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& ' ) (2 3 ) � � * + (bit) � � * + (byte) , - . / (mil)
1999 220 256M 32M 214.84280.1
2000 150 512M 64M 222.44333.1
2001 120 1G 128M 204.34316.1
2002 90 2G 256M 312.24402.0
2003 70 4G 512M 314.84401.4
2004 60 8G 1G 311.74429.4
2005 55 16G 2G 405.24625.1
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2. � � �
2.1 ������
[ \ Ð � o p �z Ó �k Ô 7 �¿ È F ÕÖ È × Ø ÙÚ z F Û o p �Ü Ý «Ú ÞF ß
à á â ã ä o p = qÚ Õ[ \ Ð � o p ���%
[ \ Ð � o p �Û o p �Ü Ý 7 Juran [1]}å æ Ú z ç [ \ Ð � o p PC ��á â �
�² � �è é [ \ X ê �á � %ë }å F Ù
PC = σ6
LSLUSL − (1)
ë ] USL Ø ² � �ì �LSL Ø ² � 0 ì �σ Ø [ \ p r Å %Kane [6]#í[ \ Ð � o p PkC Ù
PkC =
−−
σµ
σµ
33min
LSLUSL� (2)
ë ] µ F [ \ ] î %
Chan <ï[7] l ð ñ ò ó ô ��õ ö #íæ ð ñ Ð � o p Cpm%÷Ï p ø T <K ² � ¿
ù ] ú �¤T = m§�ð ñ Ð � o p Cpm�}å F Ù
( ) ( )2222 66 T
d
T
LSLUSLC pm
−+=
−+
−=
µσµσ (3)
ë ] �σ2+(µ-T)2 = E(X-T)2 � û ð ñ ò ó ô ��ü ý ø %
Pearn<ï[8] þ � ¶ o p Cpk Ð � �[ \ � � � ¼ ² � ] î �\ n �o p Cpm Ð � �í
[ \ 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
−+
−−=
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
[9] ; �ò ó ô �Ü Ý Cpm t u P q � � � ��#í Cpm � _ ¦ «Pearn <ï[8]#í
Ĉp'Ĉpk'Ĉpm� Ĉpmk o p >ü ý ø qX ê �«Johnson [10]�ò ó ô � � Ü Ý Cpm�#
����� � � 42
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 � }
[ \ Ø � � u �+ � r «Chou <ï[12] l � u [ \ ^ _ �7 � � � � & ! " # F � «Lin
[4]#í Ĉa x Ì � 5 ø �� }[ \ Ø � � $ �+ � r «Pearn<ï[13]#í¢ � % j 0 Cpu'
Cpl� � � ¿ ù 0 ì & ' � �� � «Shu [14] þ �( % Ä Å ��� Spk'Cpu'Cplq Ca�
� � ¿ ù 0 ì �#í¢ �[ \ Ð � È ) ¦ �l ¦ ± �7 �� * + ��� 3 �[ \ Ð � %
2.2 Cp ������
: � , - � �� Cp t u . ��}å ¥ 0 Ù
sLSLUSL
C p 6)(ˆ −
=
ë ]
1
)(1
2
−
−
=
∑=
n
XXs
n
ii
n
XX
n
ii∑
==
1
/ C F Cp � 100(1 –0) 1 � � ¿ ù �0 ì 2
ˆ)1(
−
P
P
C
Cn 2 3 C 7 È 4 � 5 J n F 1−n %
( ) { }222 ˆ)1()ˆ)(1( PPPPr CCnCCnPCCP −≥−=≥
{ }2221
ˆ)1( Pn CCnP −≥=−χ (5)
��2
1,122 ˆ)1(
−−=− nPCCn αχ
1ˆ
21,1
−=
−−
nCC n
Pαχ
21,1
1ˆ−−
−=
nP
nCC
αχ (6)
���������� ��� 43
Chou [3]����(6) � � � � � � � � � � �� � � � � � Cp � � C0 � � �
� � n � � � � � ! Ĉp � " 21,10 1ˆ−−
−≥ nP nCC αχ # $ % � & ' � � � �() *2
1,10 1ˆ−−
−≥ nP nCC αχ + � , - . 100(1/α)% � 0 1 $ � � � � � � � �� 2 ��3 �
� 4 5 6Matlab6.5 78� ! Ĉp 9 : ; < � � = > ? @ � � � & ' � A B � � � C D
6E F G H I 8�
2.3 Ca ������
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d
mXCa
−−= 1ˆ (7)
S T nXXn
ii
= ∑=1
� � T 1 � � � � T 1 µ � U �P � � � Ĉa � P � �V W X @ R
−−=
σ
mXn
CnC
P
a3
11ˆ (8)
"� � Y Z [ \ ] � ^ 5 N(µ, σ2) T � � � � _ � � # aC � ` a � b � W c C d � [2]R
( ) ( )( )
−−+−
−−=
2
2
11
12
exp11
cosh2
6)(aa
PC
xCxn
Cxfδδ
π (9)
ST 1≤<∞− x � 22 )]1([9]/)[( aP CCnmn −=−= σµδ
� � � � YeYf (µ, σ2)�^ 5 � � � � _ g � mX − �\ ] �f (µ-m, σ2/n)
h i22 ]/)[()]1/()ˆ1[( δδ mXnCC aa −=−− eY 2χ (1, δ)�j I � k T1 l m n \ ] �N o �
� 1�_ k T1 l E 322 )]1([9]/)[( aP CCnmn −=−= σµδ �
h i aC c δδχ ),1()1(1 2aC−− � \ ] � aC �� ` a � b 3 W c X @ R
∑∞
=
+Γ−
−−−
−−
+Γ−=0
22
)1()2/exp()2/(
11
2exp
11
2)]21([)1(2
)(k
k
a
k
aa kCx
Cx
kCxf
δδδδδ
ST 1≤<∞− x �
�p � � � � � q � � � r s t u q �v K W w x c y �n � � ; z q � { | P
����� � � 44
� � �y }~ � Z [ \ ] �� � y �� C � aC � )%1(100 α− 0 � � � y }R
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−−≥
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1
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a
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),1()ˆ1(1 2 δχ
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� � � � EX� � C� � 7 = r s E$� � * � � � � Chou [3]X Lin [4]v� � $G � � � h
i j k l m n o p q � � �� � � � � � $: ; �� � 4 5 a b Cp X aC # � � 4 5 � � $
� Ĉp X aC # � ` � + � $� � o p q � � � � � � $6 � ` � � � � � �
� � 1�� ` � � � � � � 0C $� � � � � � 1C �
� � 2�� � Y Z [ � Clevel of significanceEα�
� � 3�� ¡ ¢ £ ¤ �¥ ¦ �
� � 4�§ � ¨ �¡ ¢ £ ¤ ¥ ¦ + , - Ĉp X Ĉa�
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! " # $ �% EPOXY & ' � � ( ) * + � � 9mil , - �. / � � 0 1 �� � 2 3 4 5 6
4mil78 9 : �� ; < = > � � � ? @ A B �C D � � E F G H �I % J + � � 7� � K L
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11.5 10.3 11.8 12.0 12.5
11.6 10.6 11.8 12.2 12.2
11.6 10.8 11.9 12.2 12.5
11.3 11.1 11.9 12.2 12.6
11.7 11.2 11.9 12.2 12.6
12.8 11.3 12.0 12.2 12.8
11.7 11.4 12.0 11.0 13.4
11.8 11.4 12.0 12.4 13
11.8 11.5 12.0 12.4 13.2
11.8 11.5 12.0 12.4 12.2
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s / t u v , MINITAB w x y z 8 { | } �~ � �� 4-2 � � 4-37a � P-value� 0.701
> 0.05�. / * , � � �� � � � � � �� { | � � 7� a 25 � e h �� � p SX − Chart�
� 4-47
13.512.511.510.5
.999
.99
.95
.80
.50
.20
.05
.01
.001
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babi
lity
Sample 1
� 4-2� � � � � � � � � � � � �
� 4-3� � � � � � � � � � � �
17161514131211109
USLLSL
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� 4-4� � � � � � � � � SX − Chart
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# $ 1%& �' ( ) * + 2≥PC � 75.0≥aC "
# $ 2%, - . / 0 1 2level of significance3α = 0.05
# $ 3%�4 4-1 5 6 +7 8 9 : ; "
# $ 4%< = > ? : ; ��@ A B : ; C D 4E
X S PC aC
11.92 0.63 2.11 0.73
# $ 5%FMatlab�G �@ H I J K L M N O P Q + 2.40�1 J K L M N O P Q + 0.78"
# $ 6%R+ Ĉp = 2.11 < M N O P Q 2.40� Ĉa = 0.73 < M N O P Q 0.78�R> S �T U �
�����I J V 1 J ��W X Y Z ) * "
# $ 7%[ \ ] ^ _ ` a b V c d A B e : f �g h i j 50 k j l C 4 4-2" 4 4-2m ���n o 7 8 �: ;
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
12.5 11.7 12.0 12.2 12.4
252015105Subgroup 0
12.4
12.3
12.2
12.1
12.0
11.9
11.8
11.7
Sam
ple
Mea
n
Mean=12.03
UCL=12.33
LCL=11.72
1.0
0.9
0.8
0.7
0.6
0.5
Sam
ple
StD
ev
S=0.7192
UCL=0.9377
LCL=0.5007
���������� ��� 49
12.5 11.7 12.0 12.2 12.6
11.4 11.7 12.0 10.9 12.8
12.4 11.7 12.0 12.2 13.1
11.5 11.8 11.4 12.2 12.0
[pq����������� ��������������2C r 4-5 % r
4-6 V r 4-73�� � � � ��� � ! "
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17161514131211109
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131211
.999
.99
.95
.80
.50
.20
.05
.01
.001
Pro
babi
lity
Sample�2
����� � � 50
� 4-7� � � � � � � � SX − Chart
������������ ���
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
���������� ��� 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
� � � � � � � 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
���������� ��� 53
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[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.
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[5] ¨ © 4 ª « ¬ �NAND Flash � � ® ¯ ° ± k � � ² ³ ' ´ PC µ f � ¶ · � ¹ º »
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[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.
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[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.
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[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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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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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