Design of Experiment(DOE in short) is a methodology to obtain knowledge of a complex, multi-variable process with the fewest trails possible. DOE is the backbone of any product design as well as any process/product improvement efforts.
All these definition so cheem isn't it? Basically, it is to study the effects of factorsthat are set a various levels and which factor is the most influential.
Fundamentals of DOE
1. Response variable(Dependent variable)- measured outcome of changing a factor
2. Factor(independent variable)- the factor to be changed/varied to see the effect
3. Level- a specific condition of the factor
4. Treatment- specific combination of factor levels
To calculate the total number of experiments that need to be carried out:
N= number of experiments
r= number of replicates
l= number of level
n=number of factor
Usually there are 2 levels, high(+) and low(-).
There are 2types of factorial designs: Full and Fractional. Fractional is a fewer number of experiments and being more efficient and resource-effective. However, there will be a risk of inaccuracy.
Practical
Excel for DOE practical (full and fractional can be found in the tabs on the bottom left)
There were 3 factors that we were testing out during experiment:
Factor A: Arm length
Factor B: Projectile weight
Factor C: Stop angle
The results were tabulated as shown below for Full Factorial
Effects of each factor
Factor A: When arm length increases from 28cm to 33.3cm, the flying distance of projectile decreases from 218.61cm to 137.9cm.
Factor B: When projectile weight increases from 0.85g to 2.03g, the flying distance of projectile decreases from 207.11cm to 149.4cm.
Factor C: When stop angle increases from 50 to 90 degree, the flying distance of projectile decreases from 214.87cm to 141.6cm.
Ranking of Factors
1. Arm length(steepest gradient)
2. Stop angle
3. Projectile weight(gentlest gradient)
Interaction of Factors
The gradients of both lines are the same(negative). Therefore there’s NO significant interaction between A and B.
The gradient of both lines are the same. Therefore there’s NO significant interaction between A and C.
The gradients of both lines are the same(negative). Therefore there’s NO significant interaction between B and C.
Conclusion, AxB has more interaction compared to AxC while BxC has no interactions.
The results were tabulated as shown below for Fractional Factorial
For fractional factorial, we chose run 2,3,5 and 8 as for factor A, B and C, it has a balance of 2 highs and 2 lows.
Effects of each factor
Factor A: When arm length increases from 28cm to 33.3cm, the flying distance of projectile decreases from 164.64cm to 145cm.
Factor B: When projectile weight increases from 0.85g to 2.03g, the flying distance of projectile increases from 142.09cm to 167.6cm.
Factor C: When stop angle increases from 50 to 90 degree, the flying distance of projectile decreases from 216.16cm to 93.5cm.
Ranking of Factors
1. Stop angle(steepest gradient)
2. Projectile weight
3. Arm length(gentlest gradient)
Interaction of Factors
The gradient of both lines are different(one is + and the other is -). Therefore there’s a significant interaction between A and B.
The gradients of both lines are the same(negative). Therefore there’s NO significant interaction between A and C.
The gradients of both lines are the same(negative). Therefore there’s NO significant interaction between B and C.
Conclusion, AxB has interaction. AxC has low interaction while BxC has no interactions.
Reflection
This practical was one of the most fun and exciting practical.🎉 I have gained knowledge on how to use DOE to find the effects of each factor. Being able to do the experiment made me understand more compared to when merely reading off the slides in class. However, the prepractical task was essential as it can help to prepare us for practical day. This minimises the loss of time and we can set up the excel ready for use with graphs that are formulated ahead of time.
One of the set back we faced was that our most significant factor for both full and fractional factorial were different(for full factorial it was Factor A; for fractional factorial it was Factor B).😢 We should have gotten the same factor despite both method. We brainstormed and looked through our datas and found out that run 5 went haywire.🤯 The data collected for run 5 in full and fractional factorial has totally different values(one is 257cm and another one is 90cm). This thought us something, there might be human error and we should analyse our data on the spot and if there is error, it can be re-run to make sure we are doing it right.
With the data collected, we headed on with a challenge given by Dr. Noel which is to hit different targets of different distance. We match the average of runs and match it with the distance to get the best suitable combination. However, our first attempt we failed by shooting it too far. On the spot, we adapted and tried with a higher start angle. This time we nailed it. This made me thought that actually start angle could be a factor as well since with the same combination, it made a different outcome.
Here's a satisfying video of the target being shot.
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
Admin No: 2111335
Run order
A
B
C
Bullets
(grams)
1
+
–
–
3.35
2
-
+
–
2.35
3
–
-
+
0.74
4
+
+
-
1.35
5
+
–
+
0.95
6
+
+
+
0.32
7
–
+
+
0.35
8
–
-
-
3.12
No of experiments=8 x 2^3 =64
Excel link for DOE blog (full and fractional can be found in the tabs on the bottom left)
Full Factorial data analysis
Using the excel template provided, I keyed in the values given at the bullet column as the Avg data and changed the level of factors at the second column.
Effects of each factor
Factor A: When diameter increases from 10cm to 15cm, the mass of bullet decreases from 1.64 to 1.4925.
Factor B: When microwaving time increases from 4 minutes to 6 minutes, the mass of bullet decreases from 2.04 to 1.0925.
Factor C: When power increases from 75% to 100, the mass of bullet decreases from 2.54 to 0.585.
Ranking of Factors
1. Power(steepest gradient)
2. Microwaving time
3. Diameter(gentlest gradient)
Interaction of Factors
The gradients of both lines are different(-ve and +ve), however there is no intersection hence there is no interactions.
The gradients of both lines are different(-ve and +ve), however there is no intersection hence there is no interactions.
The gradients of both lines are the same(-ve), and there is no intersection hence there is no interactions.
Fractional Factorial data analysis
Effects of each factor
Factor A: When diameter increases from 10cm to 15cm, the mass of bullet increases from 1.55 to 1.835.
Factor B: When microwaving time increases from 4 minutes to 6 minutes, the mass of bullet decreases from 2.05 to 1.335.
Factor C: When power increases from 75% to 100, the mass of bullet decreases from 2.85 to 0.53.
Ranking of Factors
1. Power(steepest gradient)
2. Microwaving time
3. Diameter(gentlest gradient)
Interaction of Factors
The gradients of both lines are different(-ve and +ve), there is an intersection hence there are interactions.
The gradients of both lines are different(-ve and +ve), however there is no intersection hence there is no interactions.
The gradients of both lines are the same(-ve), and there is no intersection hence there is no interactions.
The gradients of both lines are the same(negative). Therefore there’s NO significant interaction between B and C.
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