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©2007 National Kaohsiung University of Applied Sciences, ISSN 1813-3851

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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

5 6 7 8 9Samsung: ; < ! � = > ? @ �

� 1-2� 128MB/512MB Micro SD , - A B C D E F G �

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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

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

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−−=

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

}11{}{ CCPCCP aa −≤−=≥

−−≥

−−=

22

1

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P a

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M �� � N O CPQRSTE�

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� Ĉp X aC # � ` � + � $� � o p q � � � � � � $6 � ` � � � � � �

� � 1�� ` � � � � � � 0C $� � � � � � 1C �

� � 2�� � Y Z [ � Clevel of significanceEα�

� � 3��   ¡ ¢ £ ¤ �¥ ¦ �

� � 4�§ �   ¨ �¡ ¢ £ ¤ ¥ ¦ + , - Ĉp X Ĉa�

� � 5�© N ª « � matlab � � ¬ ¨ Ĉp X Ĉa �8 F G H "�

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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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� 4-1� � � � � � � � � �

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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� 4-47

13.512.511.510.5

.999

.99

.95

.80

.50

.20

.05

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� 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

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� 4-7� � � � � � � � SX − Chart

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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

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� 4-9� � � � � � � �� � �

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12.912.411.911.4

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X S PC aC

12.30 0.44 3.03 0.83

��� =PC 3.03 � � � � � � 2.40� =aC 0.83 � � � � � � 0.78�� � � � � � � � �

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5.2 � � ��� �

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12.6

12.5

12.4

12.3

12.2

12.1

Sam

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UCL=12.54

LCL=12.15

0.6

0.5

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S=0.4521

UCL=0.5894

LCL=0.3147

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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.

[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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�������� 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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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

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