Design of Experiment

 DESIGN OF EXPERIMENT [10/1/22]

For this entry, I have been tasked to do data analysis for the Case studies. I have chosen Case Study 1.

The excel file for both full and fractional factorial can be found here.

Excel for Case Study 1

To start, I first tabulated the data from Case Study 1 into the template provided.

Full Factorial Design Analysis

To do a full factorial design analysis, we have to find the average of the different factors when it is "+" and "-" which is tabulated on the left, since there are 3 factors, I will plot 3 graphs and the gradient will tell me the significance of each factor in affecting the mass of unpopped popcorn yield.

From the graph, the power has the steepest gradient followed by microwaving time, and lastly, the diameter of the bowl. The steeper the gradient, the higher effect it will have on the results, which is the mass of unpopped yield. Therefore, power has the highest significance, followed by microwaving time, and lastly, the diameter of the bowl.

After determining the effect of 1 factor, I went on to determine the interaction effects between the 3 effects.

For the interaction of AB, the gradient of both graphs are different with the blue one being positive and the orange being negative. This means that there is a significant interaction between Factor A and Factor B.

For the interaction of AC, the gradient of both graphs are almost similar and only varies slightly, and it is not parallel, there is very little interaction between Factor A and Factor C. As if the 2 graphs are parallel, there is no interaction between the 2 factors which is not the case.

For the interaction of BC, the gradient of both graphs are negative, however, one is significantly steeper than the other, therefore is a significant interaction between factor B and C.

Thus, for the full factorial design analysis, power has the most significance followed by microwave time and lastly, the diameter of the bowl. In order to reduce the yield of unpopped popcorns, we can set the power and microwave time to high and since the graph of the diameter of the bowl is almost horizontal, this means that the diameter has almost no effect on the yield and can be set to either high or low.

Fractional Factorial Design Analysis

Now, I will be doing the fractional factorial design analysis. I have chosen runs#2,4,5 & 7 as for each factor, there are 2 "+" and 2 "-" values, which means that it is orthogonal. The runs in red are the runs that I will be choosing.

This time, I am able to still plot a similar graph to the full factorial, however, now, the diameter of the bowl has a clear effect on the mass of the yield. Thus, the factor that has the greatest significance is power, followed by microwave time, and lastly, the diameter of the bowl as seen from the gradient. For fractional factorial, to reduce the yield of the unpopped kernel, it is best to set power and microwave time to high ("+") and the diameter of the bowl to low ("-")