Design of experiments
Design of Experiments (DOE)
What is Design of experiments? ðĪ
- A statistics-based approach to designing experiments. ð
- A methodology to obtain knowledge of a complex, multivariable process with the fewest trials possible. An optimization of the experimental process itself. ð
- The backbone of any product design as well as any process/ product improvement efforts. ððĶī
Full Factorial design data analysis
A full factorial is the data analysis of all the possible treatments or runs. It is an analyzation of all the data collected from an experiment and it helps conclude the effects of each variable in an experiment.
Fractional factorial design data analysis
A fractional factorial is ‘less than full’. Fewer than all possible treatments are chosen to still provide sufficient information to determine the factor effect. It is more efficient and resource-effective, but you risk missing information.
Interaction effects
An interaction effect happens when one explanatory variable interacts with another explanatory variable on a response variable. This is opposed to the “main effect” which is the action of a single independent variable on the dependent variable.
DOE practical ðŽ
Conclusions & Ranking
from the graphical analysis:
· When ARM LENGTH increases from 28cm to 32.6cm, the flying distance of projectile decreases from 126.95cm to 95.525cm.
· When START ANGLE increases from 0 degrees to 20 degrees, the flying distance of projectile decreases from 120.23cm to 102.25cm.
· When STOP ANGLE increases from 60 degrees to 90 degrees, the flying distance of projectile decreases from 132.68cm to 89.79cm.
· RANKING: Stop angle (Most significant), Arm Length, Start angle (Least Significant)
Link to Full factorial design excel datasheet:
https://docs.google.com/spreadsheets/d/1Qfj6jfMmaskRr2cF7hfwSzsfIBar0odw/edit?usp=sharing&ouid=101485745405503095742&rtpof=true&sd=true
Interaction effect:
Interaction between A and B:
Runs
for low A and low B, run 1,5
Runs
for high A and low B, run 2,6
Runs
for low A and high B, run 3,7
Runs
for high A and high B, run 4,8
At LOW B, Average of
low A= (180.3+90.5)/2=135.4
At LOW B, Average of
high A= (116.5+93.7)/2=105.1
At LOW B, total effect
of A= (105.1-135.4) =-30.3 (decrease)
At HIGH B, Average of
low A= (145.5+91.6)/2=118.55
At HIGH B, Average of
high A= (88.5+83.5)/2=86
At HIGH B, total effect of A= (86-118.55) =-32.55 (decrease)
Interaction between A
and C:
Runs
for low A and low C, run 1,3
Runs
for high A and low C, run 2,4
Runs
for low A and high C, run 5,7
Runs
for high A and high C, run 6,8
At LOW C, Average of
low A= (180.3+145.5)/2= 162.9
At LOW C, Average of
high A= (116.5+88.5)/2= 102.5
At LOW C, total effect
of A= (102.5-162.9) = -60.4 (decrease)
At HIGH C, Average of
low A= (90.5+91.6)/2= 91.05
At HIGH C, Average of
high A= (93.7+83.5)/2= 88.6
At HIGH C, total effect
of A= (88.6-91.05) =-2.45 (decrease)
Interaction between B and C:
Runs
for low B and low C, run 1,2
Runs
for high B and low C, run 3,4
Runs
for low B and high C, run 5,6
Runs
for high B and high C, run 7,8
At LOW C, Average of
low B= (180.3+116.5)/2= 148.4
At LOW C, Average of
high B= (145.5+88.5)/2= 117
At LOW C, total effect
of B= (117-148.4) = -31.4 (decrease)
At HIGH C, Average of
low B= (90.5+93.7)/2= 92.1
At HIGH C, Average of
high B= (91.6+83.5)/2= 87.55
At HIGH C, total effect
of B= (87.55-92.1) =-4.55 (decrease)
The gradient of both lines are negative and different values. Therefore, there’s a significant interaction between B and C.
Fractional factorial design
2 of us worked on collecting the data for the full factorial design as there were 32 runs to complete. We split the work where 1 of us records the data and works with the catapult (changes the factors as well) and the other measures the flying distance. Below are our results.
Conclusions & Ranking from the graphical analysis:
· When ARM LENGTH increases from _28cm_ to _32.6cm, the flying distance of projectile _Decreases from _129.43cm to 109.74cm.
· When START ANGLE increases from 0 degrees to 20 degrees, the flying distance of projectile Decreases from 120.01cm to 119.16cm.
· When STOP ANGLE increases from 60 degrees to 90 degrees, the flying distance of projectile Decreases from 148.0cm to 91.21cm.
·
RANKING: Stop angle (Most significant), Arm Length,
Start angle (Least Significant)
Link to Full factorial design excel datasheet:
https://docs.google.com/spreadsheets/d/1pIao2x6TK5LkOpYLqyDPfnJ0YAhTts2-/edit?usp=sharing&ouid=101485745405503095742&rtpof=true&sd=true
Interaction effect:
Interaction between A
and B:
At LOW B, Average of
low A= 101.5 (run 5)
At LOW B, Average of high
A = 134.0 (run 2)
At LOW B, total effect
of A= (134-101.5) =32.5 (increase)
At HIGH B, Average of
low A = 154.7 (run 5)
At HIGH B, Average of
high A = 81.0 (run 8)
At HIGH B, total effect
of A= (81-154.7) =-73.7 (decrease)
Interaction between A
and C:
At LOW C, Average of
low A= 154.7 (run 3)
At LOW C, Average of
high A= 134 (run 2)
At LOW C, total effect
of A= (134-154.7) = -20.7 (decrease)
At HIGH C, Average of
low A= 101.5 (run 5)
At HIGH C, Average of
high A= 81 (run 8)
At HIGH C, total effect
of A= (81-101.5) =-20.5 (decrease)
Interaction between B
and C:
At LOW C, Average of
low B= 134 (run 2)
At LOW C, Average of
high B= 154.7 (run 3)
At LOW C, total effect
of B= (154.7-134) = 20 (increase)
At HIGH C, Average of
low B= 101.5 (run 5)
At HIGH C, Average of
high B= 81 (run 8)
At HIGH C, total effect
of B= (81-101.5) =-20 (decrease)
Answers given in question for full factorial and fractional factorial are very different from each other as the graphs made from the data for each interaction are different when comparing full factorial and fractional factorial. Therefore, the conclusion is that the data from full factorial should be used as there is more data provided hence more information can be obtained.
Case study 1 ðž
|
Run |
Diameter (cm) |
Microwaving time (min) |
Power (W) |
|
1 |
+ |
- |
- |
|
2 |
- |
+ |
- |
|
3 |
- |
- |
+ |
|
6 |
+ |
+ |
+ |
These 4 runs were chosen as all factors occur (both low and high levels) the same number of times. It is said to be orthogonal. Thus, good statistical properties.
A x B
At LOW B, Average of low A = (0.7+3.1)/2= 1.9 (-)
At LOW B, Average of high A = (3.5+0.7)/2 = 2.1 (+)
At LOW B, total effect of A = (2.1 - 1.9)= 0.2 (increase)
At HIGH B, Average of low A = (1.6 + 0.5)/2 = 1.05 (-)
At HIGH B, Average of high A = (1.2 + 0.3)/2 = 0.75 (+)
At HIGH B, total effect of A = (0.75 - 1.05) = -0.3 (decrease)
The gradient of both lines are different (one is + and the other is -). Therefore, there’s a significant interaction between A and B.
A x C
At LOW C, Average of low A = (1.6+3.1)/2= 2.35 (-)
At LOW C, Average of high A = (3.5+1.2)/2 = 2.35 (-)
At LOW C, total effect of A = (2.35 - 2.35)= 0 (no effect)
At HIGH C, Average of low A = (0.7+0.5)/2= 0.6 (-)
At HIGH C, Average of high A = (0.7+0.3)/2 = 0.5 (+)
At HIGH C, total effect of A = (0.5 - 0.6) = -0.1 (decrease)
The gradient of both lines is different (one is positive (+) and the other is negative (-). Therefore, there’s an interaction between A and C, but the interaction is small.
B x C
At LOW C, Average of low B = (3.5 + 3.1)/2 = 3.3 (-)
At LOW C, Average of high B = (1.6 + 1.2)/2 = 1.4 (+)
At LOW C, total effect of B = (1.4 - 3.3) = -1.9 (decrease)
At HIGH C, Average of low B = (0.7 + 0.7)/2 = 0.7 (-)
At HIGH C, Average of high B = (0.3 + 0.5)/2 = 0.4 (+)
At HIGH C, total effect of B = (0.4 - 0.7) = -0.3 (decrease)
The gradient of both lines are different (one is + and the other is -). Therefore, there’s a significant interaction between B and C.
Individual ð
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