CHNG2802/9202: Applied Maths for Chemical Engineers - Engineering Assignment Help

Assignment Task:

Testing outcome: Statistical comparison of experimental data using design of experiments (DOE)

Application: Process optimisation in a chemical plant using DOE

Problem Statement:
A chemical process for manufacturing a new herbicide was devised and tested in the laboratory. When the process scaled up to run in the pilot plant, the levels of a certain impurity (a by-product of the reactions) became a problem. In the laboratory, there was less than 0.8% of this impurity in the final products. But typical runs in the pilot plant had more than 2%. To make the process cost-effective, and to eliminate the need for further process steps to purify the product, it was desired to reduce the level of the impurity to less than 0.75%. To find a combination of factor levels that would do this, some experiments in the pilot were needed. The lead chemical engineer planned to conduct a full factorial design using 5 factors, including pH (X1), temperature (X2), addition time (X3), H2O level (X4) and agitation rate, RPM (X5) at two levels.

Tasks:
i. Calculate the main and interaction effects of all factors and find the most important factors and interactions. Create a design matrix table and summarize the calculated effect estimates in the table.

ii. Construct the main effect and interaction plots (only two-factor interaction) using Matlab (Matlab codes should be reported) and find the most important factors and interactions.

iii. Check if the response data is normally and randomly distributed by examining the normal probability plot of response data (normplot and lillietest in Matlab), boxplot of the response data, and the distribution of the response variable versus the actual run order.

iv. Look at the box plot of the response for each factor and find the most important factors. Explain the reason for choosing a particular factor.

v. Look at the normal probability plot of the effects and find the most significant effects.

vi. Carry out an ANOVA test using Matlab at the 0.1 level of significance as to whether or not the effect of factors and interaction (up to three-factor interaction) between them is significant in this process? Write down the Matlab codes used in this part and report the ANOVA table.

vii. Obtain a model for the response and residuals from a 25 design by fitting a regression model to the coded variables. The codified equation should include only the significant effects (main and interaction) identified by ANOVA test. Only up to three-factor significant interactions (if any) should be included in the regression model.

viii. Carry out the residual analysis of the model to evaluate the adequacy of the fitting by looking at the normal probability plot of residuals (normplot and lillietest in Matlab). In addition, calculate the coefficient of determination of the model, R2 and R2adj.

ix. Repeat the residual analysis and calculate R2 and R2adj for a new regression model using only up to two-factor significant interactions (if any) and compare the adequacy of the new model with the previous one. What is your conclusion?

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