Design of Experiment (DOE)
Design of Experiment (DOE)
For this weeks blog, I will be talking about what I have learned about applying a statistical approach to designing an experiment. As I am the CFO of the group, I have been assigned to look into case study 1 which is explores the significance of some factors that affect the yield of microwaved popcorn . The factors that have been identified are Factor A(Diameter of Bowl), Factor B(Time Spent in Microwave) and Factor C(Microwave Power Supply). Each factor will be tested at High and Low level where all factors will appear the same number of times in each level i.e. 4 runs where A is at high level and 4 runs where A is at low level etc.
For Factor A:
- High = 15cm
- Low = 10cm
For Factor B:
- High = 6 Minutes
- Low = 4 Minutes
For Factor C:
- High = 100%
- Low = 75%
Below is a table that contains the results of the differing runs and their respective factor settings.
As you can see from the graph, Factor C which is the Microwave Power Supply, has the most significant impact on the yield of microwave popcorn as it has the steepest gradient while Factor A, which is the Diameter of the Bowl, has the least significant impact on the yield of microwave popcorn as the gradient is almost 1 where it is basically just a straight line. Hence, the significance of the factors are ranked in this order Microwave Power Supply > Time Spent in Microwave > Diameter of Bowl. This trend is likely because the Diameter of the Bowl does not really affect the yield as it just increases the total amount of popcorn in the bowl which would negate any positive gain (If Any) from the increased diameter while the other 2 factors affect the yield without negating themselves.
Interaction Effect between A&B
At Low B, Average of Low A = 1.9
At Low B, Average of High A = 2.1
At Low B, Total Effect of A = 2.1 - 1.9 = 0.2
At High B, Average of Low A = 1.05
At High B, Average of High A = 0.75
At High B, Total Effect of A = 0.75 - 1.05 = -0.3
From the graph, it can be seen that the gradient of both lines are different where the blue line representing -B has a positive gradient while the orange line representing +B has a negative gradient. Hence it can be concluded that there is interaction between factors A&B albeit quite minor.
Interaction Effect between A&C
At Low C, Average of Low A = 2.35
At Low C, Average of High A = 2.35
At Low C, Total Effect of A = 2.35 - 2.35 = 0
At High C, Average of Low A = 0.6
At High C, Average of High A = 0.5
At High C, Total Effect of A = 0.5 - 0.6 = -0.1
From the graph, the lines have almost identical gradients to the point where they can be assumed to be parallel. The blue line representing -C is a straight line while the orange line representing +C is a line with a 0.1 difference between the 2 ends which indicates that the line is likely to also be a straight line where the 0.1 can be attributed to experimental errors in the data. Hence it can be concluded that there is no interaction between factors A&C.
Interaction Effect between B&C
At Low C, Average of Low B = 3.3
At Low C, Average of High B = 1.4
At Low C, Total Effect of B = 1.4 - 3.3 = -1.9
At High C, Average of Low B = 0.7
At High C, Average of High B = 0.4
At High C, Total Effect of B = 0.4 - 0.7 = -0.3
From the graph, both lines have a negative gradient with different values where the blue line representing -C has a steeper negative gradient while the orange line representing +C has a gentler negative gradient. Hence it can be concluded that there is interaction between factors B&C.
Conclusion for Full Factorial Data Analysis
The overall trend when all factors are involved in the yield of microwave popcorn is that Microwave Power Supply has a big impact, Time Spent in Microwave has a medium impact and Diameter of the Bowl has a small impact. When looking at the factors in pairs and how they interact with one another along with the significance of their interactions, Microwave Power Supply and Diameter of Bowl have no interaction, Time Spent in Microwave and Diameter of Bowl have slight interaction while Microwave Power Supply and Time Spent in Microwave have considerable interaction.
Fractional Factorial Data Analysis
During the Pre-Practical for the Design of Experiment Practical, I was introduced to Fractional Factorial Design for Data Analysis which uses the concept of statistical orthogonality to reduce the amount of runs required while still providing sufficient information to come to an informed conclusion. Statistical orthogonality in a nutshell means that all factors are tested the same number of times at a certain level (High & Low). Hence, I have chosen runs 1, 4, 6 and 7 as this combination will allow all 3 factors to be tested at high level and low level the same number of times (2@High Level & 2@Low Level) each. Below is the graph formed by using Fractional Factorial Design of all factors.
As you can see from the graph, Factor C, which is Microwave Power Supply has the steepest gradient which means that it has the most significant impact on the yield of microwave popcorn while Factor A, which is the Diameter of the Bowl has the gentlest gradient which means that it has the least significant impact on the yield of microwave popcorn. Hence, the factors are ranked in this order of significance Microwave Power Supply > Time Spent in Microwave > Diameter of Bowl. The trend obtained via Fractional Factorial Design aligns with the trend obtained via Full Factorial Design albeit the results are less obvious likely due to the decrease in available data used to plot the graph. This means that I have chosen a good set of data using statistical orthogonality as I arrived at the same conclusion by using Fractional Factorial Design which is more efficient and resource-effective than Full Factorial Design.
The Excel Spreadsheet used for this blog can be found here.
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