Design of Experiment entry

In this Design of Experiment Entry, I got to make use of Microsoft Excel to make statistics to designing experiments. Case Study 2 was my chosen case to solve. I will include the links to the Excel sheets of the full factorial and fractional factorial methods after each analysis. Here is the context for Case Study 2:

Figure 1: Case Study 2 information

Based on the given data in Figure 1, I transferred them into Microsoft Excel:

Figure 2: Transferred data in Microsoft Excel Sheet

Full Factorial Design Data Analysis

Now, I will perform Full Factorial analysis on the given data:

Figure 3: Full factorial analysis

Effects of each factor:

• When A increases from 1% to 2% , the higher the pollutant discharge, vice versa.
• When B increases from 72°F to 100°F, the higher the pollutant discharge, vice versa.
• When C increases from 200 to 400 rpm, the lower the pollutant discharge, vice versa.

To find out which factor is the most significant, we can look at the gradients of the respective factos. The steeper the gradient, the more significant it is. Hence, we are able to rank them according to their significance. A had the steepest gradient, followed by C and followed by B.

Conclusion

Therefore, from the above analysis, it can be concluded that A(Concentration of Coagulant added, 1% and 2% by weight) is the most signifant factor which means it will affect the pollutant discharge the most. This is followed by C(Stirring speed) and followed by B(Treatment temperature).

From most signifcant to least signifcant, 

A>C>B

Now, I will investigate the interaction effects of each factors on one another. 

A x B interactions

Figure 4: A x B interaction effects

From figure 4, it can be seen that the interaction beween A and B is insignificant due to the minimal difference in gradients. 

A x C interactions

Figure 5: A x C interaction effects

The gradient of both lines are different, one is (+) and other line is (-). Therefore, there is a significant interaction between A and C. 

B x C interactions

Figure 6: B x C interaction effects

The gradients of both lines are different by a little margin. Therefore, there is an interaction between A and B but the interaction is very small.

Excel link for Full Factorial analysis: https://ichatspedu-my.sharepoint.com/:x:/g/personal/firmanshah_20_ichat_sp_edu_sg/ESJX768820tBgfI_58J-xNYBzvE0WHGkXmGjmGUBQHKzOg?e=FLMweV

Fractional Factorial Design Data Analysis

I chose run numbers 2, 3, 5 and 8 from Figure 1 due to their good statistical properties where all factors occur(both low and high levels) the same number of times for the fractional factorial analysis.

Figure 7: Fractional factorial method

Effects of each factors:

• When A increases from 1% to 2% , the higher the pollutant discharge, vice versa.
• When B increases from 72°F to 100°F, the lower the pollutant discharge, vice versa.
• When C increases from 200 to 400 rpm, the lower the pollutant discharge, vice versa.

Similar to Full factorial method, to find out which factor is the most significant, we can look at the gradients of the respective factors. The steeper the gradient, the more significant it is. Hence, we are able to rank them according to their significance. C has the steepest gradient whereas gradient of A and B have equal significance but less steeper than C.

Conclusion

Based on the results, we can conclude that factor C (stirrer speed), is the most significant factor which means it will affect the pollutant discharge the most. This is due to it having the steepest gradient among the factors. This is followed by A(Concentration of coagulant) and B(Treatment temperature) where they have equal but less significance than C.

From most significant to least significant,

C>A=B

Excel link for Fractional Factorial Analysis: https://ichatspedu-my.sharepoint.com/:x:/g/personal/firmanshah_20_ichat_sp_edu_sg/ESePw6UL_NNErZcRbQ2hYpMB9iSz2qPHA4o0pKIVN5WLhQ?e=TdGHBt