Design of Experiment

 Design of Experiment                                                                                               11 January 2022

Tasks:

1. Full Factorial design data analysis

- Effect of single factors and thier rankings

- Interaction effects

2. Fractional Factorial design data analysis

- Effect of single factors and thier rankings

Case Study 2:

Excel File:DOE Excel (download file to view graph - website unable to view graph)

Full factorial design data analysis:

Effect of single factors

Table 1: Factor Levels

Level	Factor A – concentration of coagulant added	Factor B – Treatment Temperature	Factor C – Stirring Speed
+	1%	72 oF	200 rpm
-	2%	100 oF	400 rpm

Figure 1: Full factorial Data for Runs

Figure 2: Full factorial Calculation for Effect of Factors

Figure 3: Full factorial effect of factors Graph

Table 2: Full factorial total Effect of Factors

	Unit	Factor A – Concentration of coagulant added	Factor B – Treatment Temperature	Factor C – Stirring Speed
+	Ib/day	17.5	12	4
-		5	10.5	18.5
Difference		12.5	1.5	-14.5

- When Concentration of coagulant added increases from 1 to 2%, the amount of pollutant discharged increases from 5 lb/day to 17.5 lb/day

- When Treatment Temperature increases from 72 ^oF to 100 ^oF, the amount of pollutant increases from 10.5 lb/day to 12 lb/day.

- When Stirring Speed increases from 200 to 400 rpm, the amount of pollutant decreases from 18.5 lb/day to 4 lb/day.

Ranking: 

1. Stirring Speed -> 2. Concentration of coagulant added -> 3. Treatment Temperature

Interaction Effect

A x B

Figure 4: Calculation for A x B interaction effect

Figure 5: Interaction effect of A x B graph

The gradient of both lines are different by a little margin. Therefore there’s an interaction between A and B, but the interaction is small. At LOW B, when the concentration of coagulant added increases from 1% to 2%, the amount of pollutant discharged increases by 12 from 4.5 lb/day to 16.5 lb/day. At HIGH B, when the concentration of coagulant added increases from 1% to 2%, the amount of pollutant discharged increases by 13 from 5.5 lb/day to 18.5 lb/day. Since the total increase of pollutant discharged is higher at HIGH B than LOW B by a little margin, the gradient of HIGH B is a little steeper than at LOW B.

A x C

Figure 6: Calculation for Ax C interaction effect

Figure 7: Interaction effect of A x C graph

The gradient of both lines are different (one is + and the other is -). Therefore there’s a significant interaction between A and C. At LOW C, when the concentration of coagulant increases from 1% to 2%, the amount of pollutant discharged increases by 26 from 5.5 lb/day to 31.5 lb/day. At HIGH C, when the concentration of coagulant increases from 1% to 2%, the amount of pollutant discharged decreases by 1 from 4.5 lb/day to 3.5 lb/day. Since the total change of pollutant discharged at LOW C is a increase, while at HIGH C, the total change of pollutant discharged is a decrease. Therefore the gradient of both lines are of opposite values and opposite directions.

B x C

Figure 8: Calculation for B x C interaction effect

Figure 9: Interaction of B x C graph

The gradient of both lines are different by a little margin. Therefore, there’s an interaction between B and C, but the interaction is small. At LOW C, when the Treatment temperature increases from 72 ^oF to 100 ^oF, the amount of pollutant discharge increases by 2 from 17.5 lb/day to 19.5 lb/day. At HIGH C, when the Treatment temperature increases from 72 ^oF to 100 ^oF, the amount of pollutant discharge increases by 1 from 3.5 lb/day to 4.5 lb/day.

Conclusion for Full Factorial Data Anaylsis:

In conclusion, Factor C Stirring Speed is the most significant factor effecting the amount of pollutant discharged followed by Factor A Concentration of coagulant added then Factor B Treatment Temperature. Factor A and B both increased amount of pollutant discharged when their levels were increased from low to high, only Factor C decreased amount of pollutant discharged when the level was increased from low to high. In terms of interactions between the factors, there is significant interaction for A x C but small interaction for A x B and B x C.

Fractional factorial design data analysis:

Effect of single factors

Figure 10: Data for fractional runs

Figure 11: Calculation for fractional factorial factor effect

Figure 12: Fractional factorial effect of factors graph

Table 3: Fractional factorial total effect of factors

	Unit	Factor A – Concentration of coagulant added	Factor B – Treatment Temperature	Factor C – Stirring Speed
+	Ib/day	18	19	4
-		5	4	19
Difference		13	15	-15

- When Concentration of coagulant added increases from 1% to 2%, the amount of pollutant discharged increases from 5 lb/day to 18 lb/day.

- When Treatment Temperature increases from 72 ^oF to 100 ^oF, the amount of pollutant increases from 4 lb/day to 19 lb/day.

- When Stirring Speed increases from 200 to 400 rpm, the amount of pollutant decreases from 19 lb/day to 4 lb/day.

Ranking:

1. Stirring Speed/Treatment temperature -> 3. Concentration of coagulant added

Conclusion for Fractional Factorial Data Analysis:

In conclusion, the most significant factor remains C Stirring Speed but it is tied to Factor B Treatment Temperature then Factor A concentration of Coagulant added. There is a difference between the ranking for full fractional and fractional fractorial as factor B treatment temperature increased its ranking from least significant to most significant. This means that some of the data collected may be wrong hence further study is necessary.

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