1. 1 Jim Grayson, PhD MSC 605 MSC 605 Design of Experiments

2. 2 Jim Grayson, PhD MSC 605 DESIGN OF EXPERIMENTS Purposeful changes of the inputs (factors) to a process in order to observe corresponding changes in the output (response). Process InputsOutputs Douglas Montgomery, Design and Analysis of Experiments

3. 3 Jim Grayson, PhD MSC 605 Why use DOE ? A basis of action -- allows purposeful changes. An analytic study -- one in which action will be taken on a cause-and-effect system to improve performance of a product or process in the future. Follows the scientific approach to problem solving. Provides a way to measure natural variation. Permits the clear analysis of complex effects. Most efficient way to derive the required information at the least expenditure of resources. Moen, Nolan and Provost, Improving Quality Through Planned Experimentation

4. 4 Jim Grayson, PhD MSC 605 Interactions Varying factors together vs. one at a time. BUCKBUCK D O E - - + + George Box, Do Interactions Really Matter, Quality Engineering, 1990.

5. 5 Jim Grayson, PhD MSC 605 BUCKBUCK D O E - - + + Voila! George Box, Do Interactions Really Matter, Quality Engineering, 1990.

6. 6 Jim Grayson, PhD MSC 605 Experiment run at SKF -- largest producer of rolling bearing in the world. Looked at three factors: heat treatment, outer ring osculation and cage design. Results: choice of cage design did not matter (contrary to previously accepted folklore -- considerable savings) life of bearing increased five fold if osculation and heat treatment are increased together -- saved millions of dollars ! George Box, Do Interactions Really Matter, Quality Engineering, 1990.

7. 7 Jim Grayson, PhD MSC 605 Bearings like this have been made for decades. Why did it take so long to discover this improvement ? One factor vs. interaction effects ! Osculation Cage Heat 128 16 1921 26 85 17 25 George Box, Do Interactions Really Matter, Quality Engineering, 1990.

8. 8 Jim Grayson, PhD MSC 605 10621 18 23 Osculation Heat The Power of Interactions ! George Box, Do Interactions Really Matter, Quality Engineering, 1990.

9. 9 Jim Grayson, PhD MSC 605 2 Design Example 2 Consider an investigation into the effect of the concentration of the reactant and the amount of catalyst on the reaction time of a chemical process. L H reactant (factor A) 15% 25% catalyst (factor B) 1 bag 2 bags Douglas Montgomery, Design and Analysis of Experiments

10. 10 Jim Grayson, PhD MSC 605 Design Matrix for 2 2 ABABTotalAverage --+ +-- -+- +++ Main effects Interaction

11. 11 Jim Grayson, PhD MSC 605 Factor A - B -28252780 SettingsA + B -363232100 A - B +18192360 A + B +31302990 IIIIIITotal Replicates Douglas Montgomery, Design and Analysis of Experiments

12. 12 Jim Grayson, PhD MSC 605 An effect is the difference in the average response at one level of the factor versus the other level of the factor. - + A 60 90 80 100 A effect = ( [90 + 100] - [60 + 80] ) / 2(3) = 8.33 Douglas Montgomery, Design and Analysis of Experiments

13. 13 Jim Grayson, PhD MSC 605 Use a matrix to find the effects of each factor, including the interaction effect between the two factors. ABABTotalAverage --+8026.7 +--10033.3 -+-6020 +++9030 Avg + 31.7 Avg - 23.3 Effect 8.4 Douglas Montgomery, Design and Analysis of Experiments

14. 14 Jim Grayson, PhD MSC 605 ABABTotalAverage --+8026.7 +--10033.3 -+-6020 +++9030 Avg + 31.7 25 28.3 Avg - 23.3 30 26.7 Effect 8.4 -5 1.7 Completing the matrix with the effect calculations: Douglas Montgomery, Design and Analysis of Experiments

15. 15 Jim Grayson, PhD MSC 605 -10 -5 0 5 10 B AB A Dot Diagram Douglas Montgomery, Design and Analysis of Experiments

16. 16 Jim Grayson, PhD MSC 605 35 30 25 20 - + A Response Plots 35 30 25 20 - + B Douglas Montgomery, Design and Analysis of Experiments

17. 17 Jim Grayson, PhD MSC 605 35 30 25 20 - + A B - B + B - B + A - A + 26.7 20 33.3 30 Interaction Response Plot Douglas Montgomery, Design and Analysis of Experiments

18. 18 Jim Grayson, PhD MSC 605 Normal Probability Plots n Effects are the differences between two averages. n As we know, the distribution of averages are approximately normal. n NPP can be used to identify the effects that are different from noise. Soren Bisgaard, A Practical Introduction to Experimental Design

19. 19 Jim Grayson, PhD MSC 605 Construction of NPP n Can be constructed with effects on horizontal and cumulative percentages on vertical -- but this requires normal probability paper. n Can also be constructed using the inverse standard normal of the plotting point ( (i -.5) / n ). n Look for effects that are different from plotted ‘vertical’ reference line. Soren Bisgaard, A Practical Introduction to Experimental Design

20. 20 Jim Grayson, PhD MSC 605 Steps in constructing NPP 1. Compute effects. 2. Order effects from smallest to largest. 3. Let i be the order number (1 to n). 4. Calculate probability plotting position of the ordered effect using the formula ( p = [i -.5]/n). 5. Using a standard normal table determine the Z value corresponding to each left tail probability of step 4. 6. Plot the effects on horizontal axis and Z on vertical. 7. Fit a line through the most points. 8. Those ‘off the line’ are significant effects. Soren Bisgaard, A Practical Introduction to Experimental Design

21. 21 Jim Grayson, PhD MSC 605 3 4 5 2

22. 22 Jim Grayson, PhD MSC 605 Plot reference line through the majority of points. Look for effects which are off this line. 6 7 8

23. 23 Jim Grayson, PhD MSC 605 Exercise You will conduct a 2 2 experiment with 2 replicates. Factors:LH A -- Tower35 B -- Front Stop02 C -- Back Stop57

24. 24 Jim Grayson, PhD MSC 605 Requirements: 1. Collect data -- total of 16 observations (random order). 2. Fill in matrix and compute effects. 3. Put averages on a cube plot. 4. Plot effects on dot plot and normal probability plot. 5. Create appropriate response plots for significant interactions and main effects. 6. Interpret results and make recommendations to management.

25. 25 Jim Grayson, PhD MSC 605 Design Matrix

26. 26 Jim Grayson, PhD MSC 605 Cube Plot

27. 27 Jim Grayson, PhD MSC 605 Response Plots - + - +

28. 28 Jim Grayson, PhD MSC 605 Z Effect Normal Probability Plot

29. 29 Jim Grayson, PhD MSC 605 Why use 2 k designs ? Easy to use and data analysis can be performed using graphical methods. Relatively few runs required. 2 k designs have been found to meet the majority of the experimental needs of those involved in the improvement of quality. 2 k designs are easy to use in sequential experimentation. Fractions of the 2 k (fractional factorials) can be used to further reduce the experiment size. Moen, Nolan and Provost, Improving Quality Through Planned Experimentation