Experimental Design - Math Site

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Scheffé also came up with simplex-centroidexperimental designs. For three components,The design points correspond to all permutations of the pure components(e.g., 1 0 0; 0 1 0; 0 0 1), the permutations of the binary blends (½ ½ 0; ½ 0½; 0 ½ ½) and the one blend involving equal parts of all three components.CEI Inc.
The points in the simplex centroid design for three components are:x 1 1 0 0 ½ ½ 0 1/3x 2 0 1 0 ½ 0 ½ 1/3x 3 0 0 1 0 ½ ½ 1/3Note that this design only contains 7 runs. A full quadratic model forthree components requires 9, since we will eliminate the constant. To getsufficient data, it is usual to addx 1 2/3 1/6 1/6x 2 1/6 2/3 1/6x 3 1/6 1/6 2/3CEI Inc.
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Topics CoveredIntroductionFull 2 Le
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History• Agricultural field trial
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George E.P. BoxCEI Inc.
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N-space and Real Space• It is oft
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Two Level Factorial Designs• If w
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Specific Volume of Ammonia• Four
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xP+1x-1 +1Tx-1x xFull Two Level Fac
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Effect of Temperature?V0.2950.215-1
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Effect of T, P Interaction?0.270.24
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Empirical Models• It is often pre
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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 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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