PowerPoint PresentationSlide 2Slide 3Slide 4Slide 5Slide 6Slide 7Design of experiments (DOE)Design of experiments (DOE)StepsStepsDefine problemDefine experimental objectivesDefine problemDefine experimental objectivesSelect factors that influence qualitySelect factors that influence qualitySelect control & noise factorsSelect control & noise factorsSelect levels for factorsSelect levels for factorsSelect orthogonal arraysSelect orthogonal arraysSelect interactionsSelect interactionsConduct testsConduct testsAnalyze resultsAnalyze resultsDesign of experiments (DOE)Design of experiments (DOE)Breadmaking problem:Breadmaking problem:Level Factor 1 2•flour 21/3 cups all-purpose 21/3 cups special•sugar 2 Tsp 21/2 Tsp•salt 1 tsp 1/2 tsp•butter 1 Tsp 1 Tsp margarine•milk 1 cup homogenized 1 cup low-fat•dry yeast 1 tsp brand A 1 tsp brand BLevel Factor 1 2•flour 21/3 cups all-purpose 21/3 cups special•sugar 2 Tsp 21/2 Tsp•salt 1 tsp 1/2 tsp•butter 1 Tsp 1 Tsp margarine•milk 1 cup homogenized 1 cup low-fat•dry yeast 1 tsp brand A 1 tsp brand BDesign of experiments (DOE)Design of experiments (DOE)How many loaves of bread to get "best" set of ingredients?How many loaves of bread to get "best" set of ingredients?6 factors, each w/ 2 levels ––> 26 = 64!6 factors, each w/ 2 levels ––> 26 = 64!Taguchi method (Genechi Taguchi) says only a few neededTaguchi method (Genechi Taguchi) says only a few neededDesign of experiments (DOE)Design of experiments (DOE)Testing methodsTesting methodsFactors and factor levels Trial A B C D1. 1 1 1 12. 2 1 1 13. 1 2 1 14. 1 1 2 15. 1 1 1 2Factors and factor levels Trial A B C D1. 1 1 1 12. 2 1 1 13. 1 2 1 14. 1 1 2 15. 1 1 1 2Design of experiments (DOE)Design of experiments (DOE)Testing methodsTesting methodsFactors and factor levels Trial A B C1. 1 1 12. 1 2 23. 2 1 24. 2 2 1Factors and factor levels Trial A B C1. 1 1 12. 1 2 23. 2 1 24. 2 2 1Better…….."orthogonal"Standard L4 orthogonal array Better…….."orthogonal"Standard L4 orthogonal arrayDesign of experiments (DOE)Design of experiments (DOE)Which OA to use? Depends on:# of factors & interactions# of levels for each factorWhich OA to use? Depends on:# of factors & interactions# of levels for each factor# of levels usually 2 or 3 # of levels usually 2 or 3 Use L4, L8(7 factors), L12(11 factors), L16(15 factors),…..OAs - determined by # trials to be run Use L4, L8(7 factors), L12(11 factors), L16(15 factors),…..OAs - determined by # trials to be runDesign of experiments (DOE)Design of experiments (DOE)Some factors may interact. Then:Some factors may interact. Then:Factors and factor levels Trial A B C(=AxB)1. 1 1 12. 1 2 23. 2 1 24. 2 2 1Factors and factor levels Trial A B C(=AxB)1. 1 1 12. 1 2 23. 2 1 24. 2 2