Design of Experiment

This week, I learnt something called Design of Experiment. Now, what is it? It is a statistics based approach to designing experiments. A methodology to obtain knowledge of a complex, multivariable process with the fewest trials possible. An optimisation of the experimental process itself. The backbone of any product design as well as any process/ product improvement efforts. Basically, it is an easier way to figure out the least amount of trials possible based on what variables are being tested and provides an orderly and simple way to figure out which factors has the most impact on the response variable, or what you want to reduce or increase by changing the factors.

For the task assigned, I am to identify the cause of the loss of popcorn yield (formation of bullets [unpopped kernels]).

3 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%

There were 8 runs performed with the high and low levels of each of the factors and the amount of bullets formed in grams were recorded.

From this I analysed the data to find the significance of each of the factors on the formation of bullets.

These were the high and low levels of each factor.

For Full Factorial Design:

Using the data in the table given, I calculated the mass of bullets formed with the level of each factor when it was high and when it was low.

The total effect of the change in level of the factor, or the difference in the mass of bullets formed were made into the graph below.

From the graph as seen, C (Power Setting of the Microwave) is the most significant factor on the formation of bullets in grams followed by B (Microwaving Time) and then A (Diameter of Bowls to contain the Corn). Since the steepness of the graph is from C to B to A with the graph of C being the most steep and A being the least steep.

Interaction effects of the factors:

Two factors are said to interact with each other if the effect of one factor on the response variable is different at different levels of the other factor. If the gradients of the graphs are equal, then there is no interaction, however if the gradients are different, then there is an interaction between the factors.

Interaction effects of A and B

Based on the graph, the gradient of both lines are different (one is positive and the other is negative). Therefore there’s a significant interaction between A (Diameter of Bowls to contain the Corn) and B (Microwaving Time).

Interaction effects of A and C

Based on the graph, the gradient of both lines are different by a little margin. Therefore there’s an interaction between A (Diameter of Bowls to contain the Corn) and C (Power Setting of the Microwave), but the interaction is small. 

Interaction effects of B and C

Based on the graph, the gradient of both lines are different. Therefore there’s a significant interaction between B (Microwaving Time) and C (Power Setting of the Microwave).

Analysis of interaction effects

Based on the graphs, the most significant interaction is BxC followed by AxB and then AxC.

Conclusion of Full Factorial Data Analysis:

C (Power Setting of the Microwave) is the most significant factor on the formation of bullets in grams followed by B (Microwaving Time) and then A (Diameter of Bowls to contain the Corn).

BxC is the most significant interaction on the formation of bullets in grams followed by AxB and then AxC.

Fractional Factorial Design:

For fractional factorial design, there are only a few runs chosen from the total, but they should still provide sufficient information to determine the factor effect.

It is more efficient and resource-effective, however you risk missing information.

I chose to use runs 2,3,4 and 5 since they contained an equal number of high and low levels of each of the factors.

Conclusion of Fractional Factorial Data Analysis

As can be seen on the table, there are differences between the total of the average of each of the factors from the full factorial and the fractional factorial design.

The significance of the factors have changed as well with C (Power Setting of the Microwave) being the most significant factor on the formation of bullets in grams followed by A (Diameter of Bowls to contain the Corn) and then B (Microwaving Time).

Conclusion

From this task, I have learnt that both Full Factorial Design and Fractional Factorial Design have their merits, Full Factorial Design is longer but more accurate, while Fractional Factorial Design is shorter but has the risk of missing out information. And this is demonstrated clearly above. From the Full Factorial Design and the Fractional Factorial Design, the significance of B (Microwaving Time) dropped, and this is the result of missing out information from the runs that were not chosen to be analysed. Hence, in the future when doing DOE, I would choose to use Full Factorial Design because even if it takes a longer time, it is more accurate and I would not be missing out on any crucial information.

Here is the link to the excel file: https://ichatspedu-my.sharepoint.com/:x:/g/personal/gideonm_20_ichat_sp_edu_sg/EfOHpbU7_r1Nkm2H69u37psBYzmWH3_i0Lh28Z2a9CNTvA?e=qQ8mgv

This was such a fun and educational task to complete, I got to learn something new and work on my skills on excel as well!