Design of Experiment !!

1. Full factorial

Steps:

 1. Filling up data points.

 Since we were given only one data per run, I put it under the average value

2. Plotting the graph

Using the data I was given, I plotted a graph based on the different factors and different level. The data from the graph will tell us the ranking of the factors. We rank them by gradient.

3. Ranking the factors

Based on the gradients, the ranks are as such,

1. Factor C ( power )

2. Factor B ( microwaving time )

3. Factor A ( diameter )

2. Full factorial Interaction

1. Firstly we will look at the interaction between A x B

At low B, average of low A = ( 3.1 + 0.7 ) / 2 = 1.9

At low B, average of high A = ( 3.5 + 0.7 ) / 2 = 2.1

At low B, total effect of A = 0.2 ( increase ) 

At high B, average low A = ( 1.6 + 0.5 ) / 2 = 1.05

At high B, average high A = ( 1.2 + 0.3 ) / 2 = 0.75

At high B, total effect of A = -0.3 ( decrease )

After this I plotted a graph, resulting in this 

As lines are dispersing, it means there is little to no interaction between these two factors. After this, i did the same thing, but now with A x C and B x C. 

A x C interaction

At low A, average low C = ( 3.1 + 1.6 ) / 2  = 2.35

At low A, average high C = ( 0.7 + 0.5 ) / 2 = 0.6

At low A, total effect of C = -1.75 ( decrease )

At high A, average low C = ( 3.5 + 1.2 ) / 2 = 2.35

At high A, average high C = ( 0.7 + 0.3 ) / 2 = 0.5

At high A, total effect of C = -1.85 ( decrease )

Since the lines do not cross, they have little to no interaction as well.

Lastly we have B x C

At low B, average low C = ( 3.1 + 3.5 ) / 2 = 3.3

At low B, average high C =  ( 0.7 + 0.7 ) / 2 = 0.7

At low B, total effect of C = -2.6

At high B, average low C = ( 1.6 + 1.2 ) / 2 = 1.4

At high B, average high C = ( 0.5 + 0.3 ) / 2 = 0.4 

At high B, total effect of C = -1

And here is the plotted graph,

With the lines converging near the end, there is high levels of interaction between B and C.

Part 2

Next, we do the fractional factorial!

Fractional Factorial is the act of using 4 ortogonal points to do it, meaning less points, less steps and less time taken!

For it to be ortogonal, I used runs 2,3,5 and 8!

I plotted the data and formed this graph, which is the fractional factorial graph.

Using the fractional factorial, the ranking stays the same following the order of

1. Factor C ( power )

2. Factor B ( time )

3. Factor A ( diameter )

Excel files!!

https://drive.google.com/drive/folders/12IqePSHd1n-J2HBbufhBbu9XxitStN-5?usp=sharing