Design of Experiments

Case Study

What could be simpler than making microwave popcorn? Unfortunately, as everyone who has ever made popcorn knows, it’s nearly impossible to get every kernel of corn to pop. Often a considerable number of inedible “bullets” (un-popped kernels) remain at the bottom of the bag. What causes this loss of popcorn yield? In this case study, three factors were identified:

1.      Diameter of bowls to contain the corn, 10 cm and 15 cm

2.      Microwaving time, 4 minutes and 6 minutes

3.      Power setting of microwave, 75% and 100%

8 runs were performed with 100 grams of corn used in every experiments and the measured variable is the amount of “bullets” formed in grams and data collected are shown below:

Factor A= diameter

Factor B= microwaving time

Factor C= power

Full Factorial

To analyse the data, start by taking the average mass of bullets at different levels for each factor.

Effect of Single Factors and their ranking

Using the average calculated, plot mass of bullet against level of factors for all three factors.

The effects of each factors on the mass of bullets remain can be determine by the gradient of the line of each factor. 

A negative gradient means that it has a negative effect in this case means that the mass of bullets left decreases as the level of factor increases. 

A positive gradient means that is has a positive effect in this case means that the mass of bullets left increases as the level of factor increases.

Since we want to increase the yield of popcorn, a negative gradient would be ideal.

From the graph, since all the factors have a negative gradient, hence all the factors have a negative effect on the mass of bullets. 

For factor A, when the diameter of the bowl increases from 10 cm to 15 cm, the mass of bullet form decreases from 1.55g to 1.4g.

For factor B, when the microwaving time increases from 4 mins to 6 mins, the mass of bullet form decreases from 1.99g to 0.95g.
For factor C, when the power setting of microwave increases from 75% to 100%, the mass of bullet form decreases from 2.4g to 0.54g.

In order to determine the factor that has the most significant effect on the mass of bullets, we have to look at the gradient. A steeper gradient has a larger effect on the mass of bullet while a gentle gradient has a smaller effect on the mass of bullet.

From the graph, factor C has the steepest gradient among the other factors. Hence it has the largest effect on the mass of bullet.

Factor A has the gentlest gradient among the other factors. Hence it has the smallest effect on the mass of bullet.

Factor B's gradient is in between factors A and C.

Therefore, the factor with the most significant effect on the mass of bullet is C (Power) followed by B (Microwaving Time) and finally A (Diameter) .

Interaction Effects

To find the interaction effect of between two factors, perform calculations below:

After that, plot two line graphs mass of bullet remaining vs level of factor.

From the graph, the gradient of both graphs are different with one being positive and one being negative. Therefore there is significant interaction between factor A & B.

From the graph, the gradient of both graphs are different with one being positive and one being negative. Therefore there is significant interaction between factor A & C.

From the graph, the gradient of both graphs are the same with both being negative and have different value. Therefore there is significant interaction between factor B & C.

Excel

DOE blog Full Factorial.xlsx 

DOE interactions Full Factorial.xlsx

Conclusion

From the graph plotted, all of the individual factors have a negative effect on the amount of bullets left. Base on individual factors alone, in order to get the maximum amount of popcorn, I would use a bowl with large diameter, longer microwaving time and higher microwave power setting

From the interactions between factors B & C, when both of the factors are set to high, the amount of bullets left decreases. Hence to obtain the most amount of popcorn, I will set the microwaving time and power to high.

But from the interaction between factors A & C, when factor C is high and A is also high, the amount of bullets left increases.

Hence from the interactions, in order to obtain the highest yield when B & C are high, I would put factor A at low.

In conclusion, I would use a small diameter bowl, high microwaving time and high power to obtain the most popcorn.

Factional Factorial

In order to do factional factorial data analysis, first we have to choose 4 runs that both low and high level of all factors have occur the same number of times and are orthogonal from the full factorial data. I will be choosing run 1,2,3 and 6.

Effect of Single Factors and their ranking

The effects of the single factors can be found by first finding the average of the four runs for each factor just like the full factorial. 

Using the average calculated, plot mass of bullet against level of factors for all three factors.

The effects of each factors on the mass of bullets remain are the same as the full factorial. Hence refer to the explanation at the full factorial part.

From the graph, since all the factors have a negative gradient except factor A, hence factors B & C have a negative effect on the mass of bullets while factor A has a positive effect on the mass of bullets. 

For factor A, when the diameter of the bowl increases from 10 cm to 15 cm, the mass of bullet form increases from 0.73g to 0.87g.

For factor B, when the microwaving time increases from 4 mins to 6 mins, the mass of bullet form decreases from 0.98g to 0.62g.
For factor C, when the power setting of microwave increases from 75% to 100%, the mass of bullet form decreases from 1.33g to 0.27g.

From the graph, factor C has the steepest gradient among the other factors. Hence it has the largest effect on the mass of bullet.

Factor A has the gentlest gradient among the other factors. Hence it has the smallest effect on the mass of bullet.

Factor B's gradient is in between factors A and C.

Therefore, the factor with the most significant effect on the mass of bullet is C (Power) followed by B (Microwaving Time) and finally A (Diameter) .

Excel

DOE blog Fractional Factorial.xlsx

Conclusion

From the graph, all the factors have a negative effect on the amount of bullets left. Hence in order to get the most popcorn, I would use a large bowl with long microwaving time and high power to obtain the most popcorn.

Learning Reflection

When I was first introduced to DOE, I was very confuse and did not understand a single thing that Dr Noel taught us. I thought it was a pointless tool and did not put in effort on it. However after giving it a second chance, I finally grasped the concept on it and know how to apply it in this case study. 

For full factorial, it is useful when one has a lot of time on their hands as it provides a much higher accuracy as more runs are involved. I can also see the interactions between each factor to see how they work with each other on different settings. This will provide the most optimal setting to obtain the results that I want.

For Factional Factorial, it is useful when one has to see which factor has the most significant on a result. At first, I though I just have to use four experiments with equal numbers of HIGHs and LOWs investigated. After the practical, I realised that the runs have to be orthogonal to each other in order to obtain a much accurate data. By choosing four runs and plotting the graph, I can be able to see which factor has the most significant impact on the result which would be the same as the factor found in the full factorial method. This is a useful method for time consuming runs that require a long time to conduct.

After going through the DOE practical, I realise that DOE is a very useful tool when finding out impact of factors on a result and I would definitely use this tool in my FYP.