1. INT 506/706: Total Quality Management Introduction to Design of Experiments

2. Outline DOE – What is it? Trial and error experiments Definitions Steps in designed experiments Experimental designs

3. DOE A method of experimenting with the complex interactions among parameters in a process or product with the objective of optimizing the process or product

4. Trial and error experiments Involves making an educated guess about what should be done to effect change in process or system

5. Trial and error experiments Example: FactorLevel Speed55, 65 Tire28 psi, 35 psi Oil30 weight, 40 weight GasRegular (R), Premium (P)

6. Trial and error experiments

7. DefinitionsFactor The variable the experimenter will vary in order to determine its effect on a response variable

8. DefinitionsLevel The value chosen for the experiment and assigned to change the factor Gas example Tire Pressure – Level 1: 28 psi; Level 2: 35 psi

9. Definitions Controllable Factor Ability to establish and maintain level throughout experiment

10. DefinitionsEffect Result or outcome of the experiment

11. Definitions Response Variable The quality characteristic under study, the variable we want to have an effect on

12. Definitions Degrees of Freedom The number of independent data points in the samples determines the available degrees of freedom

13. Definitions Degrees of Freedom We earn a degree of freedom for every data point we collect We spend a degree of freedom for each parameter we estimate

14. Definitions Degrees of Freedom df Total = N – 1 = # of observations – 1 df Factor = L – 1 = # of levels – 1 df Interaction = df FactorA * df FactorB df Error = df Total – df EverythingElse

15. DefinitionsInteraction Two or more factors that together produce a result different than what the result of their separate effects would be

16. Definitions Noise Factor An uncontrollable, but measurable, source of variation in the functional characteristics of a product or process

17. DefinitionsTreatment The specific combination of levels for each factor used for a particular run

18. DefinitionsRun An experimental trial, the application of one treatment

19. DefinitionsReplicate A repeat of a treatment condition

20. DefinitionsRepetition Multiple runs of a particular treatment combination/setup

21. DefinitionsSignificance Used to indicate whether a factor or factor combination caused a significant change in the response variable

22. Example Factors Material Supplier Press Tonnage 3 levels of each factor Supplier Press Tonnage A20 B25 C30

23. Example Treatments – 3 x 3 Supplier Press Tonnage A20 A25 A30 B20 B25 B30 C20 C25 C30

24. Steps in planned experiments What are you investigating What is the objective What are you hoping to learn What are the critical factors Which factors can be controlled What resources will be used

25. Step 1 Establish the purpose by defining the problem

26. Step 2 Identify the components of the experiment

27. Step 3 Design the experiment

28. Step 4 Perform the experiment

29. Step 5 Analyze the data

30. Step 6 Act on the results

31. Experimental Designs OFAT or Single Factor Experiments Allows for manipulation of only one factor during an experiment

32. Experimental Designs Full Factorial Designs Consists of all possible combinations of all selected levels of the factors to be investigated To determine # of combinations or runs: Levels Factors

33. Experimental Designs Determine # of combinations: 6 Factors at 2 levels = 2 6 or 64 combinations 4 factors, 2 with 2 levels and 2 with 3 levels = 2 2 x 3 2 = 36 treatment combinations

34. Experimental Designs Full Factorials allows the most complete analysis because it can determine: 1)Main effects of factors 2)Effects of factor interactions

35. Variability 3 Sources of variability contributing to the variability in the numbers conditions of interest 1.Var. due to conditions of interest (we expect a change from manipulating some factor) measurement process 2.Var. due to measurement process (UNWANTED – errors in measuring equipment or technique) experimental material 3.Var. in experimental material (UNWANTED – trying to make material, or subjects, as similar as possible – block into groups)

36. Variability 3 types of variability 1.PLANNED, SYSTEMATIC – due to conditions of interest 2.CHANCE-LIKE VARIATION – background noise, an unplanned component from the measurement process 3.UNPLANNED, SYSTEMATIC – Biased, one of the main causes of wrong conclusions and ruined studies 1.Blocking: turns possible bias into planned, systematic variation 2.Randomization: turns bias into planned, chance like variation

37. Variability 3 Basic Principles 1.Random Assignment 2.Blocking 3.Factorial Crossing 1 and 2 are How we collect data 3 is how we construct treatments