Design of Experiment (DOE)

 Hi, this is my blog for Design of experiments.

Here is my Full factorial Design data analysis

For this blog, I was tasked to complete a full factorial and fractional data analysis on a case study. 

Here is my case study.

Given the data, I tabulated the data in an excel sheet and calculated the significance of the 3 main factors by calculating the average when each factor is positive and negative.

After getting the values of the average where the runs for different factors are positive and negative, I tabulated the data in a line graph to see the impact of each factor by determining the steepness of the line.

From the graph above, I am able to determine that the most significant to least significant is Power, Microwaving Time, and Diameter. 

I am also able to determine that when the diameter increases from 10cm to 15cm, the average number of bullets decreases from 1.48g to 1.425g, power increases from 75% to 100%, the average number of bullets decreases from 2.35g to 0.55,g and microwaving time increases from 4 minutes to 6 minutes, the average number of bullets decrease from 2g to 0.9g.

Next is the interaction for full factorial.

I took the data from the full factorial and did the interaction for A x B. I separated the data where B is low, A is low and B is low, A is high and vice versa. After that I calculated the average where B is low, A high low and B is low, A is high and B is high, A is low and B is high, A is high. I also calculated the total effect of A when B is low and the total effect of A when B is high.

This is the interaction between A x B:

From the graph above, it can be seen that the gradients of both lines are different. This shows that the interaction between A x B is significant. 

I repeated the process for B x C and A x C.

This is the interaction between B x C.

From the graph above, it can be seen that the gradient between the 2 lines is both negative and different in values based on the steepness. This means that there's a significant interaction between B x C.

This is the interaction between A x C.

From the graph above, it can be seen that the gradient of the 2 lines is different by a small margin. This shows that there is little interaction between A x C. 

In conclusion, the interaction between A x B is the most significant interaction followed by B x C and lastly, A x C is the least significant interaction.

This is fractional data analysis.

Firstly, I chose runs 2,3,5,8 because they have good statistics and the design is orthogonal.

I calculated the positive A average and the negative A average. I did the same thing for the other 2 factors.

I then plot the graph for the average of the different factors.

From the graph above, when A (diameter) increases from 10cm to 15cm, the bullets increase from 1.05g to 2.1g. When B (Microwaving time) increases from 4 minutes to 6 minutes, the bullets decrease from 2.1g to 0.8g. When C (Power) increases from 75% to 100%, the bullets decrease from 2.55g to 0.6g. The significance of the factors can be ranked from most significant to least significant based on the steepness of the lines. Most significant: Power, 2nd most significant: Microwaving time, least significant: diameter.

In conclusion, both the full factorial and the fractional data analysis have the same ranking of Power, microwaving time, and diameter from most significant to least significant. However, the fractional data analysis consumes less time compared to full factorial.

Here is the link to my excel file:

https://docs.google.com/spreadsheets/d/1WBqj3jUxwo7efUG14seH7810AQTB0rs0/edit?usp=sharing&ouid=118048116915152917341&rtpof=true&sd=true