Design of Experiment (DOE)
Case study 2
Excel files link:
Full Factorial Design:
A: When the concentration of coagulant added increases from 1% to 2%, the amount of pollutant discharged increases from 5 lb/day to 17.5 lb/day.
B: When treatment temperature increases from 72oF to 100oF, the amount of pollutant discharged increases from 10.5 lb/day to 12 lb/day.
C: When stirrer speed increases from 200 rpm to 400 rpm, the amount of pollutant discharged decreases from 18.5 lb/day to 4 lb/day
Ranking: CAB
Based on the gradients of the lines for each factor, C(stirrer speed) has the largest gradient which means it has the most significant impact on the amount of pollutant discharged, followed by A and B.
Factor interaction:
For factor interaction, 3 factors, A, B and C were compared with each other and the results were tabulated in the diagram above. The data is also translated into a graphical format to show the interaction between the 2 chosen factors.
Based on the graphs, both AxB and BxC have similar gradients between their respective factors with a small difference which means that there is still a small amount of interaction between the factors.
Conclusion:
After performing the full factorial design, the significance of each factor could be ranked based on the gradients of the lines on the graphical representation which in this case factor C (stirrer speed) was the most significant factor as it the line representing it had the largest gradient of 14.5.
The interaction between all 3 factors were also measured. Between AxB and BxC, there were minimal interaction, meaning they less affected by one another. However, factors A and C from AxC had more interaction between each other as the gradients for both lines were very different.
Fractional Factorial Design:
For the fractional design, I chose runs 2, 3, 6 and 7 to ensure the factors are all balanced and orthogonal.
A: When the concentration of coagulant added increases from 1% to 2%, the amount of pollutant discharged increases from 5.5 lb/day to 16.5 lb/day.
B: When treatment temperature increases from 72oF to 100oF, the amount of pollutant discharged increases from 16.5 lb/day to 5.5 lb/day.
C: When stirrer speed increases from 200 rpm to 400 rpm, the amount of pollutant discharged decreases from 18 lb/day to 4 lb/day.
Ranking: CAB
Based on the gradients of the lines for each factor, C(stirrer speed) has the largest gradient of -14 which means it has the most significant impact on the amount of pollutant discharged, followed by A and B while they have the same gradient meaning they have the same effect.
Reflection:
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