Design Of Experiment (DOE)
What is the point of a DOE?
- DOE is a statistics-based approach to designing experiments 🧪
- It is a methodology to obtain knowledge of a complex, multi-variable process with the fewest trials possible
- It is the backbone of any product design as well as any process/ product improvement efforts
How to determine the number of experiments?
N = r2^n
Where n = no. of factors and r = number of replicates
- DOE is a statistics-based approach to designing experiments 🧪
- It is a methodology to obtain knowledge of a complex, multi-variable process with the fewest trials possible
- It is the backbone of any product design as well as any process/ product improvement efforts
How to determine the number of experiments?
N = r2^n
Where n = no. of factors and r = number of replicates
Symbols used in DOE
+ = higher value of factor ➕
- = lower value of factor ➖
Types of factorial design data analysis
- full factorial
- fractional factorial
Full factorial design data analysis
- Data analysis of all the possible treatments and runs
- An analyzation of all data that is collected from experiment
- Helps to conclude effects of each variable in an experiment
Fractional factorial design data analysis
- "less than full"
- Fewer than all possible treatments are chosen to still provide sufficient information to determine the factor effect
- is more efficient and resource-effective, but you risk missing information
Practical DOE
EXCEL PRACTICAL
In this experiment we needed to determine the factors that will affect the flying distance of the projectile. The factors were already given to us and we needed to determine the interaction between each factor and also which was the most significant one.
The factors that were given to us were
1) Arm Length
2) Projectile weight
3) Stop Angle
Because there were 64 runs to complete and both full factorial, and fractional factorial, we split our group into 2. Me and Jasmine were doing the fractional factorial runs while Glenn and Hariz did the full factorial runs.
Above is the values we obtained from the full factorial experiment.
As seen from the results obtained, here are some conclusions:
1) Arm Length (Factor A): For Arm Length, the low value was 28cm while the high value was 33.3cm. Based on the results we collected, when arm length was increased, the flying distance of the projectile decreases. This can be seen by the average of the high value being thrown 137.9cm away and the low value of being thrown 218.61cm away.
2) Projectile weight (Factor B): For Projectile Weight, the low value was 0.85g while the high value was 2.03g. Based on the results collected, when projectile weight increases, the flying distance of the projectile decreases. This can be seen by the average value of the high value being thrown 149.41cm away and the low value of being thrown 207.11cm away.
3) Stop Angle (Factor C): For Stop Angle, the low value was 50 degrees while the high value was 90 degrees. Based on the results that were collected, when Stop Angle increases, the flying distance of the projectile decreases. This can be seen from the average value of the low value being thrown 214.87cm away and the high value being thrown 141.65cm away.
From the graph we can rank the factors from the most significant factor to least would be:
1) Arm length
2) Stop Angle
3) Projectile Weight
This is because when one looks at the graph, arm length has the steepest gradient when compared to the other factors.
Interaction between the factors (Full factorial)
Conclusions from graphs plotted (interaction):
1) AXB - The gradients of the lines plotted both negative and are around the same. This shows that the interaction between A and B is not very significant.
2) BXC - The gradients of both lines plotted are negative. This shows that the interaction between C and B is not very significant.
3) AXC - The gradients of the lines plotted both negative and are around the same. This shows that the interaction between A and C is not very significant.
Above is the values we obtained from the fractional factorial experiment.
As seen from the results obtained, here are some conclusions:
1) Arm Length (Factor A): when arm length was increased, the flying distance of the projectile decreases. This is shown as when the high value was used, the projectile was thrown on average 145.01cm away. Whereas when the low value was used, the projectile was thrown on average 164.63cm away.
2) Projectile weight (Factor B): when projectile weight increases, the flying distance of the projectile increases. This is shown as when the high value was used, the projectile flew an average of 167.56cm away. Whereas when the low value was used, the projectile flew an average of 142.09cm away.
3) Stop Angle (Factor C): when the stop angle increases, the flying distance of the projectile decreases. This is shown as when the high value is used, the projectile flew on average 93.49cm away. Whereas when the low value was used, the projectile flew on average 216.16cm away.
From the graph we can rank the factors from the most significant factor to least would be:
1) Stop Angle
2) Projectile Weight
3) Arm Length
This is because when one looks at the graph, Stop Angle has the steepest gradient when compared to the other factors.
Interaction between the factors (Fractional Factorial)
Conclusions from graphs plotted (interaction):
1) A X B - Both have different gradients with High B having a negative gradient and Low B having a positive gradient. Hence there is significant interaction between A and B.
2) A X C - Both the gradients are similar as they are both negative. Thus there is no significant difference in the interaction between A and C.
3) B X C - Both the gradients are similar as they are both negative. Thus there is no significant difference in the interaction between B and C.
Case Study
CASE STUDY Excel
In this case study, we were supposed to test the factors that affect the number of unpopped kernels (Bullets) that are left in the popcorn bag. The three factors that were identified were:
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%
Admin number: 2122122
With the template that was provided for the practical, I keyed the values that I had into one column and allowed the average to be computed but in this case the average would just be the value that I keyed in.
The table that was provided did not match the various difference in factors, thus one will need to be more careful in keying in the values. (Cross check the corresponding level factors)
Above is the values I obtained from the full factorial experiment.
As seen from the results obtained, here are some conclusions:
1) Diameter of bowls to contain the corn (Factor A): When the diameter of the bowl increases, the mass of the bullet decreases from 1.55 to 1.4275.
2) Microwaving time (Factor B) : When the microwaving time increases, the mass of the bullets decreases from 2.01 to 0.97.
3) Power setting of microwave (Factor C) : When the power increases, the mass of the bullets decreases from 2.45 to 0.5325.
From the graph the most significant factor to least would be:
1) Power
2) Microwaving time3) Diameter
Interaction between the factor (Full Factorial)
1) A X B - The gradients of the graph are both different with one being positive and the other being negative. However there is no intersection between the two lines, thus there are no interactions.
2) A X C - The gradients of the graph are both different with one being positive and the other being negative. However there is no intersection between the two lines, thus there are no interactions.
3) B X C - Both the gradients are negative, leading to no intersection between the two lines, thus there is no interaction.
Above is the values I obtained from the fractional factorial experiment.
As seen from the results obtained, here are some conclusions:
1) Diameter of bowls to contain the corn (Factor A): When the diameter of the bowl increases, the mass of the bullet increases from 1.48 to 1.77.
2) Microwaving time (Factor B) : When the microwaving time increases, the mass of the bullets decreases from 1.96 to 1.27.
3) Power setting of microwave (Factor C) : When the power increases, the mass of the bullets decreases from 2.72 to 0.53.
From the graph the most significant factor to least would be:
1) Power
2) Microwaving time3) Diameter
Interaction between the factor (Fractional Factorial):
1) A X B - Both lines have different gradients and also they intersect, thus there is interaction between A and B.
2) A X C - Both lines have a different gradients of positive and negative however they do not intersect, thus showing that A and C do not have any interaction.
3) B X C - Both lines have the similar gradients and do not intersect, thus B and C do not have any interaction.
Reflections:
Through this practical I learnt the importance of DOE and that it is easier to perform fractional factorial when one is able to as it requires lesser resources as well as lesser time. At the same time I feel that we had a lot of fun launching catapults together. The pre prac in class also made sure we were more prepared in practical and understand what was going on. While doing the practical, we realized that it was easier to have the shooter change the respective factors and the "ball retriever" to measure the distance of the ball that flew. One thing that did not go as planned was that the most significant factor for fractional factorial and full factorial was not the same. This was unusual as the other groups had the same significant factor. Furthermore it should not change based on the type of method we used.After much digging we realized that the data for run5 was inconsistent throughout both the fractional and full factorial runs. We were puzzled and confused at first but eventually we understand that human error and parallax error play a huge role in the collection of the results. We should have looked at the results between both while collecting them. This would have allowed us to realize the mistake and correct them on the spot.
Afterwards there was a challenge which was very fun as we got to shoot down our lecturers with the catapult. We were able to shoot down targets with quick thinking, thus scoring our team extra points.
1) AXB - The gradients of the lines plotted both negative and are around the same. This shows that the interaction between A and B is not very significant.
2) BXC - The gradients of both lines plotted are negative. This shows that the interaction between C and B is not very significant.
3) AXC - The gradients of the lines plotted both negative and are around the same. This shows that the interaction between A and C is not very significant.
Above is the values we obtained from the fractional factorial experiment.
As seen from the results obtained, here are some conclusions:
1) Arm Length (Factor A): when arm length was increased, the flying distance of the projectile decreases. This is shown as when the high value was used, the projectile was thrown on average 145.01cm away. Whereas when the low value was used, the projectile was thrown on average 164.63cm away.
2) Projectile weight (Factor B): when projectile weight increases, the flying distance of the projectile increases. This is shown as when the high value was used, the projectile flew an average of 167.56cm away. Whereas when the low value was used, the projectile flew an average of 142.09cm away.
3) Stop Angle (Factor C): when the stop angle increases, the flying distance of the projectile decreases. This is shown as when the high value is used, the projectile flew on average 93.49cm away. Whereas when the low value was used, the projectile flew on average 216.16cm away.
From the graph we can rank the factors from the most significant factor to least would be:
1) Stop Angle
2) Projectile Weight
3) Arm Length
This is because when one looks at the graph, Stop Angle has the steepest gradient when compared to the other factors.
Interaction between the factors (Fractional Factorial)
Conclusions from graphs plotted (interaction):
1) A X B - Both have different gradients with High B having a negative gradient and Low B having a positive gradient. Hence there is significant interaction between A and B.
2) A X C - Both the gradients are similar as they are both negative. Thus there is no significant difference in the interaction between A and C.
3) B X C - Both the gradients are similar as they are both negative. Thus there is no significant difference in the interaction between B and C.
Case Study
CASE STUDY Excel
In this case study, we were supposed to test the factors that affect the number of unpopped kernels (Bullets) that are left in the popcorn bag. The three factors that were identified were:
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%
Admin number: 2122122
With the template that was provided for the practical, I keyed the values that I had into one column and allowed the average to be computed but in this case the average would just be the value that I keyed in.
The table that was provided did not match the various difference in factors, thus one will need to be more careful in keying in the values. (Cross check the corresponding level factors)
Above is the values I obtained from the full factorial experiment.
As seen from the results obtained, here are some conclusions:
1) Diameter of bowls to contain the corn (Factor A): When the diameter of the bowl increases, the mass of the bullet decreases from 1.55 to 1.4275.
2) Microwaving time (Factor B) : When the microwaving time increases, the mass of the bullets decreases from 2.01 to 0.97.
3) Power setting of microwave (Factor C) : When the power increases, the mass of the bullets decreases from 2.45 to 0.5325.
From the graph the most significant factor to least would be:
1) Power
2) Microwaving time
Interaction between the factor (Full Factorial)
1) A X B - The gradients of the graph are both different with one being positive and the other being negative. However there is no intersection between the two lines, thus there are no interactions.
2) A X C - The gradients of the graph are both different with one being positive and the other being negative. However there is no intersection between the two lines, thus there are no interactions.
3) B X C - Both the gradients are negative, leading to no intersection between the two lines, thus there is no interaction.
Above is the values I obtained from the fractional factorial experiment.
As seen from the results obtained, here are some conclusions:
1) Diameter of bowls to contain the corn (Factor A): When the diameter of the bowl increases, the mass of the bullet increases from 1.48 to 1.77.
2) Microwaving time (Factor B) : When the microwaving time increases, the mass of the bullets decreases from 1.96 to 1.27.
3) Power setting of microwave (Factor C) : When the power increases, the mass of the bullets decreases from 2.72 to 0.53.
2) Microwaving time (Factor B) : When the microwaving time increases, the mass of the bullets decreases from 1.96 to 1.27.
3) Power setting of microwave (Factor C) : When the power increases, the mass of the bullets decreases from 2.72 to 0.53.
From the graph the most significant factor to least would be:
1) Power
2) Microwaving time
1) Power
2) Microwaving time
3) Diameter
Interaction between the factor (Fractional Factorial):
1) A X B - Both lines have different gradients and also they intersect, thus there is interaction between A and B.
2) A X C - Both lines have a different gradients of positive and negative however they do not intersect, thus showing that A and C do not have any interaction.
3) B X C - Both lines have the similar gradients and do not intersect, thus B and C do not have any interaction.
Through this practical I learnt the importance of DOE and that it is easier to perform fractional factorial when one is able to as it requires lesser resources as well as lesser time. At the same time I feel that we had a lot of fun launching catapults together. The pre prac in class also made sure we were more prepared in practical and understand what was going on. While doing the practical, we realized that it was easier to have the shooter change the respective factors and the "ball retriever" to measure the distance of the ball that flew. One thing that did not go as planned was that the most significant factor for fractional factorial and full factorial was not the same. This was unusual as the other groups had the same significant factor. Furthermore it should not change based on the type of method we used.
Afterwards there was a challenge which was very fun as we got to shoot down our lecturers with the catapult. We were able to shoot down targets with quick thinking, thus scoring our team extra points.
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