??

1
???????????

1. ?????
2. ???????
3. ??????
4. ????????
5. ????
6. ??????
7. ????????

2
???????
????????(???????)?????????
????????
????????
?????? (???)
????
??? ??
??? ??
??? ??
????
????
????
????
????
????
????
????
????
3
TAGUCHI DESIGNS
No. 1 2 3
1 2 3 4 1 1 1 1 2 2 2 1 2 2 2 1
(1) Linear Graph of Table
No. 1 2 3 4 5 6 7
1 2 3 4 5 6 7 8 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 2 2 1 1 2 2 1 2 2 2 2 1 1 2 1 2 1 2 1 2 2 1 2 2 1 2 1 2 2 1 1 2 2 1 2 2 1 2 1 1 2
a b -ab
A 1
7
C 4
B 2
a b -ab c -ac -bc abc
4
Common Orthogonal Arrays
The and orthogonal arrays are
special designs in which interactions are
generally spread across all columns. They
should not be used for experiments which include
the study of interactions
5
ORTHOGONAL ARRAY
6
ORTHOGONAL ARRAY
7
ORTHOGONAL ARRAY
8
Fractional Factorial Design
Test A B C D E F
G (1) - - - - -
- - a - -
- b - -
- ab
- - -
c - - -
ac - -
- bc -
- - abc -
- -
?????? (4) (2) (1) (6) (5) (3)
(7) ?
-124 -135 -236 1237
9
Fractional Factorial Design
(????)
Test A B C D E F
G (1)
a - -
- - b - -
- - ab - -
- -
c - - -
- ac - - -
- bc - - -
- abc - - -
-
?????? (4) (2) (1) (6) (5) (3)
(7) ?
124 135 236 1237
10
Fractional Factorial Design
Test 1 2 3 4 5 6
7 8 (1) - - -
- - - - -
a - - - -
b - -
- - ab
- -
- - c - -
- - ac
- -
- - bc - -
- - - - abc
- -
d - - -
- ad -
- -
- abd -
- - - cd -
- -
- acd - -
- - bcd -

abcd
- -
?????? (8) (4) (2) (1) (7) (9) (14)
(15) ?
I 2345 -146 1237 -12348
11
(No Transcript)
12
???????
????????(???????)?????????
????????
????????
?????? (???)
????
??? ??
??? ??
??? ??
????
????
????
????
????
????
????
????
????
13
TAGUCHI DESIGNS
No. 1 2 3
1 2 3 4 1 1 1 1 2 2 2 1 2 2 2 1
(1) Linear Graph of Table
No. 1 2 3 4 5 6 7
1 2 3 4 5 6 7 8 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 2 2 1 1 2 2 1 2 2 2 2 1 1 2 1 2 1 2 1 2 2 1 2 2 1 2 1 2 2 1 1 2 2 1 2 2 1 2 1 1 2
a b -ab
A 1
7
C 4
B 2
a b -ab c -ac -bc abc
14
Common Orthogonal Arrays
The and orthogonal arrays are
special designs in which interactions are
generally spread across all columns. They
should not be used for experiments which include
the study of interactions
15
ORTHOGONAL ARRAY
16
ORTHOGONAL ARRAY
17
ORTHOGONAL ARRAY
18
Fractional Factorial Design
Test A B C D E F
G (1) - - - - -
- - a - -
- b - -
- ab
- - -
c - - -
ac - -
- bc -
- - abc -
- -
?????? (4) (2) (1) (6) (5) (3)
(7) ?
-124 -135 -236 1237
19
Fractional Factorial Design
(????)
Test A B C D E F
G (1)
a - -
- - b - -
- - ab - -
- -
c - - -
- ac - - -
- bc - - -
- abc - - -
-
?????? (4) (2) (1) (6) (5) (3)
(7) ?
124 135 236 1237
20
Fractional Factorial Design
Test 1 2 3 4 5 6
7 8 (1) - - -
- - - - -
a - - - -
b - -
- - ab
- -
- - c - -
- - ac
- -
- - bc - -
- - - - abc
- -
d - - -
- ad -
- -
- abd -
- - - cd -
- -
- acd - -
- - bcd -

abcd
- -
?????? (8) (4) (2) (1) (7) (9) (14)
(15) ?
I 2345 -146 1237 -12348
21
(No Transcript)
22
(No Transcript)
23
(No Transcript)
24
(No Transcript)
25
LOSS FUNCTION
is the quality characteristic of interest for
product i is the quality characteristic target is
a constant that converts deviation to a monetary
value
where
26
AVERAGE LOSS FOR n PRODUCTS
It may be shown that
27
SIGNAL TO NOISE

• A logarithmic transformation of experimental
  data which
• considers both the mean and variability in an
  effort to reduce loss

• Small is Better
• Nominal is Better
• Larger is Better

28
Modeled Plastic Part Experiment
Factor Level
1 Level 2 A Injection Pressure
205 psi 350 psi B Mold
Temperature C Set Time
6 sec. 9 sec.
Condition A B C Results
1 2 3 4 1 1 1 1 2 2 2 1 2 2 2 1 30 25 34 27 30 25 34 27 30 34 25 27 30 27 25 34
Total 55 61 64 52 57
59 Average 27.5 30.5 32 26 28.5 29.5
29
Sewn Seam Experiment
30
ADVANTAGES OF TAGUCHI METHODS

• Loss function
• Simplicity in selecting a design matrix
• Parameter design strategy for making products
  robust to noise
• Designs quality into the products as opposed to
  inspecting it out
• Thousands of success stories have been compiled
  through the
• American Supplier Institute

31
DISADVANTAGES OF TAGUCHI METHODS

• Simplicity in selecting a design matrix
• Poor modeling
• Using only signal to noise ratios, ,
  , and to identify
• dispersion
• Need for replication to identify dispersion
  effects
• De-emphasis of modeling interactions
• Some analysis techniques are unnecessarily
  complex
• Not providing guidance to experimenters on how to
  recover from
• unsuccessful experiments

32
?????????????(A systematic Problem Solving
Flowchart for Taguchi Methods)
Define the scope of the problem , State the objective of the experiment Brainstorm and Select numbers and levels for controllable and noise factors
STAGE 1
Build an orthogonal design ( Inner and outer Array) designs are recently suggested by G. Taguchi. Determine the replications for each run.
STAGE2
33
Run the experiment and collect the data , Then , a graphical analysis is conducted and the Ratio is used . Important effects are determined to select a optimal condition or the experimental champion based on the best y (mean) or largest
STAGE 3
Generate the Prediction equation for ratio Conduct Confirmatory runs Compare the results Versus the prediction. Taguchis Loss Function can be another index to assess the performance of optimal condition.
STAGE 4
34
????

1. ?????????

• ????????-?????gt??????
• L8(27) L12(211) L18(21311) L36(211313)

35
????(?)

• ?????S/N?

1. ??????S/N???????????
2. ?S/N???ANOVA??,???????
3. ? ?15?????????????
4. ??????????2????????,???????????????????????

36
??????

• Step 1?????????
• Step 2?????????
• ?????????????????,????,??????
• Step 3??????
• ????????????,????????????
• Step 4???????,????

37
?????
??? ?? ?????? ??????????? ??????????? ??????????? ???????????
??? ?? ?????? 2 3 4 5
L4 4 3 3 - - -
L8 8 7 7 - - -
L9 9 4 - 4 - -
L12 12 11 11 - - -
L16 16 15 15 - - -
L16 16 5 - - 5 -
L18 18 8 1 7 - -
L25 25 6 - - - 6
L27 27 13 - 12 - -
L32 32 31 31 - - -
L32 32 10 1 - 9 -
L36 36 23 11 12 - -
L36 36 16 3 13 - -
L50 50 12 1 - - 11
L54 54 26 1 25 - -
L64 64 63 63 - - -
L64 64 21 - - 21 -
L81 81 40 - 40 - -
2-???L4?L8?L12?L16?L32?L64 2-???L4?L8?L12?L16?L32?L64 2-???L4?L8?L12?L16?L32?L64 2-???L4?L8?L12?L16?L32?L64 2-???L4?L8?L12?L16?L32?L64 2-???L4?L8?L12?L16?L32?L64 2-???L4?L8?L12?L16?L32?L64
3-???L9?L27?L81 3-???L9?L27?L81 3-???L9?L27?L81 3-???L9?L27?L81 3-???L9?L27?L81 3-???L9?L27?L81 3-???L9?L27?L81
2?3-???L18?L36?L36?L54 2?3-???L18?L36?L36?L54 2?3-???L18?L36?L36?L54 2?3-???L18?L36?L36?L54 2?3-???L18?L36?L36?L54 2?3-???L18?L36?L36?L54 2?3-???L18?L36?L36?L54
38
??????????
39
??????

• ???SN???ANOVA,?????????????,???????????????????
• ????????????????????????
• ????

40
??????

• ????????
• ???????????
• ???error?15?????????????
• ???error?15????????????
• ?,????????
• ??????error?28.78,?????????????,??????

41
??????
??????????A1B1C3D2E1F2
42
????(confirmation run)

• ?????????,????????
• ?????????
• ? ????????????????,???? ?????????
• ? ??????????
• ????????????????
• Robustness Test???

43
?????????
1.???????
2. ???????
4.????????? ????
3. ????????
6. ???? (????????ANOVA)
5. ????????SN? ??(????????) ????
7.??????????
8.????
9.?????
44
The factors in the noise array are selected as
well. Because several different types of
assemblies are run through this wave solder
process, two different types of assemblies were
used. The objective is to find one setting for
the wave solder process that is suitable for both
types of assemblies. The design will also
indicate if assembly type interacts with any of
the controllable. In addition to product noise,
both the conveyor speed and solder pot
temperature will be moved around the initial
setting given by the controllable array. This is
because it is difficult to set the conveyor speed
with any degree of accuracy and it is also
difficult to maintain solder pot temperature. So
the team of engineers chose to include these
variables in the noise array variables to
determine how much noise affects the process.
Table 1
45
?????/???Orthogonal Arrays
Eight runs will be used to test effects of the
five controllable in a Taguchi design (see
table 2a). Notice that for each factor, there are
four runs with the factor set at the high
setting. This balancing is a property of the
orthogonality of the set of runs. Table 2b lists
the array of noise factors to be run at each of
the eight setting of the controllable. This is a
Taguchi design. The combination of the inner
and outer arrays results in each urn of the
controllable being repeated over the 4
combinations of the noise factor.
Table 2a
Table 2b
46
(No Transcript)
47
(No Transcript)
48
?????
49
?????
50
????????????????
???????? ????/??????
?
?
?????? ?????
????????????, ???????????(? ?)?
1.?????????? ????? 2.?????????, ?
????? 3.??????????? ??????????? ?, ????????
??/????? ??????? ????
?
?
??????????? ??????????? ????
????????? ????????
??????????????, ???????????
?? B vs C ?????
???????EVOP?? ????????????
51
??????????
52
CAT-100 Catapult Demonstration

• ??CAT-100???,??????????????,????????????????

Upright Arm Tension Location (??????) 1 2 3
Ball Seat Position (????) 1 2 3
Projector Elevation (????) 1 2 3
Pivot Arm Tension Location (??????) 3 2 1
Ball Type(????) 1Foam(yellow), 2Whiffle(white),
3PingPong(orange) (1????2????3???)
3 2 1 Turn Table Position (?????)
53
????--????L18(21, 37)???--
L18(21, 37)???

• ??????L18(21, 37)???(????)???????,??L?????,18?????
  ????????????????????????????

A B C D E F G H
1 1 1 1 1 1 1 1
1 1 2 2 2 2 2 2
1 1 3 3 3 3 3 3
1 2 1 1 2 2 3 3
1 2 2 2 3 3 1 1
1 2 3 3 1 1 2 2
1 3 1 2 1 3 2 3
1 3 2 3 2 1 3 1
1 3 3 1 3 2 1 2
2 1 1 3 3 2 2 1
2 1 2 1 1 3 3 2
2 1 3 2 2 1 1 3
2 2 1 2 3 1 3 2
2 2 2 3 1 2 1 3
2 2 3 1 2 3 2 1
2 3 1 3 2 3 1 2
2 3 2 1 3 1 2 3
2 3 3 2 1 2 3 1
54
????--??? minitab??L18(21, 37)???--

• Stat/DOE/Taguchi/Create Taguchi Design

55
??????L18(21, 37)???
8??????????????
56
??????L18(21, 37)???
(1) ??L18(21,37)?,?Ok
(2) ?Ok, ?????
57
??????L18(21, 37)???

• ??L18(21, 37)???

58
????

• ??minitab??L18(21, 37)????,??????2??????,?????????
  ???,?????????????A?B?C?D?E?F(???????)?

No. A B C D E F G H order distance1 order distance2
1 1 1 1 1 1 1 1 1 12 98.3 35 99.2
2 1 1 2 2 2 2 2 2 17 146 36 136.2
3 1 1 3 3 3 3 3 3 16 143.2 32 150.1
4 1 2 1 1 2 2 3 3 20 114.8 21 113.4
5 1 2 2 2 3 3 1 1 25 147.9 27 148.2
6 1 2 3 3 1 1 2 2 15 63.2 18 96.5
7 1 3 1 2 1 3 2 3 4 104.8 3 106.5
8 1 3 2 3 2 1 3 1 28 145.5 34 145.1
9 1 3 3 1 3 2 1 2 13 39 14 36
10 2 1 1 3 3 2 2 1 23 327.8 26 324.3
11 2 1 2 1 1 3 3 2 29 116.1 7 111.5
12 2 1 3 2 2 1 1 3 6 135.2 31 128
13 2 2 1 2 3 1 3 2 1 238.2 24 239.8
14 2 2 2 3 1 2 1 3 5 170.7 30 172.2
15 2 2 3 1 2 3 2 1 10 101.5 33 108.3
16 2 3 1 3 2 3 1 2 2 208.5 11 227.3
17 2 3 2 1 3 1 2 3 9 145.5 19 143.8
18 2 3 3 2 1 2 3 1 8 92.2 22 94.7
59
CAT-100 Catapult Demonstration
Factor (??) Factor Name (????) Level (??)
A A Upright Arm Tension Location (??????) 1 Low level, 2 High level (1????2???)
B B Projector Elevation (????) 1 Low level, 2 Medium level, 3 High level (1????2????3???)
C C Turn Table Position (?????) 1 Low level, 2 Medium level, 3 High level (1????2????3???)
D D Pivot Arm Tension Location (??????) 1 Low level, 2 Medium level, 3 High level (1????2????3???)
E E Ball Seat Position (????) 1 Low level, 2 Medium level, 3 High level (1????2????3???)
F F Ball Type (???) 1Foam(yellow), 2Whiffle(white), 3PingPong(orange) (1????2????3???)
60
L18(21, 37) Minitab??
61
????????????????????(Main Effect Plot)

• Stat/ANOVA/Main Effects Plot

62
????????????????????(Main Effect Plot)

• ??F(????)?,A???????B(????)?C(?????)?D(??????)?E(??
  ??)??????????????

???????A2B1C1D3E3
63
???????????????? ????

• Stat/Regression/Regression

64
????????????????????
(1) ??distance?????
(2) ??A?F?????(??A?F??????)
65
????????????????????
(2)F(????)???????(P_valuegt0.05)?
(1) ???????????????(P_valuelt0.05)?
66
????????????????????

• ??A-E??
• Stat/Regression/Regression

(1)??????distance
(2)??????A-E
(3)???????
(4)????
67
???????????????? ????(??A-E??)
(2)A-E????????(P_valuelt0.05)?
???????
(1)???????????????(P_valuelt0.05)?
68
???????????????? ????(??A-E??)

• ???????
• ?????????????????????????,??????,????????????

69
?????????????????????

• ??ANOVA??????????????????
• Stat/ANOVA/General Linear Model

70
?????????????????????
(1) ??distance?????
(2) ??A?F?????(??A?F??????)
71
?????????????????????

• ANOVA Table

F(????)???????(P_valuegt0.05)?
72
?????????????????????

• ??A-E??
• Stat/ANOVA/General Linear Model

(1)????
(2)?A?E???????
(3)???????
(5)?????????
(4)???????
73
?????????????????????

• ANOVA Table (??A-E??)

A-E????????? (P_valuelt0.05)?
74
?????????????????????

• ?????????

??????????
75
?????????????????????

• ???????
• ?????????????????????????,??????,????????????

76
????????????????????????????

• ????????????????????A2B1C1D3E3
• ????????
• ?????????

77
???????

• ????
• Stat/DOE/Taguchi/Define Custom Taguchi Design

78
???????

• ????

(1)?????????????A?F ?
79
???????

• ????
• Stat/DOE/Taguchi/Analyze Taguchi Design

80
??????? Signal to Noise ratios

• ?????????SN?

(1)??distance?????
(3)?????????????
(2)??SN?
81
???????Signal to Noise ratios

• ??SN?

(2)??SN?
(1)????????
82
??????? Signal to Noise ratios

• ????(Main effect plot)
• ??F(????)?,A???????B(????)?C(?????)?D(??????)?E(??
  ??)??????????????

???????A2B1C1D3E3
83
???????????

• Stat/Regression/Regression

84
???????????
(1) ??ANRA1?????
(2) ??A?F?????(??A?F??????)
85
???????????
(2)F(????)???????(P_valuegt0.05)?
(1) ??????????(P_valuelt0.05)?
86
???????????

• ??A-E??
• Stat/Regression/Regression

(1) ??ANRA1?????
(2)??????A-E
(3)???????
87
???????????(??A-E??)
(2)A-E????????(P_valuelt0.05)?
???????
(1) ??????????(P_valuelt0.05)?
88
???????????(??A-E??)

• ???????
• ?????????????????????????,??????,????????????

89
????????????

• Stat/ANOVA/General Linear Model

90
????????????
(1) ??SNRA1?????
(2) ??A?F?????(??A?F??????)
91
????????????

• ANOVA Table

F(????)???????(P_valuegt0.05)?
92
????????????

• ??A-E??
• Stat/ANOVA/General Linear Model

(1)????
(2)?A?E???????
(4)???????
(3)???????
93
????????????

• ANOVA Table (??A-E??)

A-E????????? (P_valuelt0.05)?
94
????????????

• ?????????

??????????
95
????????????

• ???????
• ?????????????????????????,??????,????????????

96
???????????????????

• ???????????A2B1C1D3E3
• ????????
• ??????
• ?????????
• ??????

97
CAT-100 Catapult????

• ???????????????A2B1C1D3E3?????(F)???????,???????

???? ???? ?? ??
???? ????? ???? ?????
??? 302.5 300.7 381 332.5
No ??? ?? ?? ?? ??
1 332 8.89 9.43 14.76 0.15
2 322.5 6.20 6.76 18.14 3.10
3 326.5 7.35 7.90 16.69 1.84
4 320 5.47 6.03 19.06 3.91
5 317.5 4.72 5.29 20.00 4.72
???? 6.53 7.08 17.73 2.74