Design Of Experiment
- Mabelle Chan
- Feb 1, 2024
- 2 min read
Hi guys! A few weeks ago in class, I was taught this method called Design of Experiment (DOE). It seemed like not many people knew about this method! And so today I'll be documenting an example of how to apply DOE. I hope you guys learn a lot in the process!
To begin, I will be giving you some context for what I'm trying to find today!
Anyone 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 experiment and the measured variable is the amount of “bullets” formed in grams and data collected are shown below:
FULL FACTORIAL DESIGN ANALYSIS
Effect of single factors and their ranking
To do that, I plotted a table as can be seen above! I then used a graphical method shown below,
The calculations used to obtain the average difference of each factor from high to low are then used to plot the values into a graph for the significance of the main effects.
This difference is based on the gradients produced by the graph! In my findings, the most significant to least significant factor is C -> B -> A. Since C produces the steepest gradient out of the three factors, it can be understood that it contributes to the most significant change. And since C represents power, it is the most significant factor that contributes to the largest change in the amount of bullets that form.
Interaction effects
Interaction effect of AxB
From this table, we can tell that...
At B(-), the total effect of A = 0.150
At B(+), the total effect of A = -0.45
From this graph,
we can tell that the gradients for Low B(+ve) and High B (-ve) are different.
Hence, there is a significant interaction effect between Factor A (diameter) and B (microwaving time).
Interaction effect of AxC
From this table, we can tell that...
At C(-), the total effect of A = -0.455
At C(+), the total effect of A = 0.160
From this graph,
we can tell that the gradients for Low C(-ve) and High C (+ve) are different.
Hence, there is a significant interaction effect between Factor A (diameter) and C (Power).
Interaction effect of BxC
From this table, we can tell that...
At C(-), the total effect of B = -1.455
At C(+), the total effect of B = -0.580
From this graph,
we can tell that the gradients for Low C(-ve) and High C (-ve) are only slightly different. However, compared to the interaction between AB and AC the difference between BC is much lower.
Hence, there is a significant interaction effect between Factor B (microwaving time) and C (Power) is smaller than that of [diameter X power] and [diameter X microwaving time]
Conclusion
In conclusion, the single effects show that the most significant to least significant factor is C -> B -> A. Even so, it is important to look at the individual interactions which I've found! With these 3 comparisons, I can then break down which interactions are more significant than others!
From the graphs plotted above, we can tell that interaction AB is most significant, with the most obvious difference between the gradients in line comparison. As for the interaction between A and C, even though both gradient lines are opposite where one is -ve and the other is +ve, it can also be observed that both are gentler gradients, showing that the interaction effect is slightly smaller than A and B. Lastly, for interaction between B and C, it can be seen that both are positive gradients and that the difference between that is only slightly off! This proves that the interaction effect between B and C is the least significant out of the 3.
FRACTIONAL FACTORIAL DESIGN ANALYSIS
As for fractional factorial design, I chose to run 4, 5, 7, and 8 which are data that are orthogonal to cater to the considerations of a balanced design. A balanced design is where all factors, (-) and (+) occur the same number of times! This can be seen in the simplified table I’ve made...
Effect of single factors and their ranking
I plotted a table as can be seen above! then just like for full factorial design, i used a graphical method shown below,
The calculations used to obtain the average difference of each factor from high to low are then used to plot the values into a graph for the significance of the main effects.
This difference is based on the gradients produced by the graph. Just like the full factorial design, the most significant to least significant factor is C -> B -> A. Since C (power) produces the steepest gradient out of the three factors, it can be understood that it contributes to the most significant change whereby the difference in the number of bullets that form is most significant.
Comparison (between full and fractional factorial design)
Both fractional and full factorials gave the same outcome for the ranking of the significance of the factors where C -> B -> A. This shows that even with lesser values taken into account if 4 suitable experiments are selected to do the DOE, similar results will be obtained. Even though using the full factorial design method covers more bases and gives a more reliable result, in a case where a project requires someone to do a hundred experiments, doing a full factorial design method would be infeasible! And that's where fractional factorial comes to the rescue. But of course, given a project that requires little experiments to be done, a full factorial design method can be done to increase the reliability of results obtained.
Link to Full and Fractional Factorial Excel Sheet:
Reflections:
When I was first taught DOE by Mr Chua, I didn't think it would benefit me much and even felt bored. However, after needing to apply it to my pre-practical activity, practical activity, post-practical report, and now this... as I progressed from the first individual activity, I realized that what I was learning could eventually be very useful, especially for FYP or any projects I could be doing in my future studies! I remember at the start when I didn't really understand how to plot the graphs for my pre-practical submission... I had to refer to the teaching deck so often! But it's safe to say right now I'm very sure of what I'm doing and mastered Excel in the process as well HAHAH. This experience started off rocky, but in the process of learning DOE, I got to improve in other forms as well!!
Well.. I hope you guys learned a whole lot from this blog because it took me SO much time to plot all those graphs. But mainly, I hope you enjoyed this blog and understand better what exactly is DOE and the difference between full and fractional factorial! On top of that, I wish you guys all the best if you ever find that you need to use DOE for any of your future projects! See you again!
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