart will not demonstrate much stability. Obviously, as a process has been upgraded, the shop floor people might have endured frustrations along with using Xbar-R chart. Thus, graphical techniques, dealing with process capability directly, can meet fully the manufacturing needs controlling engineering quality.
In order to equating the performance measurement of six-sigma system, this article interprets process capability with two ways as the short term and long term. For the convenience of graphics developing and performance analysis, we regulate pre-control chart with upper specification limit and lower specification limit as scale±3 units. We transform Cpk and/or σ to their corresponding scale units, and every measurement is re-calculated for its frame unit prior to plot. And probability formulae for following six regions of this frame are then established with respect to new scale: ”upper red”, ”upper yellow”, ”upper green”, ”lower green”, ”lower yellow”, and ”lower red”. This article also builds formulae for calculating Type-I error and Type-II error of precontrol chart. In particular, this article contributes by adopting/providing both built-in functions and user-defined functions of Microsoft Excel, such as functions for cumulative probability of range and expected value of range.

並列關鍵字

Control chart ； Pre-control chart ； Process capability ； Process performance ； Long term indices and short term indices

參考文獻

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