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Design of experiments (DOE) Steps Define problem Define experimental objectives Define problem Define experimental objectives Select factors that influence quality Select control & noise factors Select levels for factors Select orthogonal arrays Select interactions Conduct tests Analyze results

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Design of experiments (DOE) Breadmaking problem: Level Factor 1 2 1.flour2 1/3 cups all-purpose2 1/3 cups special 2.sugar2 Tsp2 1/2 Tsp 3.salt1 tsp 1/2 tsp 4.butter1 Tsp1 Tsp margarine 5.milk1 cup homogenized1 cup low-fat 6.dry yeast1 tsp brand A1 tsp brand B Level Factor 1 2 1.flour2 1/3 cups all-purpose2 1/3 cups special 2.sugar2 Tsp2 1/2 Tsp 3.salt1 tsp 1/2 tsp 4.butter1 Tsp1 Tsp margarine 5.milk1 cup homogenized1 cup low-fat 6.dry yeast1 tsp brand A1 tsp brand B

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Design of experiments (DOE) How many loaves of bread to get "best" set of ingredients? 6 factors, each w/ 2 levels ––> 2 6 = 64! Taguchi method (Genechi Taguchi) says only a few needed

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Design of experiments (DOE) Testing methods Factors and factor levels Trial ABCD 1.1111 2.2111 3.1211 4.1 121 5.1112 Factors and factor levels Trial ABCD 1.1111 2.2111 3.1211 4.1 121 5.1112

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Design of experiments (DOE) Testing methods Factors and factor levels Trial ABC 1.111 2.122 3.2 12 4.221 Factors and factor levels Trial ABC 1.111 2.122 3.2 12 4.221 Better…….."orthogonal" Standard L4 orthogonal array Better…….."orthogonal" Standard L4 orthogonal array

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Design of experiments (DOE) Which OA to use? Depends on: # of factors & interactions # of levels for each factor Which OA to use? Depends on: # of factors & interactions # of levels for each factor # of levels usually 2 or 3 Use L4, L8(7 factors), L12(11 factors), L16(15 factors),…..OAs - determined by # trials to be run

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Design of experiments (DOE) Some factors may interact. Then: Factors and factor levels Trial ABC(=AxB) 1.111 2.122 3.2 12 4.221 Factors and factor levels Trial ABC(=AxB) 1.111 2.122 3.2 12 4.221

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Factorisation. Single Brackets. Multiply out the bracket below: 2x ( 4x – 6 ) = 8x 2 - 12x Factorisation is the reversal of the above process. That is.

Factorisation. Single Brackets. Multiply out the bracket below: 2x ( 4x – 6 ) = 8x 2 - 12x Factorisation is the reversal of the above process. That is.

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