Design of experiments (DOE) Steps 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

Design of experiments (DOE) Breadmaking problem: Level Factor 1 2 1. flour 21/3 cups all-purpose 2. sugar 2 Tsp 21/2 Tsp 3. salt 1 tsp 1/2 4. butter 1 Tsp margarine 5. milk 1 cup homogenized 6. dry yeast 1 tsp brand A 21/3 cups special tsp 1 cup low-fat 1 tsp brand B

Design of experiments (DOE) How many loaves of bread to get "best" set of ingredients? 6 factors, each w/ 2 levels ––> 26 = 64! Taguchi method (Genechi Taguchi) says only a few needed

Design of experiments (DOE) Testing methods Factors and factor levels Trial A B C D 1. 1 1 2. 2 1 1 1 3. 1 2 1 1 4. 1 1 2 1 5. 1 1 1 2

Design of experiments (DOE) Testing methods Factors and factor levels Trial A B C 1. 1 1 1 2 2 3. 2 1 2 4. 2 2 1 Better……. . "orthogonal" Standard L 4 orthogonal array

Design of experiments (DOE) Which OA to use? Depends on: # of factors & interactions # of levels for each factor Use L 4, L 8(7 factors), L 12(11 factors), L 16(15 factors), …. . OAs - determined by # trials to be run # of levels usually 2 or 3

Design of experiments (DOE) Some factors may interact. Then: Factors and factor levels Trial A B C(=Ax. B) 1. 1 1 1 2 2 3. 2 1 2 4. 2 2 1