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
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%)
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.
Case Study… Create the design with Minitab Go to Stat > DOE > Factorial > Create Factorial Design
Case Study… Output Note: Main effects confounded with 4-way interaction, 2-way interaction with 3-way interaction
Case Study… Worksheet
Case Study… Analyze the design with Minitab Go to Stat > DOE > Factorial > Analyze Factorial Design
Case Study… Normal Probability Plot of Effects
Case Study… Pareto chart of Effects
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.
Case Study... Output:
Case Study... Estimated coefficients: Reacted = – x Catalyst x Temp x Conc x Catelyst x Temp x Temp x Conc. (Can be used to predict percent reacted settings)
Case Study... Residual plots What’s next? Create factorial plots to find best settings.
Case Study... Factorial Plots
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%.
Case Study... Numerical output for the follow up experiment:
Case Study... Graphical output:
Case Study... Assessing Power: Design: 2 x 2, 1 replicate, 2 center points. Variance (MSE) = 1.28 St Dev = Size of effect: A change of 3% in reacted substrate.
Case Study... This design has low power (0.165).
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.