Design of experiment Case Study

 CASE STUDY 2 

In a wastewater treatment facility, a combination of coagulant chemicals, treatment temperature  and stirring speed were identified as a critical factor to treat the waste-water to produce clean  water. The clean water produced is recycled back into the main proses and at the same time reduce  the amount of pollutant discharged by the plant. 

8 runs were performed and the data are shown below. 

The response variable (y) is the amount of pollutant discharged (lb/day) 

A = concentration of coagulant added, 1% and 2% by weight 

B = treatment temperature, 72oF and 100oF  

C = Stirring speed, 200 rpm and 400 rpm

Excel link: https://drive.google.com/drive/folders/1AzLGqHpa4pp3zavHcMG8vznjACBMZCop?usp=sharing

	A	B	C	Y(lb/day)
1	1%	72	200	5
2	2%	72	200	30
3	1%	100	200	6
4	2%	100	200	33
5	1%	72	400	4
6	2%	72	400	3
7	1%	100	400	5
8	2%	100	400	4

 

	A	B	C	Y(lb/day)
1	-	-	-	5
2	+	-	-	30
3	-	+	-	6
4	+	+	-	33
5	-	-	+	4
6	+	-	+	3
7	-	+	+	5
8	+	+	+	4

Full factorial analysis

When the concentration of coagulant added increases from 1% to 2%, the amount of pollutant discharged increases from 5 lbs/day to 17.5 lbs/day.

When treatment temperature increases from  72oF to 100oF  the amount of pollutant discharged increases from 10.5 lbs/day to 12 lbs/day.

When the Stirring speed increases from   200 rpm to 400 rpm the amount of pollutant discharged decreases from 18.5 lbs/day to 4 lbs/day.

As the desired change is to reduce the discharged pollutant, the factor with the biggest effect is the stirring speed, followed by concentration of coagulant and lastly treatment temperature.

Both the lines have a gradient that is positive slightly different, hence there are interactions between the factors A and B but the interactions are small.

Both lines have a gradient that is negative that is the same, hence there are no interactions between the parallel lines, hence there are no interactions between factors B and C

Both lines have a negative gradient that has a big difference, hence there is an interaction between the lines and the interaction between factor A and C are significant.

For the fractional factorial,  When the concentration of coagulant added increases from 1% to 2%, the amount of pollutant discharged increases from 5 lbs/day to 17 lbs/day.

When treatment temperature increases from  72oF to 100oF  the amount of pollutant discharged increases from 5 lbs/day to 17 lbs/day.

When Stirring speed increases from   200 rpm to 400 rpm  the amount of pollutant discharged decreases from 18 lbs/day to 4 lbs/day

The impact of each factor on the pollutants discharged in decreasing order is stirring speed, coagulant added, and treatment temperature.

The trend is mostly similar to the full factorial, with the only difference being a difference in impact when the treatment temperature is changed. This is most likely due to lesser data points, resulting in data that represents the overall system less accurately.