Experimental Design - Math Site

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Empirical Models• It is often preferable to fit to some sort ofempirical model• It can be shown that the most generalpolynomial model that can be estimatedfrom a full 2 level factorial design in twofactors isy = β 0 + β 1 x 1 + β 2 x 2 + β 12 x 1 x 2CEI Inc.
Our data can be written out asβ 0 - β 1 - β 2 + β 12 = 0.29β 0 - β 1 + β 2 - β 12 = 0.14β 0 + β 1 - β 2 - β 12 = 0.40β 0 + β 1 + β 2 + β 12 = 0.19i.e. four equations in four unknowns, so thereshould be a solution.CEI Inc.
Page 2 and 3: Topics CoveredIntroductionFull 2 Le
Page 4 and 5: History• Agricultural field trial
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 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
Page 54 and 55: We cannot use 2 level factorial des
Page 56 and 57: Three Level Factorial Designs2 Inde
Page 58 and 59: Example: More on v for NH 3Estimate
Page 60 and 61: Other Response Surface Designs• A
Page 62 and 63: Box Behnken Designs• The most wid
Page 64 and 65: 3 Factor Box Behnken DesignThe actu
Page 66 and 67: Use a Box Behnken design to estimat
Page 68 and 69: Question for DiscussionWhy isn’t
Page 70 and 71:
Construction of a CCD in two factor
Page 72 and 73:
Henry SchefféCEI Inc.
Page 74 and 75:
Scheffé also came up with simplex-
Page 76 and 77:
Let’s look at an example that tak
Page 78 and 79:
Evolutionary Operation (EVOP)The te
Page 80 and 81:
Evolutionary Operation, cont’dThe
Page 82 and 83:
Geometry of 2 - D Simplex Methodnbr
Page 84 and 85:
x 2 3 2y 0 3 2Z 20 5.26 11.1Clearly
Page 86 and 87:
Geometry of 2 - D Simplex Methodnbr
Page 88 and 89:
For the next iteration, w = (2, 0),
Page 90 and 91:
Another observation from the graph
Page 92 and 93:
Warning #1The experimental runs use
Page 94 and 95:
Warning #2, and Possible CureA poss
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Experimental Design - Math Site

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