A 2^3 full factorial screening experimental design was performed to identify the
ID: 3227615 • Letter: A
Question
A 2^3 full factorial screening experimental design was performed to identify the important factors affecting the percent conversion in a chemical process. Two factors, temperature in C(x1) and reactant concentration (x2) were identified as thekey process input variables and the method of steepest ascent was applied to identify the maximum percent conversion area. Create and analyze a central composite design using the data inthe following table (in standard run order). Identify the temperature and reactant concentration setting that maximizes percent conversion. Test the residuals assumption and comment on the adequacy of the model.
Std. Run Temp L Reactant% Reactant% Conversion 1 200 15 53 2 250 15 88 3 200 25 79 4 250 25 83 5 189.65 20 58 6 260.35 20 88 7 225. 12.93 75 8 225. 27.07 84 9 225 20 86 10 225 20 89 11 225 20 83 12 225 20 81 A 25 full factorial screening experimental design was performed to identify the important factors affecting the percent conversion in a chemical process. Two factors, temperature in C (1) and reactant concentration (2) were identified as thekey process input variables and the method of steepest ascent was applied to identify the maximum percent conversion area. Create and analyze a central composite design using the data inthe following table (in standard run order). Identify the temperature and reactant concentration setting that maximizes percent conversion. Test the residuals assumption and comment on the adequacy of the model. ISt.Run! Temp Reactant Conversion 200 15 53 250 15 25 79 200 250 25 83 5 189.65 20 58 6 260.35 20 88 12.93 225 75 225 27.07 86 225 20 20 10 225 89 225 20 83 12 225 20 81Explanation / Answer
We found out a generalised model /equation to relate conversion with temp & reactant, using multipl linear regression equation.
We also used interaction effect on temp & reactant:
we used solver to optimise.
Std. Run Temp L Reactant% Reactant% temp*reactant Conversion 1 200 15 3000 53 2 250 15 3750 88 3 200 25 5000 79 4 250 25 6250 83 5 189.65 20 3793 58 6 260.35 20 5207 88 7 225 12.93 2909.25 75 8 225 27.07 6090.75 84 9 225 20 4500 86 10 225 20 4500 89 11 225 20 4500 83 12 225 20 4500 81 SUMMARY OUTPUT Regression Statistics Multiple R 0.897133 R Square 0.804848 Adjusted R Square 0.731666 Standard Error 6.058956 Observations 12 ANOVA df SS MS F Significance F Regression 3 1211.229 403.743 10.99789 0.003278 Residual 8 293.6876 36.71095 Total 11 1504.917 Coefficients Standard Error t Stat P-value Lower 95% Intercept -308.56 111.0972 -2.77739 0.024021 -564.751 Temp L Reactant% 1.647161 0.492233 3.346304 0.010136 0.51207 Reactant% 14.79328 5.469868 2.704504 0.026886 2.17974 temp*reactant -0.062 0.024236 -2.5582 0.033742 -0.11789 Now let us optimize to find out maximum conversion. Conversion= temp reactant 189.65 12.93 <-minimum values 102.8432 260.35 12.93 260.35 27.07 <-maximum valuesRelated Questions
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