Section IX , Improve

1. Section IX, Improve

2. Objectives in Using DOE • Will help you gain knowledge in: • Improving performance characteristics • Reducing costs • Understand regression analysis • Understand relationships between variables • Understand correlation • Understand how to optimize processes • So you can: • Recognize opportunities • Understand terminology • Know when to get help IX-2

3. Let’s Start with an Example: Plot a histogram and calculate the average and standard deviation Fuel Economy 16 14 12 10 Number of Cars 8 6 4 2 0 0 to <6 6 to <12 12 to <18 18 to <24 24 to <30 30 to <36 36 to <42 42 to <48 48 to <54 54 to <=60 mgp IX-2

4. MANPOWER METHOD MACHINE MOTHER MEASUREMENT MATERIAL NATURE What Might Explain the Variation? Experimental design (a.k.a. DOE) is about discovering and quantifying the magnitude of cause and effect relationships. We need DOE because intuition can be misleading.... but we’ll get to that in a minute. Regression can be used to explain how we can model data experimentally. IX-2

5. Mileage Data with Vehicle Weight: X Y=f(X) Y Let’s take a look at the mileage data and see if there’s a factor that might explain some of the variation. Draw a scatter diagram for the following data: IX-2

6. Regression Analysis Y=f(X) If you draw a best fit line and figure out an equation for that line, you would have a ‘model’ that represents the data. IX-2

7. Understanding a System There are basically three ways to understand a process you are working on. • Classical 1FAT experiments • One factor at a time (1FAT) focuses on one variable at two or three levels and attempts to hold everything else constant (which is impossible to do in a complicated process). • Mathematical model • Express the system with a mathematical equation. • DOE • When properly constructed, it can focus on a wide range of key input factors and will determine the optimum levels of each of the factors. Each have their advantages and disadvantages. We’ll talk about each. IX-2

8. 1FAT Example T(1,2) Y=f(X) Y F(1,2) Let’s consider how two known (based on years of experience) factors affect gas mileage, tire size (T) and fuel type (F). IX-2

9. One –at –a-time Design Step 1: Select two levels of tire size and two kinds of fuels. Step 2: Holding fuel type constant (and everything else), test the car at both tire sizes. IX-2

10. One –at –a-time Design Since we want to maximize mpg the more desirable response happened with T2 Step 3: Holding tire size at T2, test the car at both fuel types. IX-2

11. One –at –a-time Design What about the possible interaction effect of tire size and fuel type. F2T1 Looks like the ideal setting is F2 and T2 at 40mpg. This is a common experimental method. IX-2

12. One –at –a-time Design Suppose that the untested combination F2T1 would produce the results below. There is a different slope so there appears to be an interaction. A more appropriate design would be to test all four combinations. IX-2

13. What About Other Factors – and Noise? • We need a way to • investigate the relationship(s) between variables • distinguish the effects of variables from each other (and maybe tell if they interact with each other) • quantify the effects... • ...So we can predict, control, and optimize processes. IX-2

14. We can see some problems with 1FAT. Now let’s go back and talk about the statapult. We can do a mathematical model or we could do a DOE. DOE will build a ‘model’ - a mathematical representation of the behavior of measurements. or… You could build a “mathematical model” without DOE and it might look something like... The Other Two Possibilities IX-2

15. A Mechanistic Model for the Statapult IX-2

16. DOE to the Rescue!! DOE uses purposeful changes of the inputs (factors) in order to observe corresponding changes to the outputs (response). Remember the IPO’s we did – they are real important here. IX-3

17. (-,+) (+,+) High (+) In tabular form, it would look like: Factor B Settings Low (-) Run A B (-,-) (+,-) 1 - - 2 - + 3 + - Low (-) High (+) 4 + + Factor A Settings The Basics X1 Y A X2 B • To ‘design’ an experiment, means to pick the points that you’ll use for a scatter diagram. IX-4

18. Planning - DOE Steps • Set objectives (Charter) • Comparative • Determine what factor is significant • Screening • Determine what factors will be studied • Model – response surface method • Determine interactions and optimize • Select process variables (C&E) and levels you will test at • Select an experimental design • Execute the design • CONFIRM the model!! Check that the data are consistent with the experimental assumptions • Analyze and interpret the results • Use/present the results IX-11

19. Planning - Charter IX-11

20. Planning - Charter http://jimakers.com/downloads/DOE_Setup.docx IX-11

21. Full vs.Fractional Factorial • A full factorial is an experimental design which contains all levels of all factors. No possible treatments are omitted. • The preferred (ultimate) design • Best for modeling • A fractional factorial is a balanced experimental design which contains fewer than all combinations of all levels of all factors. • The preferred design when a full factorial cannot be performed due to lack of resources • Okay for some modeling • Good for screening IX-32

22. 2 Level Designs • Full factorial • 2 level • 3 factors • 8 runs • Balanced (orthogonal) • Fractional factorial • 2 level • 3 factors • 4 runs - Half fraction • Balanced (orthogonal) IX-21

23. Average Y when A was set ‘high’ Average Y when A was set ‘low’ Measuring An “Effect” The difference in the average Y when A was ‘high’ from the average Y when A was ‘low’ is the ‘factor effect’ The differences are calculated for every factor in the experiment IX-24

24. Looking For Interactions When the effect of one factor changes due to the effect of another factor, the two factors are said to ‘interact.’ B = Low B = High B = Low Response - Y Response - Y Strong B = High Slight Low High Low High Factor A Factor A more than two factors can interact at the same time, but it is thought to be rare outside of chemical reactions. None B = Low Response - Y B = High Low High Factor A IX-17

25. Let’s Try This Out! X1 A Y X2 B X3 C X4 D Y=f(X1, X2, X3, X4) What design should we use? Using the statapult, we will experiment with some factors to “model” the process. We will perform a confirmation run to determine if the model will help us predict the proper settings required to achieve a desired output. IX-21

26. Reasons Why a Model Might Not Confirm: There may not be a true cause-and-effect relationship.  Too much variation in the response Measurement error Poor experimental discipline Aliases (confounded) effects Inadequate model Something changed - And: - IX-21

27. Remember? IX-21

28. IX-22

29. Example Pages - Data IX-23

30. Marginal Means Plot IX-26

31. Regression Table IX-27

32. Prediction and Confirmation IX-27

33. 3 Level Designs • Full factorial • 3 level • 3 factors • 27 runs • Balanced (orthogonal) • Used when it is expected the response in non-linear IX-30

34. 2D Contour Plot Useful to see how factors effect the response and to determine what other settings provide the same response IX-9

35. 3D Response Surface Plot Helpful in reaching the optimal result IX-9

36. High Level Of Control Low Finding The Right Level Of Control Poka-Yoke (Mistake Proofing) Statistical Process Control (SPC) Written Procedures (SOPs, FMEAs, etc….) Verbal Instructions (Training, Sounds, etc….) Use the right level of control that brings long term stability to the process that you are improving. There will most likely be a tradeoff between the effectiveness, effort and cost of the control technique. IX-42

37. SOP as the control Exercise: Draw a rectangle. Draw a semi- circle along the left edge. Draw another rectangle along the right edge of the rectangle. Draw a trapezoid along the right edge of that rectangle. Draw a rectangle along the right edge of the trapezoid. What is your result? IX-42

38. 1 5 3 2 4 Class Exercise Draw the described figure IX-43