response surface methodology

1. PRESENT BY:
WAN NOR NADYAINI WAN OMAR

2. Experiment
DOE spreadsheet
Mathematical model
Validity of Data
Variable selection
Find relationship
Optimization
Design of
experiment
Analysis of
Data

4.  What response variables are to be measured, how they will be
measured, and in what sequence?
 Which factor are most important and therefore will be included in the
experiment, and which are least important and can these factor be
omitted? With the important factors, can the desired effects be
detected?
 What extraneous or disturbing factors must be controlled or at least
have their effects minimized?
 What is the experimental unit, that is to say, what is the piece of
experimental material from which a response value is measured? How
are the experimental units to be replicated, if at all?
 The choice of the factors and level determined the type, size and
experimental region. The no. of level at each factor as well as the no. of
replicated experiment units represent the total no. of experiment.

5. Box-Wilson central
composite designed
(CCD)
INDEPENDENT VARIABLE
-how many?
-what are the range? DEPENDENT
VARIABLE/RESPONSE
-conversion, yields, selectivity?
e.g.: full 34 factorial designs (four
factors each at three levels),
eight star point and two center
point

6. Variables are things that we measure, control, or
manipulate in research.
Independent Variables are those that are manipulated.
They are processing conditions that are presumed to
influence the values of the response variable.
Similar words: regressor or explanatory variables, factors.
Dependent Variables are those that are only measured
whose value is assumed to be affected by changing
the levels of the factors, and whose values we are
most interested in optimizing.
Similar words: response variables, outcomes.

7. The most common design (for the 2nd degree
model) is Central Composite Design (CCD)
Central Composite Design consists of:
(a). 2k vertices of a k-dimensional “cube” (2-level full
factorial design)  coded as ±1
(b). 2k vertices of a k-dimensional “star”  coded as ±
(c). n0≥1 “center” point replicates  coded as 0

8. Factors Symbol
Range and Levels
-1 0 +1
Molar ratio methanol: oil X1 20:1 30:1 40:1
Catalyst loading, wt% X2 2 3 4
Reaction Time, min X3 120 180 240
Reaction Temperature X4 90 120 150

9. Open spreadsheet STEP 1
Click StatisticaSTEP 2

10. Click industrial statistics & six sigmaSTEP 3
Click experimental design (DOE)STEP 4

11. Click central composite, non factorial, surface
design→ok
STEP 5

12. Pick suitable design →okSTEP 6
CCD

13. Click change factor value etcSTEP 7

14. Insert the variable and range → okSTEP 8

15. Click design display
(standard order)
STEP 9
Design display on
workbook windows

16. Select all → right click→
copy with headers
STEP 1
Paste on spreadsheetSTEP 2

17. Right click on the
column→edit
STEP 1
click file→saveSTEP 2
click file→printSTEP 3

18. Run
s
Manipulated Variables Responses
X1 X2 X3
Operating
temperature,T(oC)
Levelb Molar Ratio
(meOH: oil)
Level
b
Reaction
time,t (h)
Levelb Yield, Y1
(%)
1 50 -1 3 -1 2 -1 91.90
2 50 -1 3 -1 4 +1 84.60
3 50 -1 10 +1 2 -1 65.15
4 50 -1 10 +1 4 +1 95.95
5 70 +1 3 -1 2 -1 63.90
6 70 +1 3 -1 4 +1 94.95
7 70 +1 10 +1 2 -1 87.60
•DOE is a collection of encoded settings of the process variables. Each process variable is
called an experimental factor
•Each combination of settings for the process variable is called a run
•A response variable is a measure of process performance.
•Each value of response is called an observation.

20. Remember save the spreadsheet
(note: spreadsheet is an important in statistica)
Open spreadsheet and insert the result STEP 1

21. Click StatisticaSTEP 2
Click industrial statistics & six sigmaSTEP 3
Click experimental design (DOE)STEP 4

22. Click central composite, non factorial, surface
design→ok
STEP 5
Click analyze design tabSTEP 6

23. Click variablesSTEP 8

24. Pick variable →okSTEP 9
Click okSTEP 10

25. Analysis of the central composite (response surface) experiment windows opened.
(note: this windows is an important for analysis since it display all information needed.

26. Y = βo + β1X1 + β2X2 + β3X3 + β12X1X2 + β13X1X3 +β23X2X3 +
β11X1
2 + β22X2
2 +β33X3
2
Y : predicted response
o : intercept coefficient (offset)
1 , 2 and 3 : linear terms
11 , 22 and 33 : quadratic terms
12 , 13 and 23 : interaction terms
X1 , X2 and X3 : uncoded independent
variables
The full quadratic models of conversion and ester yield were
established by using the method of least squares:

27. Click Anova/effect
→regression coefficient
STEP 2
434232413121
2
4
2
3
2
2
2
143212
005.0001.0056.0011.0004.0198.0
003.0001.0843.0050.0978.1774.0266.0623.4048.192
XXXXXXXXXXXX
XXXXXXXXY



28.  The adequacy of the fitted model is checked by ANOVA
(Analysis of Variance) using Fisher F-test
 The fit quality of the model can also be checked from
their Coefficient of Correlation (R) and Coefficient of
Determination (R2)
 The significance of the model parameters is assessed by
p-value and t-value.
 Coefficient of Determination (R2) reveals a proportion of
total variation of the observed values of activity (Yi)
about the mean explained by the fitted model
R2=SSR/SST
 Coefficient of Correlation (R) reveals an acceptability
about the correlation between the experimental and
predicted values from the model.

29.  The F-value is a measurement of variance of data about the mean
based on the ratio of mean square (MS) of group variance due to
error.
 F-value = MS regression/MSresidual = (SSR/DFregression)/ (SSE/DFresidual)
 F table =F(p−1,N−p,α)
 p−1 :DFregression
 N−p:DFresidual
 α-value: level of significant
 Null hypothesis: all the regression coefficient is zero.
 the calculated F-value should be greater than the tabulated F-
value to reject the null hypothesis,

30. Sources
Sum of
Squares(SS)
Degree of
Freedom(d.f)
Mean Squares
(MS)
F-value F0.05
Regression
(SSR)
2807.32 14 200.52 3.39 >2.74
Residual 649.87 11 59.08
Total (SST) 3457.29 25
Click ANOVA table tabSTEP
R2>0.75
(Haaland, 1989)
SST
Residual
SSR= SST-residual
DF
DFSSR= DFSST-DF residual

31. Click predicted and profiling→
predicted vs observed value tab
STEP

32.  T-Value:
 Measure how large the coefficient is in relationship to its standard
error
 T-value = coefficient/ standard error
 P-value
 is an observed significance level of the hypothesis test or the
probability of observing an F-statistic as large or larger than one we
observed.
 The small values of p-value  the null hypothesis is not true.
Interpretation?
- If a p-value is ≤ 0.01, then the Ho can be rejected at a 1% significance level 
“convincing” evidence that the HA is true.
- If a p-value is 0.01<p-value≤0.05, then the Ho can be rejected at a 5% significance
level  “strong” evidence in favor of the HA.
- If a p-value is 0.05<p-value≤0.10, then the Ho can be rejected at a 10% significance
level. it is in a “gray area/moderate”
- If a p-value is >0.10, then the Ho cannot be rejected. “weak” or ”no” evidence in
support of the HA.

33. Click quick tab→ pareto chart of effectSTEP

34. Click quick tab→ summary effect estimationSTEP

36. Click quick tab→ fiited response surfaceSTEP 1
Choose variable→ okSTEP 2
Click okSTEP 3

38. Click quick tab→ fiited response surfaceSTEP 1
Choose variable→ okSTEP 2
Click okSTEP 3

41. Predicted
response
Click quick tab→ critical value (min,
max, saddle)
STEP 1

42. Responses Predicted Value Observed
Value
Error (%)
Ester Yield (%) 75.58 79.67 5.41
Conversion (%) 70.12 72.56 3.48

44. Right click→ graph properties all optionSTEP 1

46. • Response Surface Methodology is a powerful
method for design of experimentation, analysis of
experimental data, and optimization.
• Advantage:
– design of experiment, statistical analysis, optimization,
and profile of analysis in one step
– Produce empirical mathematical model
• Disadvantage: only single-response optimization

47.  Montgomery, D. C. 1997. Design and Analysis of
Experiment. Fifth Edition. Wiley, Inc., New York, USA.
 Brown, S. R. and Melemend, L. E. 1990. Experimental
Design and Analysis Quantitative Application in the
Social Science. Sage Publication, California. 74.
 Cornell J.A. 1990. How to Apply Response Surface
Methodology. America Society For Quality Control:
Statistic Devision . US.
 Haaland, P. D. 1989. Experimental Design in
Biotechnology. Marcel Dekker Inc., New York.