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µ ... i ' ...ii ¶ · ...iii ... iv " ' ... v " ... vi 0! ... 1 0!0! ' ... 1 0!1! " 2 (... 1 0!3! 2 4'5 ... 3 1! ' $ # ( 6 ... 4 1!0! - # " + ... 4 1!1! - # " + ' ... 6 1!3! ' $ # ... 8 1!3!0! ...8 1!3!1! # # ...11 1!3!3! 2 ## ( # / # ...14 3! ' ( ( ... 18 3!0! - ... 18 3!1! - ' #... 20 3!3! ' .7 ... 21 3!3!0! $ # Cpk...21 3!3!1! # ' 8 # .22 9! ... 27 , . ' # ... 28 , " #... 36 2 ... 40
"
'
Table 1. Specifications for thin-film transistor liquid crystal display. ... 6
Table 2. Lower bound of various capability levels for multiple characteristics... 8
Table 3. The total rank of the four bootstrap methods as T =1 PU C ,1.33 and =1:0;<.. 12
Table 4. The relationship of the sample size and estimating precision with T 1 PU C = ... 14
Table 5. The relationship of sample size and estimating precision with T 1.33 PU C = .... 14
Table 6. Sample size n required for Rγ ≥RPU, with RPU =0.75(0.01)0.95,………… 0.9,0.95,0.975,0.99 γ = , three quality characteristics and T PU C =1 ... 15
Table 7. The 150 sample observations for three quality characteristics... 16
Table 8. Calculations for process capability of overlay, critical dimension, and ……….. uniformality ... 17
Table 9. The critical value cα for dynamic process with various parameters. ... 24
Table 10. The collected 10 subgroups of size ten (Unit: mµ )... 25
"
Figure 1. Deposited layers on TFT-LCD... 5
Figure 2. Exposure process on panel window. ... 6
Figure 3(a). The total rank of the four bootstrap methods as = 0, = 1... 13
Figure 4(a). The total rank of the four bootstrap methods as = 0!33, = 1 ... 13
Figure 3(b). The total rank of the four bootstrap methods as = 0, = 3 ... 13
Figure 4(b). The total rank of the four bootstrap methods as = 0!33, = 3... 13
Figure 3(c). The total rank of the four bootstrap methods as = 0, = 9... 13
Figure 4(c). The total rank of the four bootstrap methods as = 0!33, = 9. ... 13
Figure 3(d). The total rank of the four bootstrap methods as = 0, = < ... 13
Figure 4(d). The total rank of the four bootstrap methods as = 0!33, = <... 13
Figure 5. Wafer back grinding... 20
Figure 6. An example of tool wear problem... 21
Figure 7. Plot of the changing capability of a process with tool wear. ... 21
Figure 8. Plot of the 100 observations... 25
' # ( = , ' : ; ' ( # # ! 4 * ' ' ( # * ' ' ' ' ( # # ! ' ( # # # ' + ' ! ' , # ! ' + # + # # + # # # ! ' ' ( # ( σ − = > * µ µ σ− −σ = * = 3 3 *
{
µ µ}
σ− −σ = # * 3 3 * ( USL LSL ( # * µ # *σ
! * # # ' ! $, # ? ) :0@@1;* 8A # ? /:0@@<;* ? / " :0@@B;* :1CC3;* ! # µ σ2 . ( ! # * ( * # ' , * # ' ' # # ! # ' ' ( ! ' # # ' ' ' ! # ' : ! !* - ;* ( # ' * ' + ! * ' # ( ' , * ? :0@B>;* :0@@1* 0@@B;* :0@@B;* ( * ' #( # # ! * # ! * # # -! ( # * :0@@1; # # ' . # # # # ! * v- ( v- # P1* P2* D* v P ! # P=min{P1,P2,...,Pv}! ! : v=5 ;* ( + # % 85 . 99 5 4 3 2 1 =P =P = P =P = P : 0<CC # - # ;! # # * ' P P P= × × × =1 2 ... P5 99.2522% : E9EB # - # ;* ( ' :0@@1;! :1CC3; # ' , ( # - * 0 0 0 F :1 :3 ; 0; 0GH1 3 − = = Φ
∏
Φ − + ! * :1CC9; ( # , * ( # - ( - ! * ' , =∏
= − v j PUj T PU C C 1 1 (3 ) 3 1Φ
Φ
! # ' ' ' # ! ' * ' : ;* ' : ;* ' ' : ;* ' -t : ; # ! ) ( * :1CC9; ' ' # ! : # ' * # ' * ' ; ( # # = ' ( ' ' # ! / #' ! # # :0@@>; , ( # ' ' # ( - # ' ! # ' ( - # ' ! # ' ( ! 4 # ( * ' ' - # : I :0@@9;* :0@@<;* :0@@E;;! * , ' : 8A # :0@@<;*:0@@>;* :1CC1;;! ' ( # ' ! , ' = ( * ( ' ' ' # # ! ' ' + ! # # # ' ( # ! # # ' ( 2 ' :0@BB;* ( ## # ! # * # . # ! 6 ' :0@BB; ( ' # ' # # ( . ( # ' ! ) ( * ' # ' ! ( ' ' # ( * ( # * # # ' # ! :0@@0; ' ,* Cpm # ' # # ' ( ! ( -( , # # # ( . ! , # * ( ' # # T PU C # # # ! ' ( # ' H ( ( . ( ( ' ! * ( # # - , CPU ( # ' ' # ! # * ( # ( ' ' ( # ( # / 0CC! ' ' # / + H ! , # * # , Cpk ( # ' ! * ' # ( ' * ' + # # / ! -( . # . ' ! # # ( # ' !
!
"
#
$
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igure 1! * , * # ! # , ( (* # * Figure 2! * ' #! . # ( Table 1! 0! -" !
# # . 1! $, ( (! ' 0! - # + ! # 4 ≤0.1
µ
m # ≤0.3µ
m & # ≤0.03 % &" ! % ' ( ) # ' , # # * ( # ' # ! # ' ( - # * * ( * ( & ( # ' %:C*0;! * ! * ( ' ! * - # # :% ; ( - # ' % K106 × − Φ[
1 (3 )CI]
! + * , # BB * % ≤0CC # # # # ( - ! ( - * * ( # * ( * # C!B * # + # ' # !' # ( ' , ! * ' # ( # # ! ( # * # # ' . # # # # ' ! :1CC9; # - , * # - , ' ( µ σ − − = Φ Φ0 0L : ;M 3 * ( Φ ⋅:; # ' # ' (:C*0;* Φ−0 Φ ⋅:;! ( # + * ( ' , − = = Φ 0
∏
Φ 0 0 :3 ; 3 * ( =0* 1*D* * #' ! ,* * ' ( / ,* ! 7 = * ( = Φ = Φ∏
0 :3 ; :3 ;! I * :1CC9; ( ' ( , ' ' ( = = =∏
=∏
Φ = Φ 0 0 :3 ; :3 ;! ) * ( , , # ! , # :1CC9;* = 1.00* ( ' , @@!B><N* :C!@@B><C0;1/5 K C!@@@E1@@ : + 1EC % ;! # * ( * # # ' * # ' ' # # ! ' # . # # . ( ' * ' # ' ! ' # , ( ' ! ( ' * ' ' ' # . !) * + ' ≥ C * J ' # # # + * − − = = Φ 0
∏
Φ ≥ Φ 0∏
Φ ≥ C 0 0 0 0 :3 ; :3 J; 3 3 ! ( ' ( ' '(
)
− ≥ Φ 0 Φ C 0 J :3 ; 3 !Table 2 displays the lower bound J of obtained by Wu and Pearn (2004)
for the required overall process capability are 1.00 and 1.33 for ν =1(1)5 characteristics. For example, if a process has capability requirement ≥1.00 with ν = 5, i.e., the capability for all the five characteristics is the following ≥ 0!0<3, for j = 1, 2, …, 5. ' 1! " ( ' ' # ! 0 c CT PU >
ν
0!CC 0!33 0 0!CCC 0!33C 1 0!C>B 0!3B3 3 0!0CE 0!909 9 0!033 0!93> < 0!0<3 0!9<1 ) * # R( PSpm)*γ
* # )γ
* . # . ( ' 0 ) ! # ) = O H * # / # # ! ) * # ) * ,# # / # ' ' ! # ( ' # # / + # ! ' # # ( ' ( ! ! ) + , % + # * # ' * ( . # # # ,# 'H ! & * # ( # ' ! & ' . ( ! / # # ' ( # # ' # - ! $ :0@E@* 0@B1; # * # ' # # * P Q* ( ' # + ! 4 # ' # # # ' * ( # # # ( ( * ' ' ! # # ' # ' ! 2 ' + ' # ,# p ' ' * ' # + # ' ' # # ! ' # + # :( # ; # # ' ' ' ! ' ( # + ' # ' ! ' # # ' '
µ
σ
. ( ! # ' ' # ' ' # ! ' * ( . ( ' * ' # # / n # ' ' ! # ' # ' * n ' # # . ( ! ' ( ' # / # ( # ! ' * B ( # * # / ' n* ( ( # # ! $ ' :0@B>; ' * ' : ;* ' : ;* ' ' : ;* ' -t : ; # ! ( ( ( ' ! # # ( ' ,! * * # # B ' # CPUT* * # # ) ( ˆ 1 1 * * C i B C B i T PU T PU = = *= − − = B I T PU T PU C B C i C S T pu 1 2 * * * [ ( ) ] 1 1 * ( CPUT*(i) i - ' # ! + *T PU C S # CPUT CTPU ,# # ' :0-1
α
; 0CCN ' ' F *T PU C T PU Z S C − α G* ( Zαα
+ # ' ! ! " * * # # CPUT*(i)*α
:0-α
; FCPUT*(α
B)G! * " + " * * * # ' ' # ' ' ( ' # ! ( * ' ' ' # # ' ' # ' ( ( , ! * ' ' :$ * 0@B1;! * ' CTPU* * ' ' ] [ * 0 PCPUT cPUT P = ≤ * * ) ( 1 o o P Z =Φ− * ) 2 ( Z0 Zα PL =Φ − * ) 2 ( Z0 Zα PU =Φ + * ( Φ(⋅) # # ' ! * ' * [ T ( )] PU L C P B ! * + * # ' . ( * ' ' ( ! * ' -' ( # # ' T ! * ,# ' T PU C T PU T PU C S C T =( − )/ ' ' ! . ' # # ' ,# ' ' * # CTPU* (i) * T - ( * )/ *T PU C T PU T PU C S C T = − ! :0-1α
;0CCN ' ' * * [ T ] PU T PU C C −t Sα *( tα* t1*−α
α
0-α
+ ' T - ' ! " ! ! # # # ' * ( RPU =CPUestimating/CPUT : * 1CC3; * ( # ! # ' ' . ! ' # :CPUT =1.00 or 1.33;* ' . ! 4 * ' * .( ' ( ! . R * ( ( = ( . ' # : , ;! 500 / ) 4 4 3 3 2 2 1 1 ( × + × + × + × = rank number of rank number of rank number of rank of number R ! # # ' # ' ' " # : , ; + ' CPUj : Table 2;! , # * ' + # CTPU ≥1.00 ( v= * ! !*5 ' ( CPUT ≥1.153* j=1, 2,...,5! Table 3* . ' # ( # / nK3C:0C;0CC* 01<* 0<C* 1CC* vK1:0;< CPUT =1 0!33! , # * # / >C* ( ( # ' ' # ' 1.33 T PU C = ! # ' * ( ' . 1!@99* 1!C1B* 0!031* 3!B@> ! # : - ; ' # Table 3* :( CTpu =1;! # # # # / * ( 3: ;R: ; 9: ;R: ;! ) ( * 9: ;R: ; :( CTpu =1.33 * 5 ~ 4 = v ; # ! ' ( # ' # # / :n<100;= ( # / * ' ( # S # ' ! * + * . # ! # # ( # : 9: ;;* * # # # ! ) ( * # # / :n<100;* # ' CˆTPU! ) ( # CˆPUT ( !' 3! . ' # CTPU =1*0!33 =1:0;<! = 0 =0!33 = 1 3C 3 1 0!CC> 3!@@9 1!@@> 0!@@> 0!CCB 9!CCC 9C 1!@@> 1!CC9 0!CC9 3!@@> 1!@B1 1!CCB 0!C39 3!@E9 <C 1!@@1 1!CC1 0!C19 3!@B1 1!@@ 1!C01 0!C3C 3!@>B >C 1!@B1 1!C09 0!C91 3!@>1 1!@B9 1!C0C 0!C<> 3!@<C EC 1!@@9 1!CC9 0!C0B 3!@B9 1!@B9 1!C1C 0!C3C 3!@>>
BC 1!@BB 1!C01 0!C1> 3!@E9 1!@E1 1!C1B 0!CE1 3!@1B
@C 1!@@9 1!C0> 0!C11 3!@>B 1!@EC 1!C1> 0!CB9 3!@1C 0CC 1!@BC 1!C1C 0!C1> 3!@E9 1!@@1 1!CC1 0!CE1 3!@39 01< 3!CCC 1!C0C 0!C0B 3!@E1 1!@>B 1!C9C 0!0C9 3!BBB 0<C 1!@BB 1!C01 0!C9C 3!@>C 1!@E9 1!C<> 0!C@9 3!BE> 1CC 3!CC9 1!C0B 0!C3> 3!@91 1!@E1 1!C0B 0!09B 3!B<B = 0 =0!33 3 = 3C 1!@>> 1!C1B 0!0CC 3!@C> 1!@91 1!C9B 0!001 3!B@> 9C 1!@<C 1!C9C 0!0C> 3!@C9 1!@<9 1!C9> 0!031 3!B>B <C 1!@EC 1!C39 0!0CC 3!B@> 1!@9> 1!C99 0!0<C 3!B>C >C 1!@91 1!CEC 0!019 3!B>9 1!@11 1!C@9 0!10> 3!E>B EC 1!@<9 1!C<1 0!01C 3!BE9 1!@0> 1!001 0!1@C 3!>EB BC 1!@99 1!C>1 0!0E1 3!B0B 1!@C9 1!0CB 0!331 3!><> @C 1!@9C 1!CEB 0!0>> 3!B0> 1!B3> 1!0>B 0!91B 3!<>B 0CC 1!@39 1!CE1 0!0>1 3!B1B 1!B@9 1!03> 0!3<1 3!>0C 01< 1!@>9 1!C>C 0!019 3!B<1 1!B31 1!0E1 0!<@C 3!9C> 0<C 1!@EC 1!C99 0!03> 3!B9B 1!BC9 1!0E> 0!>1C 3!3@B 1CC 1!@0B 1!009 0!1CC 3!E>B 1!EB9 1!13C 0!>3> 3!399 = 0 =0!33 9 =
3C 1!@E 1!C<1 0!00> 3!B<> 1!@9 1!CE> 0!0E 3!B09
9C 1!@01 1!CB9 0!1CB 3!E@> 1!BB1 1!00 0!3 3!ECB
<C 1!@11 1!C@9 0!119 3!E> 1!B1> 1!0B> 0!<CB 3!9EB
>C 1!@0 1!C@> 0!111 3!EE1 1!E@B 1!0BB 0!<3 3!9EB
EC 1!BB1 1!01> 0!1<9 3!E3> 1!B11 1!0B> 0!>>9 3!31B BC 1!@0> 1!0CB 0!1> 3!E0> 1!E@ 1!1E9 0!>>> 3!1>B
@C 1!B@1 1!01 0!30B 3!>>B 1!E91 1!1E1 0!EB9 3!0@>
0CC 1!BB> 1!019 0!1B 3!EC> 1!E3 1!3CB 0!B< 3!00 01< 1!@11 1!01> 0!3CB 3!>99 1!>39 1!9 1!C<9 1!@01 0<C 1!@1 1!0 0!31B 3!>9B 1!>B9 1!901 1!C39 1!B>B 1CC 1!BB 1!0<1 0!3@9 3!<E 1!>31 1!939 1!311 1!>C> = 0 =0!33 < = 3C 1!@3B 1!CB9 0!111 3!E<> 1!B> 1!0< 0!3@B 3!<@ 9C 1!BEB 1!00B 0!309 3!>BB 1!EB> 1!10> 0!><1 3!399 <C 1!B@1 1!09B 0!31> 3!>3 1!E@1 1!19 0!>9B 3!30> >C 1!B< 1!0> 0!9CB 3!<B1 1!E<B 1!1<9 0!B1B 3!0<> EC 1!B9> 1!0<B 0!9< 3!<91 1!>B> 1!33> 1!C1> 1!@91 BC 1!@C1 1!0B 0!3B1 3!<1B 1!><9 1!9 1!00 1!B3
@C 1!BE> 1!0E1 0!< 3!9<1 1!<E1 1!931 1!1BB 1!EC1
0CC 1!B3 1!0@1 0!<> 3!9C> 1!<B1 1!9EB 1!3B9 1!<< 01< 1!@C9 1!0<> 0!<09 3!91 1!<> 1!9B1 1!> 1!3<9 0<C 1!B<> 1!11B 0!<E1 3!391 1!9>> 1!<19 1!>9B 1!39>
30 40 50 60 70 80 90 100 125 150 200 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 sample size SB PB BCPB PT 3: ;! . ' # = 0 * = 1 30 40 50 60 70 80 90 100 125 150 200 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 sample size SB PB BCPB PT 9: ;! . ' # = 0!33 * = 1 30 40 50 60 70 80 90 100 125 150 200 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 sample size SB PB BCPB PT 3:';! . ' # = 0 * = 3 30 40 50 60 70 80 90 100 125 150 200 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 sample size SB PB BCPB PT 9:';! . ' # = 0!33 * = 3 30 40 50 60 70 80 90 100 125 150 200 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 sample size SB PB BCPB PT 3: ;! . ' # = 0 * = 9 ! 30 40 50 60 70 80 90 100 125 150 200 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 sample size SB PB BCPB PT 9: ;! . ' # = 0!33 * = 9 ! 30 40 50 60 70 80 90 100 125 150 200 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 sample size SB PB BCPB PT 3: ;! . ' # = 0 * = < 30 50 60 70 80 90 100 125 150 200 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 sample size SB PB BCPB PT 9: ;! . ' # = 0!33 * = <
!! + - ! - . " ! # # Rpu 0 # / ' Table 4-<! ' 9! # / # ( CTPU = !1 2 = v v=3 v=4 v=5 n Rpu Rpu Rpu Rpu 3C C!B9<B C!B9C> C!B3BE C!B3B9 9C C!B<@B C!B<E0 C!B<<9 C!B<>3 <C C!BE01 C!B>@> C!B>@9 C!B>B> >C C!BEE< C!BEBC C!BE@9 C!BBC9 EC C!BBE3 C!BBE9 C!BBB< C!BBB> BC C!B@30 C!B@3> C!B@<1 C!B@<E @C C!B@E3 C!B@@< C!@C01 C!@C1C 0CC C!@C11 C!@C3@ C!@C>0 C!@CEC 01< C!@00< C!@0<C C!@0>@ C!@0BC 0<C C!@0B1 C!@111 C!@193 C!@1>C 1CC C!@1B@ C!@31E C!@3<0 C!@3E0 ' <! # / # ( CTPU =1.33! 2 = v v=3 v=4 v=5 n Rpu Rpu Rpu Rpu 3C C!B<1C C!B93> C!B913 C!B3@E 9C C!B>11 C!B<B@ C!B<EE C!B<9C <C C!BE30 C!B>@> C!B>EC C!B>EC >C C!BBC3 C!BE@3 C!BEE9 C!BEE9 EC C!BBE< C!BB>< C!BB<> C!BB9< BC C!B@1@ C!B@1> C!B@19 C!B@1< @C C!B@BC C!B@E@ C!B@BC C!B@B< 0CC C!@C3C C!@C39 C!@C1E C!@C1E 01< C!@019 C!@01< C!@09C C!@091 0<C C!@0@C C!@1C9 C!@10B C!@11@ 1CC C!@1@9 C!@30> C!@31B C!@390 4( :0@B@; ( # # # ˆ PU C CˆPL ' (3 n t)−1 n−1( )
δ
* ( tn−1( )δ
' t ' ( n−1 # #δ
=3 nCPUδ
=3 nCPL * ! 100(1−α
)% ( ' LC CPU ! ' (α
δ
σ
µ
≥ = ≤ = − − − ( ) ) 1 Pr( ) 3 Pr( L t 1 1 t1 USL n C * ( t1 =3 nCˆPUδ
1 =3 nLC ! * ( ( ' :" ; ' # ' : ;t ' ( n−1 # #
δ
1 =3 nLC!To compute the sample size required n, we develop a MATLAB program (available on request). The simulation data is the same one in Section2.3.2 (random data generated from normal distribution). Let the desired estimation precision be R and PU
the confidence level be γ , and then the minimum sample size n (always rounding up if n is not an integer) can be calculated. Table 6 displays the sample size n required for Rγ ≥ R i th PU R = 0.75(0.01)0.95 and PU γ =0.9,0.95,0.975,0.99. We also
provide the actual estimation precision Rγ in the Table 6! , # * RPU
C!B@* ( γ K C!@< # / KE>! # # # # / KE> + ' @<N CPU )γ K B@!01N # # CˆPU * # # PU C K0!1* CPU 0!1 T B@!01N K 0!C>@* ( @<N ! " # # # # # # / + # CTPU ( , " #! ' >! # / n + Rγ ≥RPU* ( RPU =0.75(0.01)0.95* 0.9,0.95,0.975,0.99 γ = * + C K0TPU 90 . 0 = γ γ =0.95 γ =0.975 γ =0.99 PU R n γ R n Rγ n Rγ n Rγ C!E< - - - 16 0.7518 C!E> - - - - 6 - 21 0.7609 C!EE - - - - 7 0.7776 24 0.7731 C!EB - - - - 14 0.7832 28 0.7807 C!E@ - - - - 18 0.7904 31 0.7901 C!BC - - 6 - 22 0.8005 36 0.8012 C!B0 - - 12 0.8119 26 0.8107 40 0.8103 C!B1 - - 17 0.8222 32 0.8226 49 0.8201 C!B3 - - 23 0.8316 38 0.8304 56 0.8305 C!B9 - - 28 0.8414 44 0.8403 65 0.8414 C!B< 6 - 35 0.8536 52 0.8502 75 0.8502 C!B> 18 0.8608 41 0.8600 63 0.8613 88 0.8609 C!BE 26 0.8708 51 0.8710 73 0.8700 105 0.8710 C!BB 33 0.8805 60 0.8802 88 0.8800 124 0.8812 C!B@ 44 0.8909 76 0.8912 105 0.8908 146 0.8610 C!@C 54 0.9005 93 0.9004 128 0.9000 176 0.9005 C!@0 71 0.9107 115 0.9102 158 0.9103 213 0.9101 C!@1 92 0.9205 146 0.9201 197 0.9204 268 0.9202 C!@3 121 0.9306 188 0.9303 253 0.9300 339 0.9302 C!@9 164 0.9400 251 0.9402 337 0.9400 451 0.9400 C!@< 231 0.9500 350 0.9502 473 0.9505 634 0.9500
' >* ( # / * RPU γ ! ) ( * # # / ' ' ( PU R γ # ! ' # ' # ! ( . # # - . ( * # . + ! . # * # # ! ' # / + # R * (pu . ' >! ' > # / + )γ≥ pu R ( Rpu =0.75(0.01)0.95 γK C!@* C!@<* C!@E<* C!@@! pu R ' C!@1 γ K C!@< # / K 09>! # # # # / n K 0<C + ' @<N )γ K@1!C0N # # O * # # O K 0!3* 0!3×@1!C0N K0!1C* ( @<N ! ) # # 0<C " Table 7! # * # # * # * # CˆPUj * # # # # / Table 8! ' E! 0<C # ' + ! 4 :µ ;
C!CEE@ C!C>@E C!CE>9 C!CE>3 C!CB39 C!CB>C C!CEEB C!CB9@ C!CB9> C!C>9@ C!CB<3 C!CBC0 C!CE00 C!CB9E C!CB0E C!CE9E C!CBB> C!CEEE C!CBB@ C!CE0> C!CBC1 C!CEE> C!CBCC C!CB00 C!CBE3 C!CBC9 C!CB0C C!CE1@ C!CEB1 C!CE@9 C!CE00 C!CE01 C!CE19 C!CB3@ C!CB30 C!CB9> C!CBC3 C!CB<0 C!CEC0 C!CE90 C!CEC> C!CB1> C!C>>< C!CB93 C!CB>1 C!CB19 C!CB0C C!CBC9 C!CB3B C!C>@3 C!CE<E C!CB91 C!CE>< C!CE91 C!CB3B C!CB31 C!CB3E C!CE9< C!CB1C C!C@00 C!CEB> C!CE<0 C!CE3B C!CBC0 C!CB<3 C!C>>E C!CEEB C!CBBB C!CB@C C!C>3B C!CE@> C!CB<@ C!CE0B C!CE@@ C!C>3E C!CEB@ C!CBEB C!C@1> C!C>E9 C!CE9< C!CB<@ C!C@03 C!CB>3 C!C>@< C!CBEB C!CE<3 C!CE@C C!CE@B C!CBC0 C!CE3> C!CE9> C!CBB< C!CEBB C!CE9> C!CB>1 C!CEBE C!CE<3 C!CE@3 C!CEE> C!C@9< C!CB33 C!CEC@ C!CBC9 C!CEBC C!CBBB C!CB91 C!CE@9 C!CE@3 C!CEE0 C!CB3< C!C>@0 C!CBC> C!CBC< C!CE3< C!CB93 C!CB3E C!CE1E C!CB39 C!CE<1 C!CBEE C!CEE0 C!CB<C C!CE<< C!CB1> C!CEE> C!CB33 C!C>>@ C!CE9C C!CB3@ C!CE93 C!CEB0 C!CE<9 C!CB9C C!CB9C C!C@>1 C!CEBC C!CBC0 C!CE91 C!CEB0 C!C@CB C!C@00 C!CB9@ C!CE>9 C!C@31 C!CEB3 C!CE31 C!CE11 C!CEE< C!CEBE C!CE0<
# :µ ;
C!1<<@ C!1>1E C!1E0E C!1><> C!1E<> C!1E9E C!1>9< C!1>E0 C!1<BB C!1EC3 C!1>B@ C!1>33 C!1>@9 C!1<E3 C!1>@0 C!1EE> C!1<<C C!1>31 C!1>19 C!1>C< C!1EB3 C!1>13 C!1>@0 C!1<E0 C!1>0> C!1E<@ C!1>EC C!1>BB C!1<@B C!1>1C C!1EBB C!1<CE C!1>>0 C!1E1> C!1BCE C!1E3< C!1>E3 C!19EB C!1B30 C!1><3 C!1>@0 C!1E@1 C!1E0B C!1E@0 C!1EEC C!1<B0 C!1E30 C!1>>C C!1>01 C!1E0B C!1><E C!1E00 C!1<E@ C!1>9@ C!1E>C C!1ECE C!1E>@ C!1>C< C!1>9B C!1E13 C!1><E C!1><C C!1E>9 C!1B1E C!1E39 C!1>E> C!1E<E C!1>>1 C!1E<B C!1E<3 C!1<09 C!1><9 C!1E<9 C!1B91 C!1<19 C!1E39 C!1>BE C!1E93 C!1>30 C!1E0@ C!1E1> C!1B1B C!1E<C C!1E10 C!1>33 C!1>CB C!1BEE C!1>1B C!1B@9 C!1>3B C!1ECC C!1><9 C!1B0@ C!1E1B C!1E03 C!1>EC C!1<BC C!1E3C C!1><1 C!1E@9 C!1><> C!1B<C C!1E3< C!1EE9 C!1E3C C!1E<E C!1>9C C!1ECE C!1<>9 C!1>39 C!1>3B C!1E1E C!1>B0 C!1>9E C!1E1C C!1>BE C!1>1E C!1B1B C!1B3B C!1ECC C!1>3B C!1>9C C!1E@E C!1ECB C!1EC9 C!19E< C!1E03 C!1E0C C!1BEC C!1>0C C!1><0 C!1E1@ C!1>@B C!1EC1 C!1>@9 C!1<B> C!1>0@ C!1E@C C!1E13 C!1B33 C!1EC@ C!1<@1 C!1E9C C!1<@B C!1<<E C!1E@C C!1E09 C!1BE9 C!1><> C!1EB@
& #
C!C1E1 C!C1>9 C!C1<< C!C1>E C!C19B C!C1E1 C!C1EC C!C1>E C!C1<E C!C1>< C!C1>9 C!C1>< C!C1<1 C!C1EB C!C1>3 C!C1E1 C!C1<1 C!C1>9 C!C1>9 C!C19E C!C1E0 C!C1E> C!C1>B C!C1@3 C!C1B3 C!C1>< C!C1>@ C!C1E< C!C1EE C!C1<E C!C1<< C!C1>@ C!C1<@ C!C1E0 C!C1E3 C!C1<> C!C1EB C!C1B3 C!C1>E C!C1EE C!C1<9 C!C1>< C!C1BC C!C1B3 C!C1>1 C!C1>@ C!C1>E C!C1>> C!C1>3 C!C1>0 C!C1>@ C!C1EC C!C1>1 C!C1E@ C!C1<1 C!C1<< C!C1EE C!C1<9 C!C1>1 C!C1E@ C!C1>< C!C1E0 C!C1B> C!C1<1 C!C1>0 C!C1>> C!C1EB C!C1EC C!C1<< C!C1E9 C!C199 C!C1E1 C!C1E@ C!C1<@ C!C1>> C!C1>< C!C1<> C!C1E9 C!C1>> C!C1B1 C!C1>B C!C1>C C!C1<> C!C1<3 C!C1>B C!C1BE C!C1EC C!C1@9 C!C1>< C!C1<B C!C1E< C!C1>< C!C1B1 C!C1EC C!C1>> C!C1>E C!C1<9 C!C1EC C!C1EE C!C1<E C!C1EB C!C1<< C!C1E9 C!C1>C C!C1E3 C!C1>@ C!C1<> C!C1@3 C!C1<> C!C1E9 C!C19@ C!C1>< C!C1>@ C!C1>@ C!C1>B C!C1>E C!C1>1 C!C1>> C!C1E0 C!C1>@ C!C1<1 C!C1<E C!C1B> C!C1>E C!C1>< C!C1EC C!C1EC C!C1>0 C!C1>9 C!C1>3 C!C1BC C!C1E0 C!C1>E C!C1E9 C!C1>> C!C1EE C!C1<1 C!C1>B C!C1>E C!C1<E C!C1>9 C!C1E3 C!C199 C!C1>3 C!C1>9 C!C1<B C!C1>B C!C1>C C!C1E> C!C1<> ' B! ' * # * # ! & " x σˆ ˆ j PU C ˆT PU C 4 C!0µ C!CE@< C!CC>< 0!C9@@ # C!3µ C!1>@3 C!CCB3 0!11@B # C!C3 C!C1>E C!CCC@E 0!0913 0!CCBE
#
"
#
"
*
%
* . # - : ; # ( ' ' ( ! * ( ( # # 3!0! * ' ( ' # 3!1! * ( ' ( ' ! * & ) # " * ( 0@<1* ( # 0@<@! ## ' ( 0@BC ! ' # # ' * ' , ' # ! : . ( ; # / ( ' # ' # # ! # ' ## / # 5 ( ' * ( ' * #' * ' -! ,$- . / " " 8 ' # ( ( * ( ' ! # ( ( # , # ( , ! * : . ( P# . Q P # Q; ( ! , ( ! * * # , # # ! # # ' ( # # ! 0$- . " % ( # * ' ( ! # . ( . ! ( ' ' ' ( ' . ( ! * # # ' ' . ! ( ' ( ( # #' ( ! 1$' % # ( # * ' '#' ! ' # ( . ! #' ' # * : ( ;* #' ! 2$/" * +" * . '5 , ' -( ' ! : , # * # ' - # # ;! ! . : # . #' ; # * ( ' ! 4 ( ' * ( ' . ! 4 * ( ' . ! . # * . * ! . ( # . - - ( # ! ( " ! . # ' ( # , . ! ' " % ' # # . ' ( # ( # ' ! ' " # . ! " ! ' . # ' ( ' ( ' * ( . ! ' + * . ( ' ! # ( ' ( ( #' . . ' # # / ! # + ( * ( # ' ' ( # ! . * ( ' # ' ( ( ' ' . ! * # # ' ' . # + ! S + # # # # = / # # S + ! ) ( *
( ' # . ( ! ) * ( ' . # ' ( ( # ( ! <! ' . ! * & ) % % / ! # ' ' ( ! # # # ' ' # : 8 #' :0@EB;;! ) ( * # ' ' ! # ( ' # * ( * ' # ' ' ! # ' * :σ2; # # :σr2; ' :σa2;* ! ! σ2 =σr2+σa2! # * ( * ( ' ' ! * # ' ( ' ( ( ! # ' * ' # ' # # # ' ! :0@B@* 0@@0; ( # * * * ! # # * ' ( * ' ' ! # Cpm , # # ' ! * # # # # # + # ' # ! * ' ( ' * ' + 5 # ! $
( ' # * ( ( * ' ' ( # # # ! * # # ' * - - * ( # ' * # * ! # ( # ' ' ( . ( ( # * , ( ' #! > # ( ( ' # , * : ! ! USL * LSL T ;* * ! ( - * ' ' ' ! > # ( ' # ( - ! # # # ' , # ( ( ! , ' ( ' #* # ' , pk C ' ( * E! ) * # . ( ( ' ' ! t0 t1 LSL USL time ob se rv at io n >! , # ( ' #! t0 t1 time C pk E! ' ( ( ! # " / " + 01 * * # Cpk , # # ' ( ' : * 1CC>;! ' + * , # ( ( ' ( # Cpk ! ! " Cpk ( ' ' # * '5 ( ' # # # # # ' ! & ' ,* ' ' # ! :1CC>;
# Cpk , # # ' min{ , } 3 t t pk rt USL LSL C
µ µ
σ − − = * ( USL LSL ( # * tµ
#σ
rt : # ; # t ! Cpk ' # # t # # ' ! # ' # ( ( * # Cpk ' ( ' # ' ' ! * # ' ' ' 'µ
tσ
rt ' # Xt 1/ 2 [(n−2)MSE nt/( −1)] * ! ' min{ , } ˆ ˆ 3 3 ( 2) 1 t t t pk rt t d X M USL X X LSL C n MSE nσ
− − − − = = − − ! ˆrtσ
# ' + : ! !* 1 a t * ta2* D* tan; # ! MESt # + ( + Xˆai =α
ˆa+β
ˆai * ( tai + #' #β
ˆa ( ( # ! 2 1 ˆ ( ) 2 ai ai n t t i t X X MSE n = − = − ! - ! * ( 2 " ( ! :1CC>; # ' ˆCpk* ( 2 ˆ 0 2 ( 2)( ) ( ) 1 [ ( ) ( )] 9 pk b n C n b n t F x G t n t n dt nxφ
ξ
φ
ξ
− − = − + + − * x>0! ( b d= /σ! & + :4" ; #α
a*β
a # # # ' + * # # ˆCpk ' ,1/ 2 2 2 1 2 1 1 2 2 2 ˆ 12 ( ) 12 ( ) 2 (2 1) 3 1 1) ( 1)( 1) ( 1) ai a ai a ta pk n n n ai t t t i i i t d X M C iX X X iX n n X n n n n n n = = = − − = + − − + − − − − − ! ( n ' # / * Xtai i + # t !a # # # ! # ( ' k ' / n # # ! k ( ' + # # ( ! 4 * # / * ( # :n>30; # ' #! # # / # ' # ' ( : * 0@@0;! ˆ pk C * ' + # C * #
ξ
:ξ
=(µ
−M) /σ
;* # / n* .α
* cα ' ' ' P C(ˆpk ≥c Cα pk =C)=α ' # # ! *(
)
2 (3 ) 2 0 ( 2) (3 ) [ ( ) ( )] 9 C n n C n t G t n t n dt nc ξ α ξ φ ξ φ ξ α + − + − + + − = ! ' + ξ ! ) * ξ ξ= 0 0 ξ = −ξ ( ( # cα! :1CC>; , , ' cα ξ KC:C!C<;3!CC* n K<:<;<C* CpkKC!<:C!<;1!C ( .α
KC!C<! ( # ,# # cα ξ K0!CC! * :1CC>; ' ! ˆCpkα
KC!C0 C!C< ( n K<:<;3C Table 9! , # * CK0!33 # # # ' + # *α
KC!C< ( # / n K0C* ( cαK1!3C<! * # ' ' ( ˆCpk* ' . ' + ! 4 * ˆCpk * ' !' @! cα # ( # ! CpkK0!CC CpkK0!33 CpkK0!>E CpkK1!CC n
α
KC!C0α
KC!C<α
KC!C0α
KC!C<α
KC!C0α
KC!C<α
KC!C0α
KC!C< < <!1C> 1!@>E >!B>E 3!@0B B!<@0 9!@C3 0C!1>@ <!B>1 0C 1!1>> 0!E<C 1!@BC 1!3C< 3!E1C 1!BB0 9!990 3!991 0< 0!B1> 0!<0E 1!9C9 1!CCC 3!CC1 1!<CC 3!<B9 1!@BE 1C 0!>99 0!901 1!0>3 0!B>3 1!EC0 1!31@ 3!11> 1!EB3 1< 0!<3@ 0!3<C 1!C1> 0!EB1 1!<31 1!11@ 3!C13 1!>>9 3C 0!9E0 0!3C@ 0!@3E 0!E1B 1!91C 1!0>1 1!B@0 1!<B9( . # . , ( ' ' # ( ( ' . ! ' . * ( . ! ( # # USL=330.2µm LSL=279.4µm* ! # * # ( ( ' . # . # ! . ( # ( # ! ( ( 0CC ' ' / * ( , ' Table 10! B ! ' ' # ( : ( # ; # # ( ! # ! * . ( ' ( * ( . ' # ( ! % (* # # # # ' # # # ' ! ' ' ( # ' ( # # # ' ! ' + # ( ' . P ' Q Cpk >1.00! * ' # # ( ' :1CC>;* # ' # Cpk! ( # # ( !
' 0C! 0C ' / :& µm;! i 1 2 3 4 5 6 7 8 9 10 1 t 280.05 281.48 282.25 282.25 283.68 284.07 284.40 284.78 284.78 285.50 2 t 285.88 286.60 286.98 288.80 286.98 288.80 288.41 288.80 286.98 288.08 3 t 286.98 286.98 288.80 288.80 288.80 288.80 286.98 290.61 290.61 292.42 4 t 293.53 293.86 296.06 294.24 296.77 295.34 294.24 297.87 296.44 297.87 5 t 297.87 299.36 298.97 297.87 299.69 297.87 301.50 300.78 300.45 301.50 6 t 301.50 303.37 303.37 305.18 302.98 301.50 305.18 305.18 305.18 312.45 7 t 310.63 308.10 308.82 307.00 306.62 308.82 308.82 312.45 314.26 316.07 8 t 316.07 319.38 318.99 319.71 319.71 316.07 319.38 320.48 320.81 320.81 9 t 320.09 320.81 320.81 321.52 319.71 321.19 319.71 319.71 323.34 325.21 10 t 323.34 325.21 323.34 327.02 327.02 325.21 327.02 329.55 327.35 327.02 0 20 40 60 80 100 LSL 292.1 T 317.5 USL observations B! 0CC ' ! # .
α
K0C* # / n K0C* # # # ' + # C K0!CC* ( ' Cˆpk 0!E< ' . Table 9! # ' ' ( ˆ pk C * # ' ' ' ! Cˆpk 0!E< ' ( ! ' Table 10* Cˆpk # # ( Table 11! @ # ' ˆ pk C # # ! ' # Cˆpk # # ,# # # t5 ' ( # # # Cpk :CpkK0!E<; # t ! )10 * '* ( ( ' ' ' ! ' 00! # Cpk # # ! 1 t t2 t3 t4 t5 t6 t7 t8 t9 t10 ˆCpk 2.9316 3.0805 2.9058 4.8999 6.9571 3.7553 2.9135 2.6374 2.01 1.0158 2 4 6 8 10 0 2 4 6 8 sample number es tim at ed C pk Minimum Cpk value @! ' # # !
3
' ' ( # # ' ! ) ( * # ( ' # # ! * ( -( # ( * # ( # -( ' # ! * ( ' # ( ' # / + # ! ( ' # # # # ' ' # ! # / # ! ' # # # # ' # ! # # ( # / # 0CC! ' ( ' # / + # ' # ! . # . ( ' 0−γ ! ' H - ! -( , # . # -" # ' ! * # , Cpk ( # ' ! * ' # ( ' * ' + # # / ! # # ( * # ' ! -( . # . ' !, 4, % 0 " " ! . ' # = 0 = 1 2 . 0 1 3 9 > 10 9E3 C 1!@39 < 9E9 10 C 1!C31 9E3 C 0 1> 0!0>C K 3C 0> < < 9E9 3!BE9 > 1C 9E1 1 1!@9C B 9E1 1C C 1!C19 9E1 1 C 1> 0!0>C K 9C 09 > B 9E1 3!BE> 1 1E 9>@ 1 1!@91 1 9EC 1E 0 1!C<9 9>@ 0 1 1B 0!0EB K <C 1E 1 1 9>@ 3!B1> 1 3C 9>< 3 1!@3B @ 9>> 19 0 1!C39 9>B C 0 30 0!0@C K >C 11 3 0C 9>< 3!B3> 9 0@ 9E< 1 1!@<C 9 9EB 0B C 1!C1B 9EE C C 13 0!03B K EC 0< 3 E 9E< 3!BB9 < 1> 9>E 1 1!@31 1 9>B 3C C 1!C<> 9EC 3 C 1E 0!0>B K BC 13 9 1 9E0 3!B91 9 1> 9EC C 1!@31 9 9>@ 19 3 1!C<1 9E1 0 1 1< 0!0>C K @C 1C 9 9 9E1 3!B<> > 1E 9>> 0 1!@19 B 9>E 19 0 1!C3> 9>> 0 1 30 0!0@> K 0CC 1C < B 9>E 3!B99 9 0@ 9E< 1 1!@<C < 9E> 0@ C 1!C1B 9EE 0 C 11 0!039 K 01< 09 9 > 9E> 3!BBB 1 11 9EC > 1!@>C 9 9E0 0@ > 1!C<9 9EE C 9 0@ 0!03C K 0<C 0E E B 9>B 3!B<9 1 1> 9>0 00 1!@>1 E 9>E 19 1 1!C91 9EC 9 1 19 0!0>C K 1CC 10 3 03 9>3 C!10>
. ' # = 0 = 3 0 1 3 9 9 0E 9EE 1 1!@<9 C 9BC 0E 3 1!C9> 9B0 C 9 0< 0!0C> K 3C 0< 3 1 9BC 3!B@9 0 03 9B3 3 1!@E> 0 9B> 01 0 1!C1> 9B> 0 0 01 0!CEB K 9C 01 C 9 9B9 3!@1C > 13 9>> < 1!@9C 9 9>@ 19 3 1!C<1 9>@ 3 9 19 0!0>> K <C 10 < > 9>B 3!B91 0 1> 9>> E 1!@<B 1 9E0 1> 0 1!C<1 9E9 1 0 13 0!09> K >C 13 0 E 9>@ 3!B99 < 1E 9>3 < 1!@3> < 9>9 3C 0 1!C<9 9>@ < 3 13 0!0>C K EC 10 9 < 9EC 3!B9B E 1< 9>9 9 1!@3C 00 9>3 13 3 1!C3> 9>< 1 0C 13 0!0B1 K BC 0E 0C 3 9EC 3!B<1 0C 10 9<E 01 1!@91 3 9>> 1@ 1 1!C>C 9>> 9 9 1> 0!0BC K @C 10 @ 0C 9>C 3!B0B E 1C 9>9 @ 1!@<C > 9>E 1< 1 1!C9> 9>B > 3 13 0!0>1 K 0CC 0@ E B 9>> 3!B91 E 3@ 999 0C 1!@09 0C 99E 33 0C 1!CB> 9>0 E @ 13 0!0BB K 01< 11 E 09 9<E 3!B01 E 90 93< 0E 1!@19 03 93B 3@ 0C 1!C@1 99> @ @ 3> 0!1EC K 0<C 3E @ 0@ 93< 3!EC9 03 3> 91> 1< 1!@1> 0< 939 91 @ 1!C@C 99> 09 E 33 0!1<9 K 1CC 1E 0< 1< 933 3!E1B
. ' # = 0 = 9 0 1 3 9 E 19 9>> 3 1!@3C 3 9>E 1> 9 1!C>1 9>@ 3 9 19 0!0>> K 3C 10 > 9 9>@ 3!B91 < 3C 9<@ > 1!@31 9 9>C 30 < 1!CE9 9>E < 0 1E 0!0E> K 9C 19 < @ 9>1 3!B0B @ 30 9<C 0C 1!@11 3 9<E 3> 9 1!CB1 9>C 3 3 39 0!111 K <C 1B @ 00 9<1 3!EE9 @ 33 99< 03 1!@19 < 9<3 3B 9 1!CB1 9<< > < 39 0!13> K >C 30 B 01 99@ 3!E<B @ 99 939 03 1!@C1 00 939 9< 0C 1!0CB 9<C 00 E 31 0!191 K EC 30 0C 09 99< 3!E9> > 9E 939 03 1!@CB 0> 91B 9E @ 1!C@B 93@ 03 3 9< 0!3CB K BC 90 0C 0E 931 3!>BC 01 90 91< 11 1!@09 09 930 93 01 1!0C> 991 0C @ 3@ 0!1@C K @C 33 0E 19 91> 3!>B> B 9B 911 11 1!@0> @ 933 9B 0C 1!00B 990 00 01 3> 0!1B> K 0CC 93 E 1C 93C 3!>E9 0< >3 3@1 3C 1!BE9 0> 9C9 >9 0> 1!0>C 91< 0< 0< 9< 0!3>C K 01< 9> 0> 1@ 9C@ 3!>C1 0E << 3@9 39 1!B@C 0E 9C@ <1 11 1!0<B 90> 10 1C 93 0!3BC K 0<C <0 0< 33 9C0 3!<>B 1C <3 3B> 90 1!B@> 11 9C0 >3 09 1!03B 901 19 0C <9 0!901 K 1CC 9> 13 9C 3@0 3!<<1
. ' # = 0 = < 0 1 3 9 0C 1B 9<< E 1!@0B < 9<B 39 3 1!CEC 9>< < 3 1E 0!0B9 K 3C 1C @ B 9>3 3!B1B E 9E 931 09 1!@C> @ 93< <C > 1!0C> 93E @ E 9E 0!31B K 9C 9B B 00 933 3!><B @ >0 90B 01 1!B>> 01 90> >0 00 1!091 91C 03 01 << 0!9C9 K <C >0 B 0C 910 3!<B1 09 >3 3@@ 19 1!B>> 03 90C >1 0< 1!0<B 91C 00 01 <E 0!901 K >C <9 0< 1B 9C3 3!<>C E >E 3@< 30 1!@CC 0E 9C1 E0 0C 1!09B 9C> 1C 0C >9 0!9>9 K EC EC 01 13 3@< 3!9B> 0< E> 3B9 1< 1!B3B 0C 3@0 EB 10 1!11C 9C> 0< 0C >@ 0!9B9 K BC >@ 0B 1B 3B< 3!9<B 1C E3 3B0 1> 1!B1> 0@ 3B< E9 11 1!0@B 3@C 13 0< E1 0!<3B K @C E1 0B 3C 3BC 3!93> 0> EB 3E9 31 1!B99 1C 3BB EB 09 1!0E1 3@3 10 0< E0 0!<1B K 0CC E9 00 39 3B0 3!999 1< B1 39B 9< 1!B1> 39 3<1 @C 19 1!1CB 3>> 99 0E E3 0!<@9 K 01< E> 10 9< 3<B 3!3EC 1B 0C3 31< 99 1!EEC 3E 33C 0C1 30 1!1<9 3<< 9C 1< BC 0!>>C K 0<C BC 1E <C 393 3!301 11 B> 39C <1 1!B99 <C 39C @< 0< 1!0<C 3>< 9< 0@ E0 0!<@1 K 1CC EC 11 9> 3>1 3!9CC
. ' # = 0!33 = 1 0 1 3 9 3 03 9B0 3 1!@>B 3 9B3 09 C 1!C11 9B3 1 C 0< 0!C@9 K 3C 00 1 < 9B1 3!@0> B 1E 9>9 0 1!@0> 9 9>< 1@ 1 1!C<B 9>< C 1 33 0!1C> K 9C 13 B < 9>9 3!B1C 3 0B 9EE 1 1!@<> 9 9BC 0< 0 1!C1> 9B1 1 0 0< 0!C@B K <C 00 0 > 9B1 3!@0B > 0E 9E> 0 1!@99 < 9EE 0E 0 1!C1B 9EE 0 0 10 0!031 K >C 01 < > 9EE 3!B@> > 10 9EC 3 1!@9C 3 9E9 11 0 1!C91 9E1 1 3 13 0!0<9 K EC 0@ 3 < 9E3 3!B>9 > 33 9<< > 1!@11 < 9<@ 31 9 1!CEC 9>1 1 9 31 0!101 K BC 1E > @ 9<B 3!E@> 3 1> 9>B 3 1!@91 9 9>E 1> 3 1!C<> 9E9 1 C 19 0!09B K @C 1C 9 > 9EC 3!B<1 3 3B 9<3 > 1!@19 E 9<> 39 3 1!C>> 9<B 9 3 3< 0!13C K 0CC 31 1 0C 9<> 3!EBC 9 1@ 9<< 01 1!@<C 3 9<@ 33 < 1!CBC 9EC < 0 19 0!0<B K 01< 13 E 00 9<@ 3!B01 0C 3C 9<C 0C 1!@1C @ 9<@ 1E < 1!C<> 9<@ 9 < 31 0!11C K 0<C 11 E 0B 9<3 3!BC9 > 39 99< 0< 1!@3B 03 99B 33 > 1!C>9 99B 01 B 31 0!19B K 1CC 33 > 09 99E 3!E<C
. ' # = 0!33 = 3 0 1 3 9 < 10 9E3 0 1!@9C 9 9E1 1C 9 1!C9B 9E9 1 3 10 0!091 K 3C 0E < < 9E3 3!B>B 9 3C 9<@ E 1!@3B 9 9>0 31 3 1!C>B 9>1 9 3 30 0!1C> K 9C 3C < > 9<@ 3!EBB 3 31 9>C < 1!@39 9 9>C 33 3 1!CEC 9>3 9 1 30 0!1C1 K <C 3C 9 < 9>0 3!E@9 @ 3E 99B > 1!@C1 1 9<3 9C < 1!C@> 9<> 1 3 3@ 0!1<C K >C 33 B @ 9<C 3!E<1 00 <1 91B @ 1!BEC 3 91E >0 @ 1!0<1 99C 0C 9 9> 0!301 K EC 9> 00 B 93< 3!>>9 00 <B 910 0C 1!B>C 9 91C >C 0> 1!0E> 91E E E <@ 0!3@> K BC <B 0< 01 90< 3!<>B 0< <0 9C> 1B 1!B@9 09 91C <0 0< 1!039 90E 0@ 09 <C 0!3@9 K @C <9 0C 1@ 9CE 3!<EB B >< 9C< 11 1!BB1 B 909 >> 01 1!0>9 91> B 00 << 0!3@C K 0CC <B 03 0B 900 3!<>9 0E E@ 3E1 31 1!B3B 19 3B1 B> B 1!0<> 3BE 0B 0C B< 0!<B> K 01< E< 0B 3< 3E1 3!9CB 10 0C1 39C 3E 1!EB> 1C 3<@ 0C0 1C 1!191 3>B 1E 10 B9 0!>91 K 0<C @0 09 3E 3<B 3!319 1E 01C 30E 3> 1!E19 3@ 3C9 010 3> 1!3CB 31@ 3B 1E 0C> 0!B1C K 1CC 0C> 3B 3< 310 3!091
. ' # = 0!33 = 9 0 1 3 9 < 30 9<E E 1!@31 1 9>3 1B E 1!CBC 9>E 0 > 1> 0!0B1 K 3C 1> < @ 9>C 3!BC> B 9@ 93E > 1!BB1 E 93B 9B E 1!00C 991 E 0C 90 0!3CC K 9C 93 > < 99> 3!ECB 0B E3 3BE 11 1!B1> 03 3@< EB 09 1!0B> 9CC 0> 09 EC 0!<CB K <C >@ 0> 11 3@3 3!9EB 0E B0 3B@ 03 1!E@> 0< 3@C BC 0< 1!0@C 3@B 03 01 EE 0!<3> K >C E0 0> 0@ 3@9 3!9E1 0> @9 3<> 39 1!B0> 11 3>B 0C9 > 1!0BB 3>@ 1C 01 @@ 0!>B1 K EC @3 0B 1B 3>0 3!309 01 003 399 30 1!EBB 0B 3<C 0CB 19 1!1E> 3>@ 0@ 0@ @3 0!>E1 K BC 0C1 0E 1@ 3<1 3!1>1 13 009 331 30 1!E91 1> 33C 01> 0B 1!1E1 393 31 0< 00C 0!EB9 K @C 00C 13 1> 390 3!0@> 1> 013 30< 3> 1!E11 13 30> 031 1> 1!30C 31@ 1E 19 01C 0!BEC K 0CC 00@ 3< 1B 30B 3!C@C 39 0<3 1EB 3E 1!>99 1B 1BC 0<< 3E3 <!C@C 1@0 30 3< 093 1!C>C K 01< 09E 3> 39 1B3 1!@C> 3C 0<E 1<> <E 1!>BC 1@ 1E9 0>0 3> 1!9CB 1@9 31 33 090 1!C91 K 0<C 09E 3E <0 1>< 1!B>B 39 0B> 1C> E9 1!>9C 9< 139 0B1 3@ 1!93C 191 3E 9< 0E> 1!30C K 1CC 0B0 90 >B 10C 1!>09
. ' # = 0!33 = < 0 1 3 9 0C 9< 93> @ 1!BBB 01 91@ 9E 01 1!00B 99C B E 9< 0!309 K 3C 3@ 0E 00 933 3!>E> 00 BC 3@1 0E 1!B3C @ 3@@ BC 01 1!0@C 9CC 03 0C EE 0!<1B K 9C BC @ 0E 3@9 3!9<C 19 00< 33< 1> 1!E1> E 3<@ 010 03 1!1BC 3<B @ 0B 00< 0!EBC K <C 000 0E 1> 39> 3!109 1C 01> 31E 1E 1!E11 1< 30@ 033 13 1!3CB 33B 30 0E 009 0!B09 K >C 00@ 11 19 33< 3!0<C 19 0<E 1B< 39 1!><B 1E 1B9 0>C 1@ 1!3B1 1@3 1< 1E 0<< 1!CBB K EC 0<B 31 30 1E@ 1!B>1 1> 0EE 1>1 3< 1!>01 1< 1>B 0E3 39 1!931 1E@ 1@ 1> 0>> 1!0<B K BC 0E0 1E 3E 1>< 1!E@1 19 0B0 1<E 3B 1!>0B 3B 1<3 0E< 39 1!90C 1>C 3E 3C 0E3 1!131 K @C 0B1 1> 3E 1<< 1!E3C 13 0@1 19< 9C 1!>C9 39 19< 0B@ 31 1!93B 1<C 3< 19 0@0 1!301 K 0CC 0@3 1@ 91 13> 1!>91 91 101 0@E 9@ 1!<C> 13 11C 11> 30 1!<3C 10E 1E 3< 110 1!<1C K 01< 10B 90 93 0@B 1!991 3> 113 0@0 <C 1!<0C 3C 1C1 190 1E 1!<3C 0@E 3> 30 13> 1!>01 K 0<C 13@ 3B 3B 0B< 1!33B 93 1>E 0<1 3B 1!3EC 3E 0>B 1>1 33 1!<B1 09> 30 3B 1B< 1!@19 K 1CC 1E< 39 9E 099 1!01C
, 4+ # ,% ,+ * ! " # # / N---N ' 2 * U * ' * (' N---2 K C!E<= U K 0= ' K 1CCC= (' K C= N---N # / ( ' N---K C= ( : ' - (' ; V 0= K W 0= K 0 <CC= U : ; K ' 3U 0: :: ' W (' ;H1;;= = / : ; K :: ' W (' ;H1;= U U# K # : U ;= U U# H U VK 2 = ' K :: ' W (' ;H1;= (' K :: ' W (' ;H1;= = 2U ## 0: ; K U U# H U = =
N---N X ' 3U 0!# N---F U G K ' 3U 0: / ;= K -0= ( KK -0 N---N * * & "* N---K / = K 0CCCC= & " K 3!9= K C!C<= N---N 2 # / # ' # ' # N---0 K # :3!11E3* C!C<1* * 0;= 1 K # :3!11E3* C!C<1* * 0;= 3 K # :3!11E3* C!C<1* * 0;= 0 K C= 0 K C= ( 0 KK C= # U 0 K ' : * J J* 0;= # U# 0 K # : # U 0* 1;= # U # 0 K : # U 0*C*1;= 0U K : # U # 0;= 0U :0;V C 0 K0= U 0 K :& " - # U# 0;!H:3Y # U # 0;= 0 K 0 W0= = 0 KK <CC= = = = 1 K C= 1 K C= ( 1 KK C=
# U 1 K ' : * J J* 1;= # U# 1 K # : # U 1* 1;= # U # 1 K : # U 1*C*1;= 1U K : # U # 1;= 1U :0;V C 1 K0= U 1 K :& " - # U# 1;!H:3Y # U # 1;= 1 K 1 W0= = 1 KK <CC= = = = 3 K C= 3 K C= ( 3 KK C= # U 3 K ' : * J J* 3;= # U# 3 K # : # U 3* 1;= # U # 3 K : # U 3*C*1;= 3U K : # U # 3;= 3U :0;V C 3 K0= U 3 K :& " - # U# 3;!H:3Y # U # 3;= 3 K 3 W0= = 3 KK <CC= = = = N---N O N---U U K
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