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題 名 | 非常態性資料下中位數管制圖之研究=A Study on the Median Control Chart Under Non-Normality |
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作 者 | 周昭宇; 蕭武夫; | 書刊名 | 技術學刊 |
卷 期 | 13:4 1998.12[民87.12] |
頁 次 | 頁631-640 |
分類號 | 494.56 |
關鍵詞 | 管制圖; 中位數; 非常態性; Burr分配; Control chart; Median; Non-normality; Burr distribution; |
語 文 | 中文(Chinese) |
中文摘要 | 自從1924年Shewhart博士提出統計製程管制圖後,管制圖已被廣泛地應用於工業 製程管制。本文以 Burr 分配為樣本中位數的抽樣分配,發展中位數管制圖在非常態性資料 下之管制上下界限。然後再以平均連串長度( average run length )為基準,與傳統三倍 標準差之中位數管制圖作比較。 研究結果顯示:中位數抽樣分配的偏態係數大於 0.2 或小 於 -0.2 或峰態係數大於 3.8 時,若仍使用傳統三倍標準差之管制圖, 將致使誤警率增加 而提高生產成本。因此,建議品管工程師在建構中位數管制圖時,應對樣本中位數抽樣分配 之偏態係數及峰態係數作一查核。當發現有任一係數偏離常態時,應即對管制界限作適度之 修正,俾使管制圖發揮最大之製程監控效果。 |
英文摘要 | In 1924, Dr. Shewhart presented the use of control charts. Since then, control charting technique has been widely applied in industrial process control. In this article, we first demonstrate the applications of the generalized Burr distribution in determining the control limits for a median chart under non-normal measurements. Then, the proposed control limits are compared with the 3-sigma control limits based on the average run length of a median chart. The comparison results show that when the skewness coefficient of the sampling distribution of the median is greater than 0.2 or less than -0.2, or the kurtosis coefficient is greater than 3.8, the production costs will seriously increase if the control chart with 3-sigma limits is still used. Therefore, it is suggested that when establishing a median control chart, quality control engineers should examine the skewness and kurtosis of the sampling distribution of the median. If any one of these coefficients departs from normality, the engineers should properly modify the control limits such that the control charts can be of better effects in monitoring process. |
本系統中英文摘要資訊取自各篇刊載內容。