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Selecting experimental variables for response surface modeling
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# How to use statistica for rsm study

response surface methodology

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### How to use statistica for rsm study

1. 1. PRESENT BY: WAN NOR NADYAINI WAN OMAR
2. 2. Experiment DOE spreadsheet Mathematical model Validity of Data Variable selection Find relationship Optimization Design of experiment Analysis of Data
3. 3.  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.
4. 4. 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
5. 5. 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.
6. 6. 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
7. 7. 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
8. 8. Open spreadsheet STEP 1 Click StatisticaSTEP 2
9. 9. Click industrial statistics & six sigmaSTEP 3 Click experimental design (DOE)STEP 4
10. 10. Click central composite, non factorial, surface design→ok STEP 5
11. 11. Pick suitable design →okSTEP 6 CCD
12. 12. Click change factor value etcSTEP 7
13. 13. Insert the variable and range → okSTEP 8
14. 14. Click design display (standard order) STEP 9 Design display on workbook windows
15. 15. Select all → right click→ copy with headers STEP 1 Paste on spreadsheetSTEP 2
16. 16. Right click on the column→edit STEP 1 click file→saveSTEP 2 click file→printSTEP 3
17. 17. 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.
18. 18. Remember save the spreadsheet (note: spreadsheet is an important in statistica) Open spreadsheet and insert the result STEP 1
19. 19. Click StatisticaSTEP 2 Click industrial statistics & six sigmaSTEP 3 Click experimental design (DOE)STEP 4
20. 20. Click central composite, non factorial, surface design→ok STEP 5 Click analyze design tabSTEP 6
21. 21. Click variablesSTEP 8
22. 22. Pick variable →okSTEP 9 Click okSTEP 10
23. 23. Analysis of the central composite (response surface) experiment windows opened. (note: this windows is an important for analysis since it display all information needed.
24. 24. 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:
25. 25. 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  
26. 26.  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.
27. 27.  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,
28. 28. 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
29. 29. Click predicted and profiling→ predicted vs observed value tab STEP
30. 30.  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.
31. 31. Click quick tab→ pareto chart of effectSTEP
32. 32. Click quick tab→ summary effect estimationSTEP
33. 33. Click quick tab→ fiited response surfaceSTEP 1 Choose variable→ okSTEP 2 Click okSTEP 3
34. 34. Click quick tab→ fiited response surfaceSTEP 1 Choose variable→ okSTEP 2 Click okSTEP 3
35. 35. Predicted response Click quick tab→ critical value (min, max, saddle) STEP 1
36. 36. Responses Predicted Value Observed Value Error (%) Ester Yield (%) 75.58 79.67 5.41 Conversion (%) 70.12 72.56 3.48
37. 37. Right click→ graph properties all optionSTEP 1
38. 38. • 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
39. 39.  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.
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response surface methodology

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