DOE
Hello guys, it's been a long time since I blogged. Well, you guys might be concerned and must be waiting to read my blog. Well, fret not, as the wait is finally over. This time, I am back with another rollercoaster of practical adventures I faced, as well as some new things I learned. This time, I am going to talk about the 'Design of Experiment'. Well, what is this??? You might be wondering. Don't worry because I'm here to explain the 'Design of Experiment' to all of you.
Design of Experiment
Well, I am going to explain the practical session about design of experiment as well as the Case Study involved in design of experiment.
Practical
In this practical, we performed investigation of 3 factors at 2 level using DOE.
The objective of this practical is to investigate the effect of the individual factors and
identify the factor that has the most significant effect on the response variable. We performed both FULL factorial design and FRACTIONAL factorial design in this
practical. As our group had 5 people, we split up so that one group of 3 people could carry out the full factorial design while the pair could carry out the fractional factorial design. Below shows the 3 factors to be investigated, at the level of LOW(-) and HIGH(+)
We started with the full factorial design.
Full factorial design
When arm length (Factor A) increases from 26cm to 31cm , the flying distance of projectile decreases from 154.33cm to 135.5344cm
When projectile weight (Factor B) increases from 0.85g to 2.01g, the flying distance of projectile decreases from 148.53cm to 141.3344cm
When stop angle (Factor C) increases from 600 to 900, the flying distance of projectile decreases from 181.69cm to 108.1791cm.
Interaction effect of A and B
Interaction effect of A and C
Interaction effect of B and C
Factor C contributes the most to the lost in yield.
Fractional Factorial
Below is the table for fractional factorial.
When arm length increases from 26cm to 31cm, the flying distance of projectile increases from 53.56 to 65.77
When projectile weight increases from 0.87g to 2.06g, the flying distance of projectile increases from 57.71 to 61.62
When stop angle increases from 60 degrees to 90 degrees, the flying distance of projectile decreases from 65.77 to 53.56.
As factor C changed the most, factor C is the factor that contributes the most to the loss in yield.
Reflection
Overall. this lesson broadened my mind due to the numerous new details I learned. Before, this practical, working around 3 factors in an experiment would be difficult due to the overload of data. Moreover, I was not introduced to coming up with a table with the low and high values of each factor. After this practical, it was extremely easy as I was able to handle 64 pieces of data.
Doing this practical, I learned a lot of new things. When we first started doing the experiment, we had trouble finding a place for conducting the experiment as we needed a huge place for the shooting of the ball. We tried doing the experiment on the table on the first few attempts, but it did not occur to us immediately that we could conduct the experiment on the floor. Moreover, we decided to share the same sand pit by using the sand pit simultaneously to shoot the ball, which reduced the time taken for us to finish the experiment, giving us more time to focus on results and graph calculation. This shows that we would have to use our own initiative to figure out some details in the experiment and that not everything would be stated in the practical manual. This taught me to also look at the experiment beyond the practical manual, enhancing my understanding of the practical instead of simply following instructions given by the practical manual. Moreover, when we were conducting the experiment on the ground, the small ball often rolled far away from us. Sometimes, the small ball almost went under some cabinets and doors, causing it to be difficult to remove the ball. Therefore, my group members decided to cover the tiny openings at the bottom of the cabinets and the holes at the bottom of the doors using our pencil cases and the boxes which were the packaging of the catapult. This prevented the balls from entering the tiny openings at the bottom of the cabinets and the gaps at the bottom of the doors. As a chemical engineer, this taught me that I should improvise the situation and make it to my advantage as long as it does not hinder the progress of the practical and as long as it does not cause any risks to someone.
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
|
Run order |
A |
B |
C |
Bullets (grams) |
|
1 |
+ |
– |
– |
3.XX |
|
2 |
- |
+ |
– |
2.XX |
|
3 |
– |
- |
+ |
0.74 |
|
4 |
+ |
+ |
- |
1.XX |
|
5 |
+ |
– |
+ |
0.95 |
|
6 |
+ |
+ |
+ |
0.32 |
|
7 |
– |
+ |
+ |
0.XX |
|
8 |
– |
- |
- |
3.12 |
Replace
the XX with the last 2 digits of your student number, example if your student
number is 2002139, replace the XX with 39
My admission number is 2122713
|
Run order |
A |
B |
C |
Bullets (grams) |
|
1 |
+ |
– |
– |
3.13 |
|
2 |
- |
+ |
– |
2.13 |
|
3 |
– |
- |
+ |
0.74 |
|
4 |
+ |
+ |
- |
1.13 |
|
5 |
+ |
– |
+ |
0.95 |
|
6 |
+ |
+ |
+ |
0.32 |
|
7 |
– |
+ |
+ |
0.13 |
|
8 |
– |
- |
- |
3.12 |
Below is the table I made using excel sheet.
When factor A, the diameter of bowls containing the corns, increases from 10cm to 15cm, the mass of bullets decreased from 1.53g to 1.3825g.
When factor B, the microwaving time, increases from 4min to 6min, the mass of bullets decreased from 1.99g to 0.9275g.
When factor C, the power setting of microwave increases from 75% to 100%, the mass of bullets decreased from 2.38g to 0.535g .
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
Interaction Effect
Interaction effect of A and B
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.
Interaction effect of A and C
The gradients of both lines are different, although both the lines representing '-C' and '+C' have positive gradients. However, as both of the lines do not intersect, there is no interaction between Factor A and C.
Interaction between B and C
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.
Interaction between B and C
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.
In conclusion, factor C caused the highest effect on the change in mass of bullets, due to highest change.
Fractional Factorial Data Analysis
Introduction to Fractional Factorial Data Analysis
In product design, there are many prototypes to be built. As it is infeasible to run all treatments in some cases, restricting the number of runs will be more realistic. This is known as fractional factorial design.
Statistical Orthogonality
Runs 1,2,3 and 6 are the best options for a fractional factorial data analysis as all factors(both low and high) occur the same number of times. It is said to be orthogonal. This is known as good statistical properties. The selected runs are represented below in a table.
Below shows the calculation of the significance of main effects, the solving for mean.
Below is the graph of the mass of bullets(g) vs 'Low' and 'High' of factor A, B and C.
Ranking of factors(starting from highest impact to lowest impact)
1)Factor C
2)Factor B
3)Factor A
From the graph above, factor C has the steepest gradient, followed by factor B, followed by factor A, having the least steep gradient.
When factor A increases from low to high, the mass of bullets increased from 0.72g to 0.8625g
When factor B increases from low to high, the mass of bullets decreased from 0.97g to 0.6125g.
When factor C increases from low to high, the mass of bullets decreased from 1.32g to 0.265g.
In conclusion, factor C contributes the most to loss in yield due to the highest change in mass of bullets.
Below is the hyperlink:
Comments
Post a Comment