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。

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.

目錄

第一章	緒論	1
1.1	研究背景	1
1.2	研究動機與目的	2
1.3	論文架構	2
第二章	文獻探討與相關研究3
2.1	X-bar管制圖與允收管制圖的文獻探討	3
2.2	各種X-bar管制圖介紹	5
2.2.1	Shewhart X-bar管制圖	5
2.2.2	WV X-bar管制圖	5
2.2.3	WSD X-bar管制圖	8
2.2.4	SC X-bar管制圖	12
2.2.5	Burr X-bar管制圖	16
2.3	相關的允收管制圖	20
2.3.1	常態允收管制圖	20
2.3.2	Burr允收管制圖	25
第三章	Skew Normal X-bar管制圖及允收管制圖	34
3.1	Skew Normal分配	34
3.2	SN X-bar管制圖	37
3.3	SN允收管制圖	38
第四章	模擬研究	46
第五章	實例	54
第六章	結論	62
參考文獻   	63

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(c)f(x)ïTUV	ÍIçp:d:f:= . . . . . . . . . . . . . . . . 9
2.2 f(x)WXYV:(a)f(x)7TUÍWX#4=(b)f(x)ïTUÍW
X#4=(c)Z[Ö3&WXÖ3= . . . . . . . . . . . . . . . . . . 10
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N(¹; ¾2
n ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1  Ž¸ïÍSNÖ3(a)SN(0)=(b)SN(5)=(c)SN(-5)= . . . . . . . . 36
4.1 þxU^Xòô_8`ab(m=30) . . . . . . . . . . . . . . . 51
4.2 þxU^Xòô_8`ab(m=50) . . . . . . . . . . . . . . . 52
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5.2 deíîh¶ô(a)SNFnormal32=(b)250cbootstrap
i

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