Experimental Design - Math Site

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History• Agricultural field trial work of Fisher* inthe 1920s• Chemical industry work of George Box,starting in 1951 with the publication of hiswork term notes from ICI***R.A. Fisher, ”Studies in Crop Variation. II. The Manurial Response of Different PotatoVarieties”, J. Agricultural Sci., 13, 311-320 (1923)** G.E.P. Box and K.B. Wilson, ”On the experimental attainment of optimal conditions”, J.Roy. Statist. Soc., B13,1-45 (1951)CEI Inc.
Ronald A. FisherCEI Inc.
Page 2 and 3: Topics CoveredIntroductionFull 2 Le
Page 6 and 7: George E.P. BoxCEI Inc.
Page 8 and 9: N-space and Real Space• It is oft
Page 10 and 11: Two Level Factorial Designs• If w
Page 12 and 13: Specific Volume of Ammonia• Four
Page 14 and 15: xP+1x-1 +1Tx-1x xFull Two Level Fac
Page 16 and 17: Effect of Temperature?V0.2950.215-1
Page 18 and 19: Effect of T, P Interaction?0.270.24
Page 20 and 21: Empirical Models• It is often pre
Page 22 and 23: The solution is easier if we use ma
Page 24 and 25: X t X =1 1 1 1-1 -1 1 1-1 1 -1 11 -
Page 26 and 27: 0.255β = (X t X) -1 X t y =0.040-0
Page 28 and 29: What if we havethree factors?CEI In
Page 30 and 31: Three Independent Variables• Our
Page 32 and 33: Exercise (left to student)Show that
Page 34 and 35: x 1 x 2 x 3-1 -1 -1-1 -1 1-1 1 -1-1
Page 36 and 37: However, you can confirm thatx 1 =
Page 38 and 39: Generators• I used the relationsh
Page 40 and 41: Resolution• In our 4 run subset o
Page 42 and 43: Plackett Burman Designs• In gener
Page 44 and 45: Plackett Burman Designs• The Plac
Page 46 and 47: Significance, Variances and ErrorBo
Page 48 and 49: NoteAlthough the V( ) notation sugg
Page 50 and 51: Aside on NomenclatureIf the predict
Page 52 and 53: estimation design”. Briefly, test
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We cannot use 2 level factorial des
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Three Level Factorial Designs2 Inde
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Example: More on v for NH 3Estimate
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Other Response Surface Designs• A
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Box Behnken Designs• The most wid
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3 Factor Box Behnken DesignThe actu
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Use a Box Behnken design to estimat
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Question for DiscussionWhy isn’t
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Construction of a CCD in two factor
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Henry SchefféCEI Inc.
Page 74 and 75:
Scheffé also came up with simplex-
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Let’s look at an example that tak
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Evolutionary Operation (EVOP)The te
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Evolutionary Operation, cont’dThe
Page 82 and 83:
Geometry of 2 - D Simplex Methodnbr
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x 2 3 2y 0 3 2Z 20 5.26 11.1Clearly
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Geometry of 2 - D Simplex Methodnbr
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For the next iteration, w = (2, 0),
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Another observation from the graph
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Warning #1The experimental runs use
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Warning #2, and Possible CureA poss
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Experimental Design - Math Site

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