DESIGN OF EXPERIMENT
Hey everyone! Welcome back to my blog 😁In this blog, I will be solving a case study using the DOE method😶Curious to see how I did it? Read on to find out more!
WHAT IS DOE?
DOE (Design Of Experiment) is a methodology to obtain the knowledge of complex, multi-variable processes with the fewest trials possible.
Let's say we want to find out the effects that a few factors may have on a process. We can do so by varying the values of the factors to see whether the increase or decrease of these factors will affect the process. A much more practical and simpler way would be to use DOE to do so. In DOE, various levels are set for each factor to ensure that a balanced design can be achieved. This allows for a more fair comparison across the factors.
After which, the results of the different runs are obtained and we can rank the factors based on how significant their effect is on the dependent variable.
The fundamentals of DOE are as follows:
1. Response variable (dependent variable)
2. Factor (independent variable)
3. Level
4. Treatment
To determine the number of experiments we have to carry out, we have to use the formula N=r2^n,
where N is the total number of experiments, r is the number of replicates, and n is the number of factors.
In the given case study, there is only 1 replicate, so r=1. There are 3 factors (diameter, microwave time, and power setting of microwave), so n =3. 2^3=8, so the total number of experiments (runs) we have to carry out is 8!
In this case study, I will be examining the significance of the effects of different factors on the loss of popcorn yield. 8 runs were conducted with the HIGH(+) and LOW(-) values of the factors, to see how many un-popped kernels (bullets) remained in the bag.
1. Full Factorial data analysis
1. I made use of the template given to us, and matched the values accordingly. The excel formula rounds up the values to the nearest whole number. This is how the table looks like:
3. Afterwards, I plotted a graph of the amount of bullets (Dependent variable) remaining vs the HIGH and LOW values of the factors (Independent variable):
LET'S STUDY THE RESULTS!
1.1 Interaction effects for Full Factorial
For example, the diameter with a longer microwaving time has different effects than with a shorter microwaving time.
So, we have to determine the effect of the amount of bullets remaining when 2 different factors interact with each other.
As shown in the graph, the 2 graphs DO NOT intersect with each other. Hence, there is no interaction.
2. Fractional Factorial data analysis
We will now move on to carry out the Fractional Factorial data analysis for the case study. So, what is the difference between Full Factorial and Fractional Factorial?
In Fractional Factorial, fewer runs are chosen to provide sufficient information to determine the effects of the differen factors. It is more efficient and resource-effective, but the downside is that you may risk missing information😓
For the case study, we will have to choose a subset of 4 runs from a 8 run factorial design. But how do we fractionalise? The 4 runs have to be selected in a way where the design is balanced and varied. It should have good statistical orthogonality, where all factors occur (with both high and low levels) the same nummber of times.
E.g. Factors A, B, and C need to have 2 HIGH(+) and LOW(-) levels each. That is how we can determine which 4 runs to use.
For this, I have chosen Runs 1,2,3 and 6. The number of times the HIGH and LOW levels occurred are the same, hence it is balanced.
Now, we will calculate the significance of the effects of the different factors:
And a graph can be plotted:
LET'S STUDY THE RESULTS!
From the above graph, Factor C has the most significant effect as its gradient is the steepest (2.66), whereas Factor A has the least significant effect as its gradient is the gentlest (0.29)
-When Factor A increases, the amount of bullets decreases from 2.005g to 1.715g.
-When Factor B increases, the amount of bullets decreases from 2.215g to 1.505g.
-When Factor C increases, the amount of bullets decreases from 3.19g to 0.53g.
Conclusion:
Now, we can rank the factors from the most significant to the least significant:
1. Factor C (Power setting of microwave)
2. Factor B (Microwave time)
3. Factor A (Diameter)
Excel files:
My own file (with fractional factorial data analysis included):
Template used for Full Fractional data analysis :
3. Learning Reflections:
Learning about DOE and putting it into practice was not easy for me😰One obstacle I faced was selecting the appropriate 4 runs for the fractional factorial. At first, I did not understand how to select the runs. I was able to understand how the runs are selected during the tutorial lessons as the slides were able to explain the concept to me. I found the illustration of the balanced design using a cube very helpful and from there, I was able to understand why only certain runs can be selected for the fractional factorial.
However, it was different for the case study as the runs had different HIGH and LOW levels. I later on discovered that the number of HIGH and LOW levels have to occur the same number of times. In this context, when choosing 4 runs, the number of times a HIGH level has to occur is 2 times, and the number of times a LOW level has to occur is 2 times. This has to apply to all 3 factors. Using this understanding, I found it easier to select the 4 runs that will give a balanced design.
From here, I learned that I have to go through enough practice using the factorial fractional data analysis to really get the hang of choosing 4 selected runs from 8 runs. Now that I understand how to do data analysis for fractional factorial design, I plan to apply it in my subsequent projects, like for my FYP or prototype for this module😄
Practical:
In the practical, we were to determine the effects of 3 factors:
1. Factor A : Arm length
2. Factor B: Projectile weight
3. Factor C: Stop angle
On the distance travelled by the projectile. We carried out the full factorial data analysis first, followed by the fractional factorial. The following results were obtained for the Full Factorial run:
Conclusion:
Between the 2 graphs, there is an intersection. Hence, there is an interaction between A and C.
Between the 2 graphs, there is no intersection. Hence, there is no interaction between B and C.
The same data analysis can be done for Fractional Factorial:
During the DOE practical, I had a lot of fun releasing the catapult at varying levels of factors with my group mates😊Our group managed to finish the first, which I was very happy about😀However, there was some discrepancy with our results. This is because as the weight of our catapult increased, the distance travelled by the catapult also increased. If the weight of our catapult increases, the distance travelled should decrease instead because the heavier weight would drag it down.
I figured that this discrepancy could probably be due to the angle at which we released the catapult from. One of our catappults could not go all the way down, and hence there was a difference between the 2 catapults that were released based on the different HIGH and LOW factors. Next time, we should check and see if there is any faulty equipment before carrying out the runs.
For the group challenge, we were tasked to release the projectile and see if it could hit the targets at different distances. How my group went about doing this was to compare the distance of the target to the nearest distance we obtained from the practical run, and made the adjustments to our catapult accordingly. We changed the arm length, projectile weight, and stop angle according to how near/far the target was from the catapult.
Unfortunately for the group challenge, my group and I were not able to win any points😭But that's okay! There were 2 instances where we almost hit the standee, but it was not counted as our catapult bounced. In order to fix this, we should consider the release angle (either high, low, or medium) depending on the distance from the target. I realised we did not take that into much account as we relased our catapult from the same angle most of the time.
Additionally, I realised that the tension in the rubber bands we had was not as high as other groups', and hence it could have affected the distance travelled by our catapult.
To end it off, I found using the DOE method really effective and useful because it allowed me to account for all the different levels of factors, to reach a more balanced design for data analysis. This allowed me to make a fair comparison between the different factors. I do see myself using this method whenever I have to carry out experiments in the future😁
And with that, that's the end of my blog for DOE! I hope you guys enjoyed reading through and were able to learn new things with me as well😊See you guys in the next blog!😄💥
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