&3 -

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???????????(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??

• 23 Design ????23-1 Designs?
• ???(?)

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??????????(Generator)

• ABC???????????(Generator)?

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23-1?????

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

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23-1 Design (IABC)

• ?23-1 Design (IABC) ???4???,4-13????,???????????
  ???

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23-1 ?????????

• ContrastA abca-b-c ContrastAB abcc-a-b
• ContrastB abcb-a-c ContrastAC abcb-a-c
• ContrastC abcc-a-b ContrastBC abca-b-c
• AEA 1/2(abca-b-c) AEBC
• AEB 1/2(abcb-a-c) AEAC
• AEC 1/2(abcc-a-b) AEAB

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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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23-1 Design (I-ABC)??Aliases

• ?23-1 Design (I-ABC)??Aliases?
• lA ? A-BC
• lB ? B-AC
• lC ? C-AB
•  
• WHY?

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????????

• ???????????? 23-1 Design,????? IABC,????
  I-ABC,???
• lA ? ABC
• lA ? A-BC
• ??
• (lA lA )/2? A
• (lA lA )/2? BC
• ????????????????????????,??ABC??,?????,???????????
  ???

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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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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 ???
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26-2 Design (I ABCE BCDFADEF) ?Aliases

• A BCE DEF ABCDF
• B ACE CDF ABDEF
• C
• E
• F
• AB
• BC
• ABD
• ???Aliases??????

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26-2 Design???

• 26-2 Design (I ABCE BCDFADEF)
  ??16???,16-115????,?????6?????????2???????
• ?????
• ContrastA aeabfacfabceadefabdacdabcdef
• -(1)-bef-cef-bc-df-bde-cde-bcdf
• ????
• AEA ContrastA / 8
• SSA ContrastA2 / 16
• ????????????

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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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??2k-p Design

• ??p????(Generators)?
• 24-1 Design (IABCD)
• 26-2 Design (I ABCE BCDF)
• ????(Effect)?2p?Aliases?
• 23-1 Design (IABC)?,lA ? ABC
• 26-2 Design (I ABCE BCDF) ?,lA ?
  ABCEDEFABCDF
• ???2k-p-1???(??Aliases)??????

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?2k-p??????(Blocking)

• 26-2 Design (I ABCE BCDF) ?,?ABD????

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Why/When to Use RSM?

• ???????(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