Design Of Experiment 🍥

In the Design of Experiment tutorial lesson, I learnt to determine the total number of experiments (N) that the process engineer needs to carry out and what does each experiment (treatment) entail. Using the factorial design table, in DOE, it is a practice to use "+" and "-" symbols to indicate high and low level respectively. Full and fractional factorial design were taught as well. Including how to fractionalize the data so that it is orthogonal - good statistical properties. During tutorial lessons, I was also tasked to do data analysis for Full Factorial Design Interaction Effect between factors. 

Thus, in this individual task, I am tasked to do Case Study 2, on a waste water treatment facility.

My process is blogged here :)

Case Study 2:

Factor A = Concentration of coagulant added ( "-" is 1, "+" is 2)

Factor B = Treatment temperature ("-" is 72, "+" is 100)

Factor C = Stirring speed ("-" is 200, "+" is 400)

Figure 1: Case Study materials given

Full factorial design:

Figure 2: Converted data from given

Effect of single factors and their rankings:

Runs where A is "+" = 30 + 33 + 3 + 4 = 70/4 = 17.5
Runs where A is "-" = 5 + 6 + 4 + 5 = 20/4 = 5

Runs where B is "+" = 6 + 33 + 5 + 4 = 48/4 = 12
Runs where B is "-" = 5 + 30 + 4 + 3 = 42/4 = 10.5

Runs where C is "+" = 4 + 3 + 5 + 4 = 16/4 = 4
Runs where C is "-" = 5 + 30 + 6 + 33 = 74/4 = 18.5

Figure 3: Showing the significance of each factor

From the above graph, it is possible to determine the most significant factor by looking at the gradient of each line on the graph. 

The steeper the line, the more significant the factor is in this case. Thus, in this waste water facility case study, the most significant factor is factor C (Stirring speed) followed by factor A (Concentration of coagulant added) and factor B (Treatment temperature). 

Thus, factor C is the most significant factor in affecting the amount of pollutant discharged as it changes from "-" to "+".

Interaction effect (A x B):

At LOW A, average of Low B = 6 + 5 = 11/2 = 5.5
At LOW A, average of High B = 4 + 5 = 9/2 = 4.5

At HIGH A, average of Low B = 30 + 3 = 33/2 = 16.5
At HIGH A, average of High B = 33 + 4 = 37/2 = 18.5

Figure 4: Interaction effect graph of A x B

The higher the difference of the gradient of both lines, there is more significant interaction between the factors. 

From the above graph, although the gradient of the lines is positive and negative, the difference in the gradient is not significant. Thus, the interaction between factors A and B is not as significant as the interaction between factors A and C.

Interaction effect (A x C):

At LOW C, average of Low A = 5 + 6 = 11/2 = 5.5

At LOW C, average of High A = 30 + 33 =  63/2 = 31.5

At HIGH C, average of Low A = 5 + 4 = 9/2 = 4.5

At HIGH C, average of High A = 4 + 3 = 7/2 = 3.5

Figure 5: Interaction effect graph of A x C

As seen from the graph above, both lines have very different gradient, whereby, one line is a positive gradient while the other line is a negative gradient. 

Therefore, there is a significant interaction between factors A and C. 

Interaction effect (B x C):

At LOW C, average of Low B =  5 + 30 = 35/2 =17.5

At LOW C, average of High B = 6 + 33 = 39/2 = 19.5

At HIGH C, average of Low B = 4 + 3 = 7/2 = 3.5

At HIGH C, average of High B = 5 + 4 = 9/2 = 4.5 

Figure 6: Interaction effect graph of B x C  

From the above graph, the gradient of both lines are different by a little margin. Therefore, there is an interaction between factor B and C, but the interaction is small. 

Side note: If both lines are parallel, then there is NO interaction between the factors

Fractional factorial design:

For Fractional factorial design, I will be using runs 2,3,5,8.

Figure 7: Fractional factorial design data (chosen 4)

Effect of single factors and their rankings:

Runs where A is "+" = 30 + 4 = 34/2 = 17
Runs where A is "-" = 6 + 4 = 10/2 = 5

Runs where B is "+" = 6 + 4 = 10/2 = 5
Runs where B is "-" = 30 + 4 = 34/2 = 17

Runs where C is "+" = 4 +  4 = 8/2 = 4
Runs where C is "-" = 30 + 6  = 36/2 = 18

Figure 8: Showing the significance of each factor

From the above graph, it is seen that factor C is the most significant in affecting the amount of pollutant discharged by the plant. As it has the steepest line which means the gradient is higher, resulting in it being the more significant factor as compared to factor A and B.

Conclusion:

To conclude my findings from this case study, I found out that the difference between full factorial design and fractional factorial design is not very significant and that they both still gave a similar results on effect of single factors and their rankings. Thus, fractional factorial design is very much preferred when time is limited.

The below attached excel file is what I have done for this individual blog.

Excel file:

CPDD individual blog entry (1).xlsx