在偏斜常態資料下的允收管制圖設計

Design of Acceptance Control Chart for Skew Normal Data

江俊佑(Jyun-You Chiang)

指導教授 ： 蔡宗儒

淡江大學/管理學院/統計學系碩士班/碩士(2006年)

https://doi.org/10.6846/TKU.2006.00326

摘要

在計量管制圖中，最廣為各界使用的就是X-bar管制圖和$R$管制圖，X-bar管制圖管制製程平均數mu是否維持在一給定的水準mu_0上，當製造商生產的紀錄非常良好時，我們可以允許其製程平均可以在一個小範圍(mu_L,mu_U)中偏移，而不至於產生過多的不良品，因此，可將統計假設H_0:mu=mu_0轉換成H_0:mu_L<=mu<=mu_U，結合規格界限、生產者風險及消費者風險，發展出另一個新的管制圖，此即為允收管制圖。傳統的允收管制圖只能適用在常態分配資料下，如果應用在非常態資料中，將會高估型一或型二誤差。Chou et al. (2005)利用Burr分配設計出適用於非常態資料的允收管制圖，不過此一管制圖在資料呈對稱分配時，無法退化到一般常態分配下之允收管制圖，進而限制其實用性。本論文利用Skew
Normal分配設計允收管制圖， 因為Skew Normal分配可以完全退化到常態分配，所以Skew Normal允收管制圖也適用於常態分配資料的平均數監控。

關鍵字

計量管制圖 ； 允收管制圖 ； 型一誤差 ； 型二I誤差

並列摘要

In variable control charts, the X-bar and R charts are widely used to monitor the process mean and variability of the quality characteristic. When manufacturer's record was very well, we can accept the process mean shifts between a predetermined interval (mu_L,mu_U), and will not produce many nonconforming units. In this design, an acceptance control chart can be constructed by combining with the specifications, producer's risk and consumer's risk. Conventional acceptance control chart is designed to monitor the process mean of normal data. But it always results in a higher probabilities of type I or type II errors when the chart is used to monitor the non-normal data. Chou et al. (2005)developed an acceptance control chart based on the Burr distribution and they used it to monitor the process mean of non-normal data. The main disadvantage of Burr acceptance control chart is that it can not reduce to the conventional acceptance control chart when it is used to monitor symmetric data. The thesis develops a new acceptance control chart based on the Skew Normal distribution to overcome the problem. The Skew Normal acceptance control chart can be used to monitor the process mean whenever the process data is symmetric and it can reduce to the conventional acceptance control chart when the data is symmetric.

並列關鍵字

Variable control charts ； Acceptance control chart ； Type I error ； Type II error

參考文獻

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