Experimental Design - Math Site

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Evolutionary Operation (EVOP)The term Evolutionary Operation (or EVOP) is dueto George Box*, although the method as presentlyknown (using the “simplex” algorithm) is due toSpendley et al**; the numerical algorithm wasfurther refined by Nelder and Mead***.*G.E.P. Box, “Evolutionary operation: A method for increasing industrialproductivity”, Applied Statistics 6, 81-101 (1957).**W. Spendley, G.R. Hext and F.R. Himsworth, “Sequential application ofsimplex designs in optimization and EVOP”, Technometrics 4, 441-461 (1962).***J.A. Nelder and R. Mead, “A simplex method for function minimization”,Computer Journal 7, 308-313 (1965).CEI Inc.
Evolutionary OperationThe basic idea is to determine (by some othertechnique) the factors that influence theresponse. EVOP can then be used to determinewhat values of these factors to use to maximize(or minimize) the response.If n factors have been found that influence theresponse, n + 1 runs that are linearlyindependent are made (e.g. if there are 2important factors, 3 runs are made at conditionsthat do not lie on a straight line).CEI 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
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X t X =1 1 1 1-1 -1 1 1-1 1 -1 11 -
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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 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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