DOE
Hi I am back with my 4th blog, DOE!!!!
Design of Experiments (DOE)
- A statistics-based approach to designing experiments.
- A methodology to obtain knowledge of a complex, multi-variable 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.
N = total number 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
Based on the results above, Factor C causes the highest impact on the mass of bullets, followed by Factor B, followed by Factor A, causing the lowest impact on the mass of bullets. Factor C has the steepest gradient , followed by Factor B , followed by Factor A , having the least steep gradient.
Ranking of factors(starting from highest impact to lowest impact)
1) Factor C, the power setting of microwave
2) Factor B, the microwaving time
3) Factor A, the diameter of bowl containing the corns
When factor A, the diameter of bowls containing the corns, increases from 10cm to 15cm, the mass of bullets decreased from 1.87g to 1.72g.
When factor B, the microwaving time, increases from 4min to 6min, the mass of bullets decreased from 2.16g to 1.44g.
When factor C, the power setting of microwave increases from 75% to 100%, the mass of bullets decreased from 2.89g to 0.71g.
Data Analysis for Full Factorial Design Interaction Effect (A x B)
At LOW B,
Average of low A=(3.12+0.74)/2=1.93
Average of high A=(3.81+0.95)/2=2.38
Total effect of A=(2.38-1.93)= 0.45 (increase)
At HIGH B,
Average of low A=(2.81+0.81)/2=1.81
Average of high A=(1.81+0.32)/2=1.065
Total effect of A=(1.065-1.81)= -0.745 (decrease)
The gradients of both lines are different as the line representing '-B' has a positive gradient whereas the line representing '+B' has a negative gradient. However, as both of the lines do not intersect, there is no interaction between Factor A and B.
Data Analysis for Full Factorial Design Interaction Effect (A x C)
At LOW C,
Average of low A=(3.12+2.81)/2=2.965
Average of high A=(3.81+1.81)/2=2.81
Total effect of A=(2.81-2.965)= -0.155 (decrease)
At HIGH C,
Average of low A=(0.74+0.81)/2=0.775
Average of high A=(0.95+0.32)/2=0.635
Total effect of A=(0.635-0.775)= -0.14 (decrease)
The gradients of both lines are different, although both the lines representing '-C' and '+C' have negative gradients. However, as both of the lines do not intersect, there is no interaction between Factor A and C.
Data Analysis for Full Factorial Design Interaction Effect (A x C)
At LOW C,
Average of low B=(3.12+3.81)/2=3.465
Average of high B=(2.81+1.81)/2=2.31
Total effect of B=(2.81-2.965)= -1.155 (decrease)
At HIGH C,
Average of low B=(0.74+0.95)/2=0.845
Average of high B=(0.81+0.32)/2=0.565
Total effect of B=(0.635-0.775)= -0.28 (decrease)
The gradients for both lines are different, although both the gradients for both the lines representing the '-C' and the lines representing the '+C' are negative. As the lines do not intersect with each other, there is no interaction between B and C.
Fractional Factorial Data Analysis
Based on the results above, Factor C causes the highest impact on the mass of bullets, followed by Factor B, followed by Factor A, causing the lowest impact on the mass of bullets. Factor C has the steepest gradient , followed by Factor B , followed by Factor A , having the least steep gradient.
Ranking of factors(starting from highest impact to lowest impact)
1) Factor C, the power setting of microwave
2) Factor B, the microwaving time
3) Factor A, the diameter of bowl containing the corns
When factor A, the diameter of bowls containing the corns, increases from 10cm to 15cm, the mass of bullets increased from 1.78g to 2.07g.
When factor B, the microwaving time, increases from 4min to 6min, the mass of bullets decreased from 2.28g to 1.57g.
When factor C, the power setting of microwave increases from 75% to 100%, the mass of bullets decreased from 3.31g to 0.53g.
Conclusion:
Based on both the full and fractional factorial analysis, increasing power setting of the microwave and the microwave time will definitely increase the mass of the bullets. However, for the diameter of bowl is contradictory as the mass of the bullets decrease when the diameter of the bowl increases. Because by theory, when the diameter of the bowl increases, the mass of the bullets will also increase. Fractional factorial may be more efficient and resource effective compared to full factorial, but you may risk full information. The case study is a good example of that to prove that information from fractional factorial is not really accurate.
Learning Reflection:
Before the practical starts, our lecturer taught us about DOE and the two analysis methods: full factorial and fractional factorial. He also taught us how to do the 2 methods on Excel. Thanks to Mr Noel, I am able to do the 2 methods on the graph for pre-practical. I even learn how to do interaction effects between 2 factors before coming for practical. What I learnt is that full and fractional factorial methods have their pros and cons. Full factorial method is time consuming. Fractional factorial could be more efficient in terms of time but it does not give the complete information. Initially, I thought it was the first time I did DOE, until Mr Noel reminded us that we did it a year ago during my CP5202 module Practical 3: Investigation of parameters that affect leaching.
During the experiment, it was really unexpected that when the length of the arm increases, the distance travelled by the ball will decrease. By theory it should have been that the length of the arm increases, the distance travelled by the ball increases. To be honest, I was not sure what really went wrong? During the competition, my group almost hit 2 targets using the ball, what a pity!!!! Overall, I am okay with the practical, I just did not find it really exciting compared to the previous practicals. But it is still fine, I guess. But I enjoyed doing the pre-practical task!!! Here is what I did for pre-practical!!!!
Here is my group results for the experiment we did:
1) Full Factorial
2) Fractional Factorial:
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