Session 3 – Central composite designs, second order models, ANOVA, blocking, qualitative factors An intensive practical course mainly for PhD-students on the use of designs of experiments (DOE) and response surface methodology (RSM) for optimization problems. The course covers relevant background, nomenclature and general theory of DOE and RSM modelling for factorial and optimisation designs in addition to practical exercises in Matlab. Due to time limitations, the course concentrates on linear and quadratic models on the k≤3 design dimension. This course is an ideal starting point for every experimental engineering wanting to work effectively, extract maximal information and predict the future behaviour of their system. Mikko Mäkelä (DSc, Tech) is a postdoctoral fellow at the Swedish University of Agricultural Sciences in Umeå, Sweden and is currently visiting the Department of Chemical Engineering at the University of Alicante. He is working in close cooperation with Paul Geladi, Professor of Chemometrics, and using DOE and RSM for process optimization mainly for the valorization of industrial wastes in laboratory and pilot scales.” Schedule and details: The course took place at the University of Alicante and would not had been possible without the support of the Instituto Universitario de Ingeniería de Procesos Químicos.

1. Process/product optimization
using design of experiments and
response surface methodology
Mikko Mäkelä
Sveriges landbruksuniversitet
Swedish University of Agricultural Sciences
Department of Forest Biomaterials and Technology
Division of Biomass Technology and Chemistry
Umeå, Sweden

2. Contents
Practical course, arranged in 4 individual sessions:
 Session 1 – Introduction, factorial design, first order models
 Session 2 – Matlab exercise: factorial design
 Session 3 – Central composite designs, second order models, ANOVA,
blocking, qualitative factors
 Session 4 – Matlab exercise: practical optimization example on given
data

3. Session 1
Introduction
 Why experimental design
Factorial design
 Design matrix
 Model equation = coefficients
 Residual
 Response contour

4. Session 2
Factorial design
 Research problem
 Design matrix
 Model equation = coefficients
 Degrees of freedom
 Predicted response
 Residual
 ANOVA
 R2
 Response contour

5. Session 3
Central composite designs
Design variance
Common designs
Second order models
Stationary points
ANOVA
Blocking
Confounding
Qualitative factors

6. Session 4
Uncontrolled factors
Factor coding
Realized vs. planned
Response transformation
Coefficients
Observed vs. predicted
Residuals
ANOVA
Contour
Estimated prediction variance
Confidence interval

7. Research problem
A cuboidal (α=1, nc=3) central composite design to
study the effect of three factors on a response
 Inlet air temperature, T: 0-90 °C
 Slit height, S: 70-150 mm
 Sludge feeding, F: 275-775 kg/h
 Ambient RH (%) included as an uncontrolled
factor
Cuboidal design
α = 1

8. Research problem

9. Research problem
Factor coding?
Uncontrolled factors?

10. Research problem
N:o T S F RH
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17

11. Research problem

12. Research problem

13. Research problem

14. Research problem

15. Research problem
Parameter df Sum of
squares (SS)
Mean
square (MS) F-value p-value
Total corrected
Regression
Residual
Lack of fit
Pure error

16. Research problem

17. Research problem
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18. Research problem

19. Session 4
Uncontrolled factors
Factor coding
Realized vs. planned
Response transformation
Coefficients
Observed vs. predicted
Residuals
ANOVA
Contour
Estimated prediction variance
Confidence interval

20. How to continue?
Literature
 Myers RH, Montgomery DC, Anderson-Cook CM, Response Surface Methodology,
Process and Product Optimization Using Designed Experiments, 3rd ed., John Wiley &
Sons, Hoboken, New Jersey, 2009 (recommended)
 Eriksson L, Johansson E, Kettaneh-Wold N, Wikström C, Wold S, Design of
Experiments, Principles and Applications, 3rd ed., Umetrics, Umeå,2008 (useful for
beginners)
Software
 Matlab (The MathWorks, Inc.), Modde (Umetrics), Design Expert® (Stat-Ease, Inc.),
JMP (SAS Institute Inc.), Minitab (Minitab Inc.)

21. Thank you for participating!
You can contact me via
 E-mail (mikko.makela@slu.se)
 ResearchGate (https://www.researchgate.net/profile/Mikko_Maekelae)
 LinkedIn (https://www.linkedin.com/in/mikkomaekelae)