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ù ] ú �¤T = m§�ð ñ Ð � o p Cpm�}å F Ù
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[ \ X ê �[ \ � ¼ Ï p ø �\ n �É Ê � � o p Cpk� Cpm� � ú �#ío p Cpmk%÷
Ï p ø T<K ² � ¿ ù ] ú �¤T = m§�[ \ Ð � o p Cpmk�}å F Ù
{ }( )223
,min
T
LSLUSLC pmk
−+
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µσ
µµ (4)
�á â [ \ Ð � o p = 7 Kane [6] ; � Cp > f = ô �#í Cp o p > α�β�«Chou<ï[3]#í Ĉp'Ĉpu'Ĉpl � Ĉpk� � � n ô �'� 4 � � n ô �«Boyles
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Ĉp'Ĉpk'Ĉpm� Ĉpmk o p >ü ý ø qX ê �«Johnson [10]�ò ó ô � � Ü Ý Cpm�#
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í Cpm> � � 0 ì q � � � %
�[ \ Ð � o p ���7 Montgomery [11] ; � � � ù �õ ö + [ \ Ð � o p Cp>
� � 0 ì � � �� � 0 ì ø � "[ \ Ð � «Chou <ï[2]#í Ĉp'Ĉpk x Ì � 5 ø � }
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2
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# $ 2%, - . / 0 1 2level of significance3α = 0.05
# $ 3%�4 4-1 5 6 +7 8 9 : ; "
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X S PC aC
11.92 0.63 2.11 0.73
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11.0 11.5 11.8 12.0 12.2
12.8 11.6 11.8 12 12.2
12.8 11.6 11.9 13 12.2
12.3 12.4 11.9 12.0 12.4
11.3 11.6 11.9 12.2 12.4
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252015105Subgroup 0
12.4
12.3
12.2
12.1
12.0
11.9
11.8
11.7
Sam
ple
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n
Mean=12.03
UCL=12.33
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1.0
0.9
0.8
0.7
0.6
0.5
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ple
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ev
S=0.7192
UCL=0.9377
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X S PC aC 12.03 0.48 2.79 0.76
��� =PC 2.79 � � � � � � 2.40�� =aC 0.76 � � � � � � 0.78�� �� � �� � �
! " # $ % & ' ( ) * + , - " # . % & ' / 0 1 2 3 + , 4
56 7 8 9 : � # ; < �5= > ? 50 @ A B � 4-34C D E �F G H � " # I J K
L M N O P �Q " # R S � T U V W X Y Z 4-8 [ Z 4-9 \ Z 4-10]�^ _ ` " # & ' a
b 4 � 4-3c H � d e f g < ��
11.4 11.9 12.3 12.3 12.6
11.5 11.9 12.2 12.3 12.6
11.6 11.8 12.2 12.3 12.8
11.7 11.9 12.2 12.4 12.7
11.6 12.0 12.2 12.5 12.7
11.7 12.0 12.5 12.5 12.9
11.7 12.4 12.0 12.5 12.9
11.9 12.2 12.5 12.6 13.1
11.9 12.2 12.4 12.6 13.1
11.9 12.1 12.4 12.6 12.2
252015105Subgroup 0
12.5
12.4
12.3
12.2
12.1
12.0
Sam
ple�
Mea
n
Mean=12.25
UCL=12.47
LCL=12.04
0.7
0.6
0.5
0.4
0.3
Sam
ple�
StD
ev
S=0.4958
UCL=0.6465
LCL=0.3452
![Page 13: · 39 55 ˘ ©2007 National Kaohsiung University of Applied Sciences, ISSN 1813-3851 E-mail : ghlin@cc.kuas.edu.tw ˘ˇˆ˙˝˛ ˚˜ !"](https://reader030.vdocuments.pub/reader030/viewer/2022021512/5af19ac07f8b9ac2468f87fb/html5/thumbnails/13.jpg)
���������� ��� 51
� 4-8� � � � � � � � � � �
� 4-9� � � � � � � �� � �
17161514131211109
USLLSL
12.912.411.911.4
.999
.99
.95
.80
.50
.20
.05
.01
.001
Pro
babi
lity
Sample�3
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� � � � � � � 52
� 4-10� � � � � � � � SX − Chart
���������� �
X S PC aC
12.30 0.44 3.03 0.83
��� =PC 3.03 � � � � � � 2.40� =aC 0.83 � � � � � � 0.78�� � � � � � � � �
! " # $ % & ' (
5.�����
5.1 ����
� ) * + , - . / 0 1 2 3 � 4 5 6 4 7 (8 9 : ; � ) * + , � < = > �? @
A B � 5 6 C D (E F G H Chou [3]I Lin [4] � J K �LM N O �J P �Q R � . S T U V
� � � � ) * ! " W O X (�Y P ���Z [ \ � ] ^ _ ` ^ ) * � � a b @ c
d e f �g " h ; � ! " W O �? @ i j k � l m (n o p q r s t u v w x y z { | L
� } P h ; l m �B ~ � � � � � � � � � � I� � \ E � � � (
5.2 � � ��� �
E F � � � V� � � V� � � � � � � k h ; ! " W O �� p q r s t u v � g � �
� �� � �Q R � � � � W O � �e ��4 � � ) . � � � [ � k � � ) * � �
j � ? @ ¡ � � ¢ - C £ + ¤ ¥ ¦ § (
252015105Subgroup 0
12.6
12.5
12.4
12.3
12.2
12.1
Sam
ple�
Mea
n
Mean=12.34
UCL=12.54
LCL=12.15
0.6
0.5
0.4
0.3
Sam
ple�
StD
ev
S=0.4521
UCL=0.5894
LCL=0.3147
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���������� ��� 53
� � �
[1] Juran, J. M., Juran’s Quality Control Handbook, McGraw-Hill, New York.
[2] Pearn, W. L., Lin, G.H. and Chen, K.S., 1, “Distributional and nferential Properties of the Process precision and Process accuracy indices, ”Communications in Statistices:Theory and Methods, Vol. 27, No.4, 1998, pp. 985-1000.
[3] Chou, Y. M., Owen, D. B., S.A, “Lower confidence Limits on Process Capability Indices,” Journal of Quality Technology, Vol. 22, No.3, 1990, pp. 223-229.
[4] LIn, G.H., “A decision-making procedure on process centering: a lower bound of the estimated accuracy index,” Journal of Statistcs & Management System, Vol.9, No.1, 2006, pp. 205-224.
[5] ¨ © 4 ª « ¬ �NAND Flash � � ® ¯ ° ± k � � ² ³ ' ´ PC µ f � ¶ · � ¹ º »
² ¼ �2007�8 ½ (
[6] Kane, V. E., “Process Capability Indices,” Journal of Quality Technology, Vol.18, No.1, 1986, pp. 41-52.
[7] Chan, L. K., Cheng, S. W., and Spiring, F. A., “A New Measure of Process apability: Cpm,” Journal of Quality Technology, Vol.20, No.3, 1988, pp.162-175.
[8] Pearn, W. L., Kotz, S., and Johnson, N. L., “Distribution and inferential Properties of Process Capability Indices,” Journal of Quality Technology, Vol. 24, No.4, 1992, pp. 216-231.
[9] Boyles, R. A., “Process capability with asymmetric tolerances,” Comm-unications in Statistics: Computation & Simulation, Vol.23, No.3, 1994, pp. 615-643.
[10] Johnson, T., “The relationship of Cpm to squared error loss,” Journal of Quality Technogy, Vol.24, No.4, 1992, pp. 211-215.
[11] ¾ ¿ À Á ÂMontgomery. Douglas. CÃÄ Å �Æ Ç È ÂÉ d Ã�� � ¡ Ê �Ë Ì �Í Î Ï Ð (
[12] Chou, Y. M., Polansky, A. M., and Mason, R. L., “Transforming on-normal data to normality in statistical process control,” Journal of Quality Technology, Vol.30, No.2, 1998, pp. 133-141.
[13] Pearn, W. L., Shu, M. H., Hsu, B. M., “Lower confidence bounds for Cpu and Cpl based on multiple samples with application to production yield assurance,” international joural of production research, Vol.42, No.12, 2004, pp. 2339-2356.
[14] Shu, M. H., “Manufacturing capability assurance for product with Multiple charcterisics: A case study applied to low dropout voltage regulator,” international joural of industrial engineering, Vol.13, No.1, 2006, pp. 41-50.
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� � � � � � � 54
� �
�������� PC � � � 95%� � � � PC � � � � � �
n
0C 10 20 30 40 50 60 70 80 90 100
1.0 1.65 1.37 1.28 1.23 1.20 1.18 1.16 1.15 1.14 1.13
1.1 1.81 1.51 1.41 1.36 1.32 1.30 1.28 1.27 1.26 1.25
1.2 1.97 1.64 1.54 1.48 1.44 1.42 1.40 1.38 1.37 1.36
1.3 2.14 1.78 1.66 1.60 1.56 1.53 1.51 1.50 1.48 1.47
1.4 2.30 1.92 1.79 1.72 1.68 1.65 1.63 1.61 1.60 1.59
1.5 2.47 2.06 1.92 1.85 1.80 1.77 1.75 1.73 1.71 1.70
1.6 2.63 2.19 2.05 1.97 1.92 1.89 1.86 1.84 1.83 1.81
1.7 2.80 2.33 2.18 2.09 2.04 2.01 1.98 1.96 1.94 1.93
1.8 2.96 2.47 2.30 2.22 2.16 2.12 2.10 2.07 2.06 2.04
1.9 3.13 2.60 2.43 2.34 2.28 2.24 2.21 2.19 2.17 2.15
2.0 3.29 2.74 2.56 2.46 2.40 2.36 2.33 2.30 2.28 2.27
2.1 3.45 2.88 2.69 2.59 2.52 2.48 2.45 2.42 2.40 2.38
2.2 3.62 3.01 2.82 2.71 2.64 2.60 2.56 2.53 2.51 2.49
2.3 3.78 3.15 2.94 2.83 2.76 2.72 2.68 2.65 2.63 2.61
2.4 3.95 3.29 3.07 2.96 2.88 2.83 2.79 2.77 2.74 2.72
2.5 4.11 3.43 3.20 3.08 3.00 2.95 2.91 2.88 2.85 2.83
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���������� ��� 55
��� ����� aC � � � =1C 0.75 � Ĉa � � � � �
σµ m−
n 1-α
0.25 0.50 0.75 1.00 1.25
0.90 0.95 0.93 0.88 0.85 0.83
0.95 0.97 0.97 0.92 0.88 0.85 10
0.99 0.99 0.99 0.98 0.93 0.90
0.90 0.95 0.89 0.85 0.82 0.81
0.95 0.97 0.93 0.87 0.84 0.82 20
0.99 0.99 0.98 0.92 0.88 0.85
0.90 0.94 0.87 0.83 0.81 0.80
0.95 0.97 0.90 0.85 0.83 0.81 30
0.99 0.99 0.96 0.89 0.86 0.83
0.90 0.93 0.85 0.82 0.80 0.79
0.95 0.97 0.88 0.84 0.82 0.80 40
0.99 0.99 0.93 0.87 0.84 0.82
0.90 0.92 0.84 0.81 0.80 0.79
0.95 0.96 0.87 0.83 0.81 0.80 50
0.99 0.99 0.91 0.86 0.83 0.82
0.90 0.91 0.83 0.81 0.79 0.78
0.95 0.95 0.86 0.82 0.80 0.79 60
0.99 0.99 0.90 0.85 0.83 0.81
0.90 0.90 0.83 0.80 0.79 0.78
0.95 0.94 0.85 0.82 0.80 0.79 70
0.99 0.99 0.89 0.84 0.82 0.81
0.90 0.89 0.82 0.80 0.79 0.78
0.95 0.93 0.84 0.81 0.80 0.79 80
0.99 0.98 0.88 0.84 0.82 0.80
0.90 0.88 0.82 0.80 0.78 0.78
0.95 0.92 0.84 0.81 0.79 0.78 90
0.99 0.98 0.87 0.83 0.81 0.80
0.90 0.88 0.81 0.79 0.78 0.78
0.95 0.91 0.83 0.80 0.79 0.78 100
0.99 0.97 0.87 0.83 0.81 0.80