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題 名 | 非常態性資料之全距管制圖=Ranges Control Chart for Non-Normal Data |
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作 者 | 周昭宇; 鄭炳宏; | 書刊名 | 工業工程學刊 |
卷 期 | 14:4 1997.10[民86.10] |
頁 次 | 頁401-409 |
分類號 | 494.56 |
關鍵詞 | 全距; 管制圖; Burr分配; 非常態性; Range; Control chart; Burr distribution; Non-normality; |
語 文 | 中文(Chinese) |
中文摘要 | 自從1930年以來,統計方法在工業製程管制的應用就備受重視。而在這期間,管 制圖扮演著極重要的角色。當處理一個計量值的品質特性時,一般都是用全距管制圖 (Rchart)來監控製程的變異水準,並以平均數管制圖來監控製程的平均水準。而在這二種 管制圖書,通常均使用三倍標準差為管制上下界限。傳統上,一般都假設測量值的母體分配 為常態。這個假設的真實性,則視測量值的偏態和峰態而定。由中央極限定理可知,只要抽 樣數夠大,則樣本平均數的抽樣分配趨近常態分配;然而,即使母體呈常態分配,全距(range) 的抽樣分配亦非對稱,且測量值往往也不服從常態分配。因此,在母體不為常態的情況下, 使用三倍標準差為管制上下界限之全距管制圖,其偵錯之機率可能會變大。本文嘗試利用Burr 所發展之Burr分配,在非常態資料下,選定全距管制圖的管制上下界限,並比較其與傳統 常態假設下之全距管制圖之差異。 |
英文摘要 | Control charts have played a key role in industrial process control since the 1930's. When dealing with a quality characteristic of numerical measurements, the X-bar and R charts are generally used to control the process mean and variability, respectively. Traditionally, 3-sigma control limits are constructed in both charts. The numerical measurements are usually assumed to be normally distributed. However, this assumption may not be true. Although the sampling distribution of X-bar approaches normality as the sample size is sufficiently large, the sampling distribution of R is always asymmetrical, no matter what the underlying distribution is. Therefore, if the 3-sigma limits are still used in the R chart, the control ability may be reduced. This paper employs the Burr distribution to construct the control limits for an R chart under non-normality and then, compares the non-normal control limits with the traditional 3-sigma limits based on the average run length of an R chart. |
本系統中英文摘要資訊取自各篇刊載內容。