Design Of Experiment

 Hello and welcome back to my blog! 

Today I'll be sharing with you about Design of  Experiment!

Have you ever thought about the most effective way to make most of the popcorn kernel pop? Well, I was given a case study on it and here are the results I have gotten from it after studying the different parameters. The data is shown below: 

Run order	A	B	C	Bullets (grams)
1	+	–	–	3.58
2	-	+	–	2.58
3	–	-	+	0.74
4	+	+	-	1.58
5	+	–	+	0.95
6	+	+	+	0.32
7	–	+	+	0.58
8	–	-	-	3.12

Factor A is the diameter of the bowl. 

With the High being 15 cm and the low being 10cm.

Factor B is the microwaving time. 

With the High being 6 minutes and the low being 4 minutes.

Factor C is the power setting of the microwave. 

With the high being 100% and the low being 75%. 

Now with these values, I performed Full Factorial Design Interaction effect on it.

 

This was the overall interaction between the 3 factors. From the graph, Factor C has the steepest gradient followed by Factor B and lastly Factor A. This would mean that Factor C is the most significant factor as it causes the biggest change, as shown in the graph, when the power setting was 75% there was an average of 2.715 grams of kernels un-popped (bullets). These bullets then drop to an average of 0.6475 when the power setting was increased to 100%. 

Next after I have performed then analyse the interaction between each factor.

First, I compared the interactions of A and B. 

This was the data I obtained after looking through all the runs. 

As seen in the graph above, there is some significance interactions between A and B. This is because the gradient completely change from a positive one to a negative one when factor B is increased to the high value.  

Next would be the interaction between C and B. 

The graph above is similar to A and B. This means that there is some interaction between C and B however it is not as significant compared to A and B. 

The last interaction would be C and A. 

As seen from the graph, both lines are almost parallel to each other. This would mean that there is little interactions between the two factor.

Overall, the most significant factor is C followed by B and lastly A. There is a significant interaction between A and B while there is a not much between C and A. In order to achieve the least bullets left, one should use 100% power setting for 6 minutes with a bowl diameter of 15 cm.  

Fractional Factorial

For Fractional Factorial, I picked runs 1,2,3 and 6. 

This was the table of values that I referred to in order to carry out fractional factorial.

Next, I calculated the average highs and lows of each factor. 

Lastly, I plotted a graph to compare which factor was the most significant. 

The conclusion was that the significance of the factors were the same as when I carried out the full fractional. The order of significance starting from the most significant would be Factor C, then B and lastly A. 

The link to the excel sheet is here!

When I was learning Design of Experiment, I never would have thought that it would be possible to lessen the number of runs as well as combinations when wanting to study the effects of a number of factors by half. This was a new concept as I thought that when we cut the number of runs as well as combinations, we would be losing out on information that would affect the data and may give us false information.

After going through the tutorial as well as the practical, I have realised that the impression I was under was wrong. This is because from the tutorial and practical, it was made clear to me that the results I would get from carrying out fractional factorial was enough to get enough information on which factor was the most significant one. However by carrying out fractional factorial, it was not enough to figure out if there was any interactions between the factors. 

With that I know understand that if I am trying to find out which factor is the most significant one, I can carry out Fractional Factorial by choosing options that are statistically orthogonality.