6 sigma??

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6 sigma??

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Title: 6 sigma??

1
6 sigma??
2
6sigma???
3sigma????? 6sigma?????
????1015????? ????66,807????? ?????? ??????????? ??????? ??????99 ????CTQ ????5????? ????3.4????? ???????????? ??????????? ????,??,??,???? ????99 ???????????CTQ
4sigma????30?????1???????? 5sigma??????????1??????
?? 6sigma????????????1????????
3
6sigma???
3sigma????? 6sigma?????
???54,000???????? ?????????????????40,500? ???2????????? ???2?????????? ??????5????? ????1350??????? ?????54,000??? 25????1??????? 100????????????????3? 16????1??????? 100??6????????? ????????10???1????? 20??????????? ????35???
4
6sigma??(????)
?? Tools Tools
Define (??) 1)Process Mapping 3)Pareto Analysis 2)Logic Tree 4)QFD, FMEA
Measurement (??) 5)Gage RR 7)Process Capability 6)Rational Subgroup
Analysis (??) 8)Hypothesis Test 10)Graph Analysis 9)Regression
Improvement (??) 11)DoE(Design of Experiment) 12)ANOVA 11)DoE(Design of Experiment) 12)ANOVA
Control (??) 13)SPC 13)SPC

6sigma???????,???????????

5
Yf(x)
Question 1) Y?X??????? Question 1) Y?X???????
Y X1Xn
???? ????
Output Input
?? ??
?? ????
??????? ????
6
Yf(x)

Question 2)??X????,????????????Y?
6sigma???????????(CTQ)???,??????

7
6sigma???????
?? ???? Focus
Define(??) 1)?????/??????
Measurement (??) 2)????????CTQ 3)??Y????? 4)??Y????? 5)?Y???????? Y Y Y Y
Analysis (??) 6)????Y??? 7)????Y??? Y X1Xn
8
6sigma???????
Improvement (??) 8)????????????? 9)?????????????? 10)???????(?????) X1Xn ????????Xi ????????Xi
Control (??) 11)???X????? 12)??????????????? 13)???????????????????? ????????Xi ????????Xi ????????Xi

6Sigma Process??D-M-A-I-C5??????????13??
6Sigma?????????,????,???????,?D-M-A-I-C???????????
?????,??1?????????1???????????????????????

9
?????????

???????
??????????

10
?????????

?????
S(???Total Sum of Squares)?????
????(Unbiased Variance)S?????(n-1)
???????or????

11
?????????

??????
??(Parameter)??????????
???(Statistics)????????

12
?????????
?? ?? ???
??(Mean) ??µ ????
?? (Variance)
?? (Deviation)
13
?????????

Sigma???
Sigma?????,????????
Sigma????????????????(Standard Deviation)???(Varia
tion),?????????????
Sigma????????????,???Sigma?DPU(????,Defect Per
Unit),PPM??????

14
?????????

???????Sigma????,???????????
Sigma?????????,?????

15
?????????

???????????????(s)????????(T)??????(USL or
LSL)????????3???,?????3Sigma??????

16
?????????

????????????60?,????5???????,?????????,70?????????
????

17
?????????

????N(60,52)
??????N(0,12)
70?????Z-??
???????75???,????????Z2??2s?
Z??????????(s)????????????????(USL,LSL)???????

18
?????????

Z-????
70???????????
????????1
?????X????(µ)??????????(s)???Z????
??????(or??)?X??????????????????????????
Z??????????,??????????,???Z??2.0,???????1?????
??0.0228?

19
Z????
20
???????? Z-?

21
???????? Z-?

?????(??)?????????
?????????,???????????
???????????????(Z)????6 s??,????????????

22
?????????????????
??????? ???????
?????????????? ????????????????
Zst(sst) Zlt( s lt )
Cp Cpk
?? ??????
?????????? ??????????
6 s Zst6.0,Cp2.0 6 sZlt4.5,Cpk1.5
Zst3Cp Zlt3 Cpk

???????????????????,?ZltltZst????
ZshiftZst-Zlt ?ZstZlt1.5

23
6 sigma?????????

????????(1.5 s)

24
???????????????
???? ??????? (??????) 1.5s??????
1s 317,000 697,700
2s 45,500 308,700
3s 2,700 66,810
4s 63 6,210
5s 0.57 233
6s 0.002 3.4

6Sigma????????3.4PPM,?Cp2.0,Cpk1.5

25
4Block Diagram
Poor
2.5 2.0 1.5 1.0 0.5
A B
C
Z shift ????
Good
1 2 3 4 5
6
Z st
Poor
Good
??
26
4Block Diagram

A????????,????????
B???????,???????
C??????,??????
DWorld Top?????

27
???????

??????
Process Mapping
Process Mapping????????,??Process???
???????????????
Process Mapping??
??Process??(????????????Process)
?????????Process?????

28
???????

??????,????
????Process,????
??Key Process??(Yield, Cost, ????,????,Cycle
time?)
??????,?????(Process Loss?????/??Cycle
time/????/Flow??)
QFD(Quality Function Deployment)??????
QFD??????????,???????????(??),????CTQ???,?????????
?

29
???????

QFD Process
??????,???????,????????????????????????
?????????,????????????????
??????????????????????,????????????????,??????Part
??(CTQ)
?????????????(CTQ)????
QFD????????????????,??????????
??QFD??????????,???????CTQ,??????

30
???????

FMEA(Failure Modes Effects Analysis)?????????
FMEA?????????????????????,?????????????????
FMEA Process
????????Brainstorming???????????
????????????????????
????????????????
????????????????

31
???????

?????
??????????????
????80????20??
??????????????
????????????,??????,??????????????????

32
???????

???????????
Brainstorming??????????????
Brainstorming??
Free Wheeling?Team??????????Idea
Round Robin???,Team?????Idea
Card Method????,Team??Idea?????,?????

33
???????

Brainstorming?????
????
??Idea????
Idea??????????
???Idea????
????????
Logic Tree(Structure Tree)
????????,??????
Break-down(??)?????MECE(??????????)
MECE(Mutually Exclusive and Collective
Exhaustive)(???,????????)

34
???????

?????????Benefit??(??/????)
?????,??????
??????????
??????,?????????????
??????
?????????????????

35
??(Measurement)
36
?????

?????

????
????/Bottle Neck/Issue ??
37
?????

?????(?????)
Inch or??????????????
????????????
?????(?????)
??????????????
?????????

38
?????

????(White Noise)
White Noise????????????????(????)
????????????????
???????
??????????????
Z.st???

39
?????

????(Black Noise)
Black Noise??????????????,?????,????????(????)
???????????
?????,?????????????
?????????????,?????????

40
???????????
Line1
Line2
Line3
???1 ???2 ???3
???4 ???5 ???6
???7 ???8 ???9

?????Line 1,2,3????(?Line????????)????
?????Line????????????

41
?????

Rational Subgroup(????)
?????????,???????????????????????
Rational Subgroup??Subgroup????????,Subgroup??????
??,???Grouping
?????????????????
???????????????????????????,?????

42
????

???????

Short-term Capability (6s)
st
st
? ?
st
st
Long-term Capability (3s)
lt
SL
SU

???????,?????????(4M)??,????????????????

43
????

???????
????????,??????????????????????????(????)?,??????
??????????
Six Sigma???????????(or????s)?,????6?????????????
????

44
????

??/?????????
???????????????,?????????????????,????????????????
,??,????????,??????,???????????
Short Term Process Capability Index????????
Zlt(slt),Cpk
Zlt3Cpk

45
????

???????????????????,???????????,???????????,??????
???????,??????????????????????????
Long Term Process Capability Index????????
Zlt(slt),Cpk
Zlt3 Cpk

46
Gage RR

Gage RR???????
?Blind?????
??????????
??????????????????????
????????
???????????,???Gage RR?????????????

47
Gage RR

????Tolerance????Gage?????,?Study
Var?20???,???????Process
Gage RR????,??????????????????????,????????,???6s
Project???????????????????

48
Gage RR

???????Gage RR
??Parts????????????,?gono go?
1V?????,
2????????20???

49
? ?
???? ???1 ???1 ???2 ???2
???? 1 2 1 2
1 G G G G
2 G G G G
3 NG G G G
4 NG NG NG NG
5 G G G G
6 G G G G
7 NG NG NG NG
8 NG NG G G
9 G G G G
10 G G G G
50
? ?
???? ???1 ???1 ???2 ???2
???? 1 2 1 2
11 G G G G
12 G G G G
13 G NG G G
14 G G G G
15 G G G G
16 G G G G
17 G G G G
18 G G G G
19 G G G G
20 G G G G

??????4???????????,????????
Gage RR320 10015

51
Gage RR

?????Gage RR?Minitab??
Gage RR?Graph??
P39

52
Gage RR

53
Gage RR

X bar???
?????????,?????????
??????50??????????,????????
???????????????????,??????????????????,???????????
????
?????(???,????)?????????,????Parts??????

54
Gage RR

R???
?????????????
??????????????

55
Gage RR

Number of Distinct Categories4
??????????????????

4?Categories
????????????,?3????????2??????4????????,??????????
???????,??????????????????(?????????????)???????
56
Gage RR

Number of Distinct Categories????
Number of Distinct Categories01???(??????)
Number of Distinct Categories24????????
Number of Distinct Categories5?????

57
Gage RR

?????Gage RR?Minitab??
Gage RR Study-ANOVA Method
P36

58
Gage RR

59
Gage RR

Study Var???????????????????????(Gage
RR)(???????20??)
Tolerance????????????,??????????????(????Gage
RR???????)

60
Gage RR

61
Gage RR

?????Gage RR?Minitab??
??Monitor Cover?Six Sigma Theme
Spec2.31.5
???????,3?????10???????2?

63
Gage RR

??????Gage RR??
CTQ???Spec?2.0000.015?

?? ???1 ???2 ???(1-2)
1 2.003 2.001 0.002
2 1.998 2.003 0.005
3 2.007 2.006 0.001
4 2.001 1.998 0.003
5 1.999 2.003 0.004
????? ?R0.015
64
Gage RR

?????? ?R/50.015/50.013
????(5.15/1.19)(R)4.33(0.003)0.013
???????(0.0130.030)10043.3
??)????????????????(???4.33)???????5.15/d?????,
d??????,5.15?Gage????????5.15s99??

65
?????????d?
???? ???? ???? ???? ????
???? 2 3 4 5
1 1.41 1.91 2.24 2.48
2 1.28 1.81 2.15 2.40
3 1.23 1.77 2.12 2.38
4 1.21 1.75 2.11 2.37
5 1.19 1.74 2.10 2.36
6 1.18 1.73 2.09 2.35
7 1.17 1.73 2.09 2.35
8 1.17 1.72 2.08 2.35
9 1.16 1.72 2.08 2.34
10 1.16 1.72 2.08 2.34
66
Gage RR

Gage RR??
?????
???2?????5???
???????????
??????????????????
?????
????2-3??????10???????2-3?
????????????????,??????????

67
Gage RR

??????????
??(Linearity)?????Gage???????????????????????????
???,????1????????????

68
Gage RR
69
Gage RR

??????????
???(Stability)???????????????????????????????????

Time1
70
Gage RR

??(Bias)???????????????????(Accuracy)

71
Gage RR

???(Repeatability)1????????????????????????????

Repeatability
72
Gage RR

???(Reproduceability)????????????????????????????
???

???1
???2
???3
Reproduceability
73
Gage RR

Gage RR????
Gage RR???,????????????????????????,???????,?6s
Project???,???????????????????

????????Gage ??
20?? Accept
20-30 ???????????????Accept
30?? ?????
74
Gage RR

?????(?????)
?????????????/Spec?????10??????????
????????????????
?)?????0.020?,???????0.002
Gage RR?Sampling??
???????,?????Spec????????,????????????

75
Gage RR

Gage RR????
?????????????????
Gage RR Study
Gage RR Study???3?
???(Repeatability)
???(Reproduceability)
??????
???Process?Spec????????????????????

76
Gage RR

?????? ????? ??Error??

77
Gage RR

Gage RR???
Gage RR????????????
?????????(Gage????????)
??????????(or ???)
???????,????????????????(?????????,?????????Y???
X??)

78
?????

????Rational Subgrouping
Rational Subgroup?6 Sigma?????????
????????????????????????
?????????????????
????????????

79
?????

Rational Subgroup????????????????????X??,??5M??
?????
Man?????,??????,?????
Machine???????,???????
Material??LOT,????,????
Method????????????
Measurement??????,???????

80
?????

Rational Subgrouping??
????TV Back Cover??????,?????????????Rational
Subgrouping??
?????X???????
?????????????????
????????????
??????????????????????
???????Lot,??Lot?????

81
????

????????
??????????

SL
SU
82
????

?????????

K
SL
SU
M
83
????

????
K????(??K0,CpCpk)
M(Mid-range)?????
T(Tolerancne)??
SU(Upper Spec)????
SL(Lower Spec)????

84
????

????????????

SU
85
????

????????????

86
????

?????Minitab??
?????????????,??????,?????????????Project,????????
,????????????????X????????Y????
X????,??,????,???,??,????

87
????

88
????

????????
P47

89
????

90
????

?????Minitab??
????????
P48

91
????

??Submit Command
P49

92
????

?????Minitab??
P50

93
????

????????????Cp,Cpk,Cpu,Cpl?????????????Pp,Ppk,Ppu,
Ppl
??????????,??????????,??????Zst,??????????????????
?????????????????????????????????
??????????,?????????,?????????,??????????????Zlt?

94
????

?????Minitab??
P51

95
????

?????Minitab??
P52

96
???????

????
D(Defect)??or??(??)
?????????????????????????
?????????????????
DO(Defect Opportunity)????(??)
?????????(??)???????
????????????????

97
???????

U(Unit)??
???????????
?????
DPU(Defect Per Unit)
???????????
DPO(Defect Per Opportunity)???????
??Unit???????????????????

98
???????

DPMO(Defect Per Million opportunity)(????????)
1,000,000????????
DPO 1,000,000 ??Six Sigma??
P(ND)None Defect???
????????????
P(ND)1-DPO

99
???????

DPU/DPO/DPMO/P(ND)??
???100????,????100?????,??????10???,
DPU/DPO/DPMO/P(ND)?????
DPUD/U
DPU100/1001.0(100)???????,?????????1????

100
???????

DPOD/(UOpp)
DPO100/(10010)0.1(10)?????????????????1???????
?10?
DPMODPO1,000,000
???DPMO?0.11,000,000 DPMO
P(ND)1-DPO1-0.10.9(90)

101
???????

??????????
??????
??
Y??
DPU?????
r
e????2.71828

102
???????

r0?
?Ye-dpu
?????????,Y???0

103
???????

Process Yield(??)
??750???34?????,??DPU/DPO/DPMO/Yield/Sigma?????(??
??10?????)
DPU??????34 7500.0453
DPO???(??????)34 (750 10)0.00453
Yield??Ye-dpu2.7138-0.0450.955995.6

104
???????

DPMODPO 1,000,0000.0045 1,000,0004,500PPM
?????45,000PPM???
SigmaZinv(0.9556)1.5(??)1.711.53.21
Zinv??Z?????????,???????????

105
???????

?????
YFT(First Time Yield)(???????)
???????????????
???????????????????
YRT(Rolled Throughput Yield)??????????
????????????????????????,????????????
????????????????????,??????????

106
???????

YNA(Normalized Yield)????
???????????????
?????????????????

107
??????
????(YRT) ???????(YF)
??????? ???????
?????????? ???????????
????????? ???????????
???????? ??????????
????????????? ?????????????
YRTe YFS/U
YY1Y2Yn S????
U????
108
???????

VFT(First Time Yield)

109
???????

??A???100?Unit(??)
???70??????????
???30?????????
15???????,15????
?????Final Yield(YF)?????85
?First Time Yield(YFT)???????????,???????YFT?70?

110
???????

YRT(Rolled Throughput Yield)
??A?3???????????,YRT/YND????????

??1
??2
??3
YFT80 YF100
YFT70 YF90
YFT90 YF95
111
???????

YRF???????YFT??
YRT0.80.70.90.504(50.4)
??????
??????????
??????,????????????
YND(Normalized Yield)
??n??????

112
???????

??YND(Normalized Yield)
?????YFT79.6
????????????,?YND(Normalized Yield)????Sigma?
??YRF???????????(?????)
??????(??)?????,??????

113
???????

???????????????
Process Mapping??????????????????

114
???????

YRFY1Y2Y3Y4
0.990.910.990.991/30.970.98 0.9035
YNA(YRT)1/3(0.9035)1/40.9749
??(??)??1-0.97490.0251
????????0.0251??Z?,??Z1.96

115
???????

????(YRT)Minitab??
P62

116
???????

????(YRT)Minitab??
P62

117
???????

????(YRT)Minitab??
P63

118
???????

????(YRT)Minitab??
P64

119
???????

????(YRT)Minitab??
P64

120
??(Analysis)
121
Graph??

??????
????????,??????
???????????????Focusing
????????????????
?????
???????,??(??)Graph???

122
Graph??

?Graph??????????
Graph????,?????????????,??????????
???Graph????,???????,??????????

123
Graph??

Graph???Minitab??
???????Compressor(???)????????????????,???3?????3?
???,???3???????????

124
Graph??

??Histogram(???)
GraphgtHistogram
P67

125
Graph??

126
Graph??

??Plot
GraphgtPlot
P68

127
Graph??

128
Graph??

??Box Plot
GraphgtBox Plot
P69

129
Graph??

130
Graph??

??Matrix Plot
Graphgt Matrix Plot
P70

131
Graph??

132
????(Hypothesis Test)???

????????
?????????????,?????????????????????????????????
??????(??)
???Flatron Monitor????????????
LG Digital TV?????Digital TV?????
6s????Tool??????????????Tool?????
019 PCS????????????

133
????(Hypothesis Test)???

?????????
???(Null HypothesisHo)?????????
?????????,?????????(or??)?
???????
????(Alternative HypothesisHi)????????????
???????????,????????????
Ho????????(?????????)

134
????(Hypothesis Test)???

?????(Type ?Errora)???????,????????,????????
?????(Type ? Errorß)???????,????????,???????
?
?????(Test Statistic)??????????Ho,?????????????
?????(Significance Level)??????a0.05(or0.01,0.10
)Ho????????

135
????(Hypothesis Test)???
136
????(Hypothesis Test)???

??????
???????Sample(??)???????
Hoµ1µ2
Hoµ1µ2µ3µn
Ho s1s2
Ho s1s2 s3 sn

137
????(Hypothesis Test)???

??????????????
?????H1µ1?µ2
?????H1µ1 lt µ2
µ1 gt µ2
?????H1s1? s2
?????H1s1 lt s2
s1 gt s2

138
????(Hypothesis Test)???

???????
???????Z,T-test???
??????????????????(F-test)
F-test???2?????????
???????x2(chi-Square)???
??????

139
????(Hypothesis Test)???

????????????
???????????
??????,?????????,???????????
??,???????,???????/????????
??,???????????????????????

140
????(Hypothesis Test)???

?????????
??????????(Ho,Hi)
???????(a0.10,0.05,0.01)
???????(Z,T,Chi-square???)
???????
?????????,????
P(Probability)???lta???????(H1)
P(Probability)???gta???????(Ho)
??????????????

141
????(Hypothesis Test)???

???????????

???
???(Ho)??
???? (H1)??

???
???(Ho)??
???? (H1)??

???
(a)
142
????(Hypothesis Test)???

????????
??????????????????(Ho)
??????????????????(Ho)
0?????????????(Ho)
0?????????????(Ho)
Minitab?????
P-Value???a??????(Ho)
P-Value???a??????(Ho)

143
????(Hypothesis Test)???

?????Minitab??
?????Transmission Housing?10CTQ,10?CTQ?8?Fixture
Brake??????,??????8????Fixture?????????,??Fixure?
???????,?X??????????????

144
????(Hypothesis Test)???

?????Minitab??
P76

145
????(Hypothesis Test)???

146
????(Hypothesis Test)???

?????Minitab??(1???????)
P77

147
????(Hypothesis Test)???

148
????(Hypothesis Test)???

?????Minitab??(1???????)
P78

149
????(Hypothesis Test)???

150
????(Hypothesis Test)???

?????Minitab??(1???????)
P79

151
????(Hypothesis Test)???

?Sample??????Target ???????????
?,????Sample?Target????(Ho??,H1??)
??,???????Fixture 1?????Target Mean??????

152
????(Hypothesis Test)???

?????Minitab??(2???????)
P80

153
????(Hypothesis Test)???

154
????(Hypothesis Test)???

155
????(Hypothesis Test)???

X2(Chi-square)
?????(Goodness of fit test)
?????????or???????????????
???????????????????????
????
HoP1P2Pn
H1P1P2Pn
????????????50??????????

156
????(Hypothesis Test)???

???(Contingency Table)
??????????????????
???????????????????????????,?????????(????),???(?
???)???????
????
Ho??(???????????)
H1??(???????????)

157
????(Hypothesis Test)???

???(E),???(O),X2???
???(Expected Frequency)????????????
???(Observed Frequency)?????????????
X2????

158
????(Hypothesis Test)???

X2(Chi-square)???
?3???Monitor????????????????,???????(???)?(???)???
???????,??????,???N309?Monitor????4?????????
??X2(Chi-square)??
???(Ho)????????????????(????)
????(H1)?????????????????(????)

159
????(Hypothesis Test)???

????
A??
B??
C????
D????

160
????(Hypothesis Test)???
??? A B C D
1 15 21 45 13
2 26 31 34 5
3 33 17 49 20

????
???(Ho)???????????????(??)
????(H1)????????????????(??)

161
????(Hypothesis Test)???

?????Minitab??
P84

162
????(Hypothesis Test)???

163
??(Improvement)
164
????(ANOVA)???

???????(ANOVA)?
?????,?????????????????
?????????????????????????????????????????,??Y???
(???)????????????????????
??X???,?????????Y????

165
????(ANOVA)???

??????????Y???(???)???????????,??
???????????????
?????????
??(Factor)???????????
??(Level)??????????
???(Sum of square)?????????,?????????
??Balance/Unbalance????????????????????

166
????(ANOVA)???

???????
One Way ANOVA??2???????1??????
Balance ANOAV??2????????
?????(DoEDesign of Experiment)??????,????????Y
????????????

167
????????

????????
???????
?????(????)Y
????(????)X
???????
??????
????????
????
????
????

168
????????

??????
???????????
??Y(????)????X(????)????????
???????,????????
????????
??????????
????????????????
??????????

169
????????

?????(????)Y
??????????Y
?????(Logic Tree?),??Yn???????X????
??????????????63???,???????
???Y???,?????????????????

170
????????

?????????????,??????????
??????????,???????,????????????
??????????,???Y??Gage RR,?????20

171
???????

????(????)X
???????
??????????????
?????????????
Blocking??(???????)
????

172
???????

??????
??????????????????
????
?????
Flow Chart
??????
?????
?????
?????????
Process Mapping
Rolled Through Yield

173
???????

????
?????????????,?????,??????????????????????,
????????Blocking?
????????
?????????????????????????????,???????????????????
???????????

174
???????

??????
???????????????????????
????????????????,?????2??
Y??????????????????
??????????,?????????,?????????????
????????????????(????????,??????????????)
??????????????????,???????,????????

175
???????

??????
????????10?????
???
???
???
???
????
????
Noise??
Blocking
Sample???
??

176
???????

???????
???
??????????????????????????
???
???????????????????????
???????
??Unit???
???????

177
???????

???
?????????,??????????????
??????????
???????????
???
?????Run ??Sample?????,??????
??
?????,???????

178
???????

????
????,?????,??????,????????????????????,??????
Noise??
????????,????????,?????????????Noise??,??????????

179
???????

Blocking
Block???????,??????????????,????????Blocking??
Blocking???????,??????,?????
Blocking????Blocking????,????????,??????
?????
???????????,?????,??

180
???????

???
??????????????,???????????,????????????????,3?????
?????????????
?????????
??????????,????,?????????????
?????????
????????????????????
?????????????????

181
???????

??????,??????????????,??????
??????????????????????
???????
???????????,???Mechanism,????????????????
??????????,??????????

182
???????

????
GRAPH??
Capability Analysis
Histogram
Box Plot
Pareto
Scatter Plot
Cube Plot
Main effect plot???????
Interaction plot???????

183
???????

????
P-value,?????
T-test,F-test,Chi-square
?????(ANOVA Tables)
?????(Regression)

184
???????

????
???????????
??/??/???????????????
?????????????????
???????(???)????
????????????
??????????
??????Y???????????
????????????

185
???????

????????????????
??????????
????
???????????????????????
??????????????????????????
????????????????????????(??????)

186
???????

????
?????????????
??????????????
???????????????????????
/-??????????????,????2?????????

187
???????

???????
???????????
?????????????
?????????????????
?????????????????????????????????
?Cost(????)???,???????
???????????

188
???????

????????????????
????????Y???????
???????????????
???????????
?????????CTQ
???????,????????

189
?????

?????
???1???????????????,???????????????
??????????????????????,?????????????,??????,??????
????????????????????????(A160?,A265?,A370?,A47
5?),????3?,???12??????????????????????,?????

190
?????

?????(A)?????(??Kg/mm2)?????

???? ???? ???? ????
A1 A2 A3 A4
????? 8.44 8.59 9.34 8.92
????? 8.36 8.91 9.41 8.92
????? 8.28 8.60 9.69 8.74
191
?????

??????Minitab??
P97

192
?????

193
?????

194
?????

195
?????

196
?????

197
?????

?????
??2????????????
?????????????(Yield,)?????????????????????????,??
?????,??????
??????
????(A)A1(180 ?),A2(190 ?),A3(200 ?) , A3(200 ?)
??(B)B1(??M???),B2(??Q???),B3(??P)

198
?????

??????

??A ??B A1 A2 A3 A4
B1 97.6 98.6 99.0 98.0
B2 97.3 98.2 98.0 97.7
B3 96.7 96.9 97.9 96.5
199
?????

??????Minitab??
????????
P101

200
?????

P102

201
?????

P102

202
?????

P103

203
?????

P103

204
?????

??????A3200?,????B1?????
?????????????,???????,??????????????????

205
?????(Factorial Design)

????????
n???,????????k?????,????????????????
???????
2n???n?,???????2??
3n???n?,???????3??

206
?????(Factorial Design)

???????
???????????????
???????????????
22??
????(A0,A1)????Mold(B0,B1)??????????(balance)???4?
???

207
?????(Factorial Design)

????

A0 A0 A1 A1 ??
B0 31 165 82 110 88 72 352 517
B0 45 165 82 110 88 72 352 517
B0 46 165 82 110 88 72 352 517
B0 43 165 82 110 88 72 352 517
B1 22 84 30 37 38 29 134 218
B1 21 84 30 37 38 29 134 218
B1 18 84 30 37 38 29 134 218
B1 23 84 30 37 38 29 134 218
?? 249 249 486 486 735
208
?????(Factorial Design)

??????Minitab??
P106

209
?????(Factorial Design)

P106

210
?????(Factorial Design)

P107

211
?????(Factorial Design)

P108

212
?????(Factorial Design)

P108

213
?????(Factorial Design)

P109

214
?????(Factorial Design)

P109

215
?????(Factorial Design)

P110

216
?????(Factorial Design)

P110

217
?????(Factorial Design)

P111

218
?????(Factorial Design)

????(mix)1??,mold-1?????????
mold?????(mix)????????
Main effects plot????????,????????????

219
?????(Factorial Design)

Interaction Plot
P112
???????(mix,mold)??????????,??????????????????

220
?????(Factorial Design)

???????
??2?????????,?????????3????????,????????,????????

Y
Y
Y
X
X
X
?????? (?????)
???????
????????
221
?????(Factorial Design)

Cube plot

222
?????(Factorial Design)

??????????????(mix)1??,mold-1??
???????????
mold?????????????

223
?????(Factorial Design)

23??
???????????????,??????????????????????Filter(???)?
??,Filet???????????????,???????2??????

224
?????(Factorial Design)
Factor Level Level
-1 1
A. ????(Temp) ?? ??
B.??(Time) ? ?
C.?????(Conc.) ? ?

??Run??2?(?2???)?????(Yield)?,???????????????2?(?2
???)?,?????1?????

225
?????(Factorial Design)

????

RUN Temp Time Conc. Yield
1 -1 -1 -1 65
2 1 -1 -1 43
3 -1 1 -1 46.5
4 1 1 -1 43
5 -1 -1 1 59.5
6 1 -1 1 44
7 -1 1 1 51
8 1 1 1 43
226
?????(Factorial Design)

??????Minitab??
P115

227
?????(Factorial Design)

P115

228
?????(Factorial Design)

P116

229
?????(Factorial Design)

P117

230
?????(Factorial Design)

P117

231
?????(Factorial Design)

P118

232
?????(Factorial Design)

P118

233
?????(Factorial Design)

P119

234
?????(Factorial Design)

P119

235
?????(Factorial Design)

Main effects plot
P120

236
?????(Factorial Design)

?Yield?temp/time/conc?????plot Graph
????????Low Level(-1)???(-1)????(?????),????High
Level(1)???(1)?
?????????????????,????????????????
???????
???????????

237
?????(Factorial Design)

Interaction plot
P121

238
?????(Factorial Design)

TempTime?????????????,?????????,????????
TempConc??????,?????????,?????????
TimeConc??????,???????????????????

239
?????(Factorial Design)

Cube plot(?????)

51
44
46
1
43
time
60
44
1
43
65
conc
-1
-1
temp
1
240
?????(Factorial Design)

temp(1??),time(1?),conc(1?)??temp(1??),time(-1
?),conc(-1?),?????
????,????????????????,???????????????
?????,?????????,???????????(???????????????????)

241
?????(Fractional factorial design)

????????(Fractional factorial design)
????????????,???????,????????????
???????
??????????????????
???????????,???????

242
?????(Fractional factorial design

??????????????????????????,??????????????????????
????????,????????????????(2n3n??????)
??,???????????????????????

243
?????(Fractional factorial design

???????????(Fractional factorial design)
???????????Screening?
???/?????????????,???????
?????(Fractional factorial design)???
?????????????????????
?????,????????

244
?????(Fractional factorial design)

25??
P124

245
?????(Fractional factorial design)

25??
?32????16???????
X1X2X3X4X5-1?
X1X2X3X4X51??
???????????,?????????
?????????,??????????
??????????????

246
?????(Fractional factorial design)

??????????,??????,???????????????,???????????
??X1X2X3X4X51?16???
????????????????
?????????????????

247
?????(Fractional factorial design)

P125

248
?????(Fractional factorial design)

25??
??16???????????
??2????2?
??2????2?
??2????2?

249
?????(Fractional factorial design
1
X5
1
X2
-1
-1
1
-1
X3
-1
1
X1
1
-1
X4
250
?????(Fractional factorial design

???4????23-1????,?23?????,???????????????or-?4
???,???2??????????????????X3????????Z1,X2?????????

???Column ???Column ???Column ???Column ????Column ????Column ????Column ????Column ????Column
Run X1 X2 X3 X1X2 X1X3 X2X3 X1X2X3 ???
1 -1 -1 1 1 -1 -1 1
2 1 -1 -1 -1 -1 1 1
3 -1 1 -1 -1 1 -1 1
4 1 1 1 1 1 1 1
251
?????(Fractional factorial design

X1,X2,X3?????2???????????
X3 ColumnX1 X2 Column
X1 ColumnX2 X3 Column
X2 ColumnX1 X3 Column

1
X2
1
-1
X3
-1
-1
1
X1
252
?????(Fractional factorial design

25??
?????????,????????,?????????????5?????,?????????
???????????(liter/min)
??????()
??(RPM)
??????(?)
????????????????????

253
?????(Fractional factorial design
Factor -1 1
1.???(feed rate) 10 15
2.???(catalyst) 1 2
3.??(RPM) 100 120
4.??(temperature) 140 180
5.??(concentration) 3 6
254
?????(Fractional factorial design