????(DOE)???????????

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????(DOE)???????????

• ????? ???
• ??????????????

????????????????????Montgomery, D.C., 2001.
Design and Analysis of
Experiments, 5th Edition, (John Wiley SonsNew
York)???
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1 DOE??

• ????

• ?y??????????
• ????x1, x2, , xp?y???????
• ????x1, x2, , xp?y???????
• ????x1, x2, , xp???????z1, z2, , zp??????

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????????

• Best-guess approach

• No Good, Guess Again
• Switching the levels of one (perhaps two) factors
  for the next test based on the outcome of the
  current test
• Good Enough, Stop!

• On-factor-at-a-time

• Selecting a baseline starting point
• Varying each factor over its range with the other
  factors held constant at the baseline level
• Interactions ruin everything

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One-factor at a time ???
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?????(DOE)

• ??????????????????????, ??????????????????.
• ??
• ???????
• ??????, ??????
• ??????
• ??????
• ??????????
• ???????
• ???????????

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• Example
• Optimizing a Process

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????

• ??(Replication)
• ??????
• ??????
• ???(Randomization)
• Averaging out the effects from uncontrollable
  variables
• ???(Blocking)
• ????????

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DOE???

• ????????
• ????????
• ??????
• ?????????
• ????
• ????
• ?????
• Follow-up run and confirmation test
• Iterative
• No more than 25 of available resources should be
  invested in the first experiment

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Notes

• ???????????
• ??????????????
• ????????????????
• ??
• ??
• ??
• ?????????
• ???????????????

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???????

• ???????
• Variance Model
• ???????
• ???????
• ?????????
• ???????????
• ?????????
• ???????????
• ??????

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???????(Another Prospect)

• ????(Screening Experiments)
• ???????????
• Plackett-Burman Design
• Group-Screening Designs
• ????
• ?????????
• ???????????
• ?????????
• ???????????
• ????
• ???(Optimizing)
• ??????

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2 ?????(ANOVA)
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????

• ? F0 gt Fa,a-1,a(n-1) ,?????????????????
• ??,?????
• a ??????

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Example???????
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ANOVA ??

• ?? F0 gt F0.01,3,20 4.96,??,?a
  0.01?,??????????????????,????????,Hardwood????????
  ?????

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3 ???????

• ????????

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• ????????

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Example
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• ????
• ??F0(Primer Types) 28.63 gt F0.05,2,12 3.89
• F0(Application Methods) 61.38 gt
  F0.05,1,12 4.75
• ?????????????????
• ? F0(Interaction) 1.5 lt F0.05,2,12
  3.89,??????????????????????
• ????(?)

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2k??????

• k???,????2???(,-) ,?2k???(? n 1 ?)?
• ??????????,???????,????????????????
• ????????????????(linear effect) ,???????????

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23??????
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Example for 23 Design

• A ??
• B ????
• C ????

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ANOVA ?_Example
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2k Design with Center Points

• ???????????
• ?????????(Balanced Design)
• ??????????

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Example
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ANOVA?_Example
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4 ???????????(2k-p)

• 2k-p Design??k???,?????????,??2k-p????
• 2k Design????????k(???)??????,??2416?2664?28256
  ??????,?26??,64?????64-163????,????C616?????????
  ?,C6215??????????????,??63-6-1542????????(?)????
  ??????
• ?,??????????????????????,???????(????????),???????
  2k?????????,?????????????????????

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2k-p????

• 2k-p Design?????????Screening Experiments,????????
  ???????????????,?????????????
• ????????????
• ????????????

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2k-p????

• ??????????????????????????????????
• ?????????????????????????????
• ?????????????????????????????????? ?

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23-1?????

• ????ABC???,????? I ABC?
• ????ABC??-?,????? I -ABC?

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Alias ??

• ??A??????????BC???????????,????????????A??????,??
  ?,????ABC???????????????Alias,? lA ? ABC ????
• ??,?23-1 Design (IABC)??Aliases?
• lA ? ABC
• lB ? BAC
• lC ? CAB

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??????????(Resolution)

• ??
• ????????R???,p-???????????R-p???????????Alias?
• ??????????????????????????Alias????????2????????
  Alias??23-1 Design?
• ?????????????????????????2????????Alias?2???????
  ??Alias??24-1 Design (IABCD)?
• ?????????????????????????2????????Alias?2???????
  ?3????????Alias??25-1 Design (IABCDE)?

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???????????,?????
???????
???????
??????
???? ?3k, 3k-p, CCD,
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24-1 Design Example

• ?? 241.DX5, 24-1 Design (IABCD)
• A???? B???? C???? D??????
• ????Y????

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2k-2 Design (1/4 ????)

• 2k-1 Design ???? Generator IABCDE. ???????????
• 2k-2 Design ???? Generators?
• 26-2 Design (I ABCE BCDF),??????2k-1
  Design,?????????????????
• ??? IABCE ? I BCDF ??4?,??ABCE?BCDF?,????????
  ??????,??????
• (ABCE)(BCDF) AB2C2DEF ADEF
• ????????? IABCEBCDFADEF

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26-2 Design_Example

• ?? 262.DX5,
• 26-2 Design
• (I ABCE
• BCDFADEF)
• ??????
• A ????
• B ????
• C ?????????
• D ??????
• E ??????
• F ????
• ???? Y????

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5 ??????

• ???????(Response Variable)????????.
• ???????????.
• ??????????????
• ???
• ???
• ???
• ?? ?????????(??), ????? ?????.

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RSM?????

• ??????? Y f(x1, x2) e
• ????(Response Surface) ? f(x1, x2)
• ????????, ? f(x1, x2) ????????. ?
• Y b0b1x1b2x2bkxke (first order)
• Y b0?bixi?biix2i? ? bijxixje (second
  order)

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???? - Example
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The Method of Steepest Ascent

• ?? ??????????????????.
• ?? ?????????????, ????, ?? First-order Model
  ????.
• Steepest Ascent ???????????(?????????????),
  ?????????.
• ???????, ??? Steepest Descent.

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Steepest Ascent - ??
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Steepest Ascent - Example

• 525.DX5
• ?? ?1 ???? (35 min.)
• ?2 ???? (155 oF)
• ???? Y ?????? (40)
• Coded Variable (X1X2) (-1 1 -1 1)
• Natural Variable (? 1 ? 2) (30 40 150
  160)

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Example 525 ?????

• ?????
• Error ???
• First-order Model
• ???? ( Fit? )

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Example ? ANOVA Table
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Example?????

• ?????????(Regression Model)?
• y 40.44 0.775x1 0.325x2
• x1?x2???(0.775 and 0.325)??????standard error
  sqrt(MSE/d.f.e) 0.10??? ???????.
• ?????????
• ?????????????? (?Coded Variable ???), ??? ?x1
  1, ??x2 (0.325/0.775) ?x1 0.42

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Example ???????(?)
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Example ???????(?)
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Example ???????(?)-ANOVA

• ?????????(Regression Model)?
• y 78.97 1.00x1 0.50x2
• ?????????????.

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Steepest Ascent ??

• 2k nc center point ? CCD ? ??
• First-order Model ??, ?Curvature??? ?????????.
• ?????????? ???Step Size ?xi.
• ?????Step Size gt
• ?xi / bi ?xk / bk
• ??xi???Natural Variable ??????.

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Second-order Model ???

• ?????????, First-order Model????? ????
  Second-order Model ?????Model????????????(??)??.

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Central Composite Design (CCD) - Example

• 534.DX5

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CCD ???
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CCD Example ? ANOVA
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CCD Example ?????
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CCD Example ?????_Contour Plot
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6 ?????????????

• ??????, ??????????
• ?? Model ?????? (Lack of Fit)
• ????? (Blocking)
• ???? Model ???????????
• ?????? (Pure Error) ???
• ???????
• ????????
• ?? Model ????????????

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?? Model ? RSM ??

• ???? ?? (Othogonal)
• 2k nc center point
• 2k-p nc center point, ???????III??, Why?

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????? - Example

• 23
• ???? Pure Error - 4 d.f. ? Lack-of-fit
• ?? Model????????
• 23-1 4 center point
• 3 d.f. ? Pure Error - 1 d.f. ?
  Curvature
• ?? ????????
• 23-1, n 2
• 4 d.f. ? Pure Error - ????
  Lack-of-fit
• ?? ????????????
• ???23 4 center point

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?? Model ? RSM ??(1/2)

• ???? ?? (Orthogonal) ? ???? (Rotatable)
• Central Composite Designs (CCDs)
• 2k ?2k-1 (???V) 2k ??? (Axial Points) nc
  center point
• Factoral Points 2k?2k-1 (???V) ?????????????
• Axial Points ????????
• Center Points????????? Pure Error

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Information Surfaces and Contours_22 Design
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Information Surfaces and Contours_32 Design
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Information Surfaces and Contours_Second-order
Rotatable Design
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CCD ??
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?? Model ? RSM ??(2/2)

• Face-centered Central Composite Design (FCCD)

• ?? a 1??, ??? CCDs?
• ?????????????, ???????
• ???? (Rotatability) ??, ???????

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Evolutionary Operation (EVOP)

• ?????????????????????????????, ??????, ?????????
  (drift). ?????????????????.
• EVOP ????????, ???????, ??????????,
  ????????????????.
• 2k center point, ? cycle ?????.

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EVOP ???
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???????
??????????????, ?????, ???????.
??????
Screening Experiments
- ?????? - 2k-pnc ???? III (?)??.
2k-pnc
2knc
Fold Over
- ???????
-???????
-???????
One Factor
- ??????
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?????????
????
- ??????
- ?????, ?????????????. - 2knc, ? 2k-pnc ????
III ??.
Steepest Ascent
?????
CCD
Box-Behnken
Hybrid
- ??????? 3
- ???? 3, 4, 6. - ??????
- ??????? 5
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7 The Variance Model

• ??????????(???????)????????,?????Variance
  Model???????????????
• ??
• ?????????????,????a????
• ??ANOVA???MSE?MSTreatment?
• ??????????
• ?????????
• ???????

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Example

• ????????????????

Random Select
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• ????,??????????????,?????????8.86??1.90,?????????

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