1. Design Experiments Using Minitab Yanling Zuo( 左燕玲 ), PhD Minitab Inc.

2. MINITAB DOE Overview DOE menu Factorial

3. 3 © Minitab Inc., 2003 MINITAB DOE Overview Response Surface → ً← Mixture

4. 4 © Minitab Inc., 2003 MINITAB DOE Overview Taguchi

5. Case Study A quality team is studying how a catalytic reaction converts substrate into a final product. A sketch of the converter Feed 100% Reactants 70% products, 30% reactants catalyst Rev/min Temperature

6. Case Study… Factors identified after brainstorming: Feed rate – Flow rate settings for feed tank (10,15 ml/min) Catalyst (A, B) Agitation rate (100, 120) Temperature (140º, 180º C) Percent concentration (3%, 6%)

7. Case Study... Response: Percent of substrate reacted Data collection: The team has enough budget to perform 35 runs. They could run a full factorial design (2 5= 32). However, a better approach is to run a fractional design, analyze results, and decide on subsequent experimentation. What’s next? Create a ½ fraction design.

8. Case Study… Create the design with Minitab Go to Stat > DOE > Factorial > Create Factorial Design

9. Case Study… Output Note: Main effects confounded with 4-way interaction, 2-way interaction with 3-way interaction

10. Case Study… Worksheet

11. Case Study… Analyze the design with Minitab Go to Stat > DOE > Factorial > Analyze Factorial Design

12. Case Study… Normal Probability Plot of Effects

13. Case Study… Pareto chart of Effects

14. Case Study... Significant factors: Catalyst (B) Temp (D) Concentration (E) Catalyst x Temp (BD) Temp x Concentration (DE) What’s next: Remove non-significant effects and refit models.

15. Case Study... Output:

16. Case Study... Estimated coefficients: Reacted = -88.37 – 32.75 x Catalyst + 1.02 x Temp +23.25 x Conc + 0.27 x Catelyst x Temp -0.16 x Temp x Conc. (Can be used to predict percent reacted settings)

17. Case Study... Residual plots What’s next? Create factorial plots to find best settings.

18. Case Study... Factorial Plots

19. Case Study...

20. Conclusions: Feed rate and agitation do not have a significant impact Catalyst B, a temperature of 180ºC, and 3% concentration maximize substrate consumption. Followup experiment: The team had budget for 19 additional runs. They used Catalyst B and run a 2 2 full factorial design with 2 center points to detect curvature in the response. They centered experiment at currently known optimal settings,180ºC, 3%.

21. Case Study... Numerical output for the follow up experiment:

22. Case Study... Graphical output:

23. Case Study... Assessing Power: Design: 2 x 2, 1 replicate, 2 center points. Variance (MSE) = 1.28 St Dev = 1.131 Size of effect: A change of 3% in reacted substrate.

24. Case Study... This design has low power (0.165).

25. Case Study... Conclusions: A quadratic effect on catalytic reaction due to temperature and concentration is present. This design has low power, not the best choice. A better design would include 2 replicates, but would require 12 runs (assuming 2 center points per replicate) rather than 6. Additional consideration: Consider using response surface methodology to model the curvature.