Case Study 3 Questions

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Kenyatta University *

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Chemistry

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Nov 24, 2024

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Case Study 3 Factorial Design of Experiments to Optimize a Chemical Process This case study is about a process that produces a chemical whose yield (weight in grams) needs to be maximized while minimizing the cost ($) of production. 3.1 Define Phase The objective is to maximize the yield and minimize the cost. The members of the Six Sigma project team brainstorm to identify the following factors that may be affecting the yield and cost:  Processing time  Processing temperature  Catalyst 3.2 Measure and Analyze Phases Because it is impractical to design an experiment with all possible processing times, processing temperatures, and catalysts, the project team shortlisted the levels of the above three factors to what is shown in the table below for the experiment. Inasmuch as there are 3 factors and 2 levels of each factor, there are 8 (2 3 ) runs possible for a full factorial replication of the experiment. Although it is possible that the time (morning shift or afternoon shift) of performing the experiment too has an effect on the yield or cost, the team knows that one replication of the experiment can be conveniently performed within the duration of a shift. In other words, the shift type is the same for all 8 runs in a replication. Hence, the shift type is not considered a factor withineach replication. However, the team wants to perform two replications of the experiment (2 * 8 runs = 16 runs) to gather additional data for more reliable analysis, and this means that not all 16 runs will be from the same shift. This in turn means that the potential effect of the shift type must somehow be studied in the experiment. Hence, the team decides to perform a 2-block experiment, where one replication is performed in the morning shift

(block) and the other in the afternoon shift (block). (Note: If an entire replication cannot be performed within the duration of a shift, the shift type must be considered the fourth factor with two levels: morning andafternoon. In that case, 16 (2 4 ) runs are possible for a full factorial replication of the experiment.) 1. Create the factorial design of the experiment as shown in the case study pdf file.Randomize the run. Label two empty columns as “Yield” and “Cost” and enter the data that is shown in the table below. Ensure that what you enter in your worksheet matches the factor levels. Blocks Time Temp Catalyst Yield Cost 1 20 150 Ajuba 42.7636 27.5306 1 20 150 Tapori 43.3937 30.5424 1 20 200 Ajuba 45.1931 31.0513 1 20 200 Tapori 44.7077 34.6241 1 50 150 Ajuba 44.7592 29.3841 1 50 150 Tapori 45.5991 32.6394 1 50 200 Ajuba 48.4665 31.7457 1 50 200 Tapori 49.204 36.8941 2 20 150 Ajuba 43.2976 28.0646 2 20 150 Tapori 43.0617 30.2104 2 20 200 Ajuba 44.8891 30.7473 2 20 200 Tapori 45.3297 35.2461 2 50 150 Ajuba 45.3932 28.7501 2 50 150 Tapori 45.1531 33.0854 2 50 200 Ajuba 49.0645 32.3437 2 50 200 Tapori 48.672 37.4261 3. Analyze Phase The team wishes to consider the potential effects of all of the possible factors and their interactions. 2. Analyze the factorial designexperimental data for ‘Yield’ as shown in the pdf file. Create Pareto chart and normal plot of the standardized effects. Show and discuss the ANOVA results. 3. Eliminate the non-significant factors and non-significant interactions and repeat # 2. 4. Analyze the factorial design experimental data for ‘Cost’ as shown in the pdf file. Create Pareto chart and normal plot of the standardized effects. Show and discuss the ANOVA results.

5. Eliminate the non-significant factors and non-significant interactions and repeat #4. 6. Develop main effects plots and interaction plots for ‘Yield’. Explain the results. 7. Develop main effects plots and interaction plots for ‘Cost’. Explain the results. After analyzing the effects of all the factors and their interactions on Yield and Cost, the team wishes to find out the optimal combination of factors that maximizes Yield and minimizes Cost. 8. Use the response optimizer to find out the optimal combination of factors that maximize the Yield and minimize the Cost, considering 1) a target of 51 gramsis appropriate for Yield, with no upper limit and a lower limit of 41 grams, and 2) a target of $31 is appropriate for Cost, with no lower limit and an upper limit of $41.

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