Design of Experiment

DOE

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Design of Experiment is a statistics-based approach to design experiments.

- It is used to obtain results of a complex, multi-variable process with the fewest trials possible.

- It is the backbone of product designs as well as any process/product improvement efforts.

For this topic, we made use of DOE to determine which factors are most influential on the experimental output.

Fundamentals of DOE:

1. Response variable (Dependent variable) - Outcome that is being measured 

2. Factor (Independent variable) - Experimental variable that is varied to see its effects on the response variable

3. Level (low/ high) - the specific condition of the factor for which we wish to measure. +ve and -ve signs are being used to denote the factor level.

4. Treatment - specific combination of factor levels 

To determine the number of experiments (N) that needs to be carried out, use 

N = r2^n

where n is the number of factors, and r is the number of replicates

2 types of factorial design: full & fractional.

Fractional factorial means that only a 'fraction' of the treatments are being chosen to provide information to determine the factor effect. Although this method of testing is more efficient and resource-effective, it has higher risk of causing inaccuracy in the results obtained as compared to using full factorial method.

Practical

For this practical session, we were tasked to study the effects of the factors affecting the flying distance of projectile (dependent variable) using full & fractional factorial designs.

The 3 factors that were being varied:

Factor A : Arm length

Factor B : Projectile weight

Factor C : Stop angle

Each factors were being separated into high and low levels, and each run we did were of different combinations. We repeated every different combinations 8 times and the average flying distance of projectile is being calculated. 

Using full factorial data analysis:

• When arm length increases from low to high, the flying distance of  projectile decreases from 97.09 cm to 76.82 cm

• When the projectile weight increases from low to high, the flying distance of  projectile increases from 90.35 cm to 83.56 cm

• When the stop angle increases from low to high, the flying distance of  projectile decreases from 89.08 cm to 84.83 cm

From the values, we can see that the arm length is the most significant factor as its graph has the steepest gradient. This is followed by projectile weight. Then the least significant factor, stop angle, with the most gentle gradient.

Interaction between A and B for full factorial:

Interaction between A and C for Full factorial:

Interaction between B and C for Full factorial:

Most interaction -> Least interaction:

A and C > A and B > B and C

Using the graphical method, we can deduce that the most significant interaction occurs between factors A and C as the graph for E is the steepest and the interaction between A and C graphs have the greatest gradient difference. This indicates that there is a significant interaction between factors A and C and a change in level for factors A and C has a significant effect on the projectile distance. 

Graph F has the most gentle gradient and the most similar gradients in the B and C interaction graph. This shows that factors B and C have the least interaction and a change in level for factors B and C would not have a significant effect on the projectile distance.

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Using fractional data analysis:

As mentioned above, for fractional data analysis, only a few sets of data will be used. We used run 2, 3, 5, 8 where they have equal highs and lows for the factors. Hence, they would be statistically orthogonal.

• When arm length increases from low to high, the flying distance of  projectile decreases from 94.43 cm to 79.15 cm

• When the projectile weight increases from low to high, the flying distance of  projectile increases from 86.63 cm to 86.95 cm

• When the stop angle increases from low to high, the flying distance of  projectile decreases from 88.70 cm to 84.875 cm

Interaction between A and B for Fractional factorial:

Interaction between A and C for Fractional factorial:

Interaction between B and C for Fractional factorial:

Interaction graph for factors D, E and F (Fractional factorial analysis)

Most interaction -> Least interaction

B and C > A and B > A and C

Using the graphical method, we can deduce that the most significant interaction occurs between factors B and C as the graph for F is the steepest and the interaction between B and C graphs have the greatest gradient difference. This indicates that there is a significant interaction between factors B and C and a change in level for factors B and C has a significant effect on the projectile distance. 

Graph E has the most gentle gradient and the most similar gradients in the A and C interaction graph. This shows that factors A and C have the least interaction and a change in level for factors A and C would not have a significant effect on the projectile distance.

Link 🔗 to the data sheet: CPDD DOE practical data sheet mavis.xlsx 

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Reflection:

During the tutorial session, I recall myself being very confused as to what values we were supposed to key into the excel sheet and also how to plot the interaction graphs. However, I got all of that figured out with the help of my friends so it's no big deal. 

During the practical session, we faced some problems with the projectile flight distance because our projectile would not land on the tray of sand. Hence, we improvised and kept our experiment small. We charged the catapult with only 2 gear teeth. It was definitely not because someone had a bad childhood experience.

We also had a challenge where we had to shoot down several targets that were of different distance using our own factor combinations. For example, the furthest target was around 167 cm away while the closest target was only 66 cm away. Due to the fact that we kept our experiment in a small area, the flying distance of our projectile we recorded was very short compared to the other groups and we did not have a big range of distance to work with. We tried our best to play around with the different combinations of factors and managed to hit the furthest target on our second try. 

This practical was really fun and it is the most enjoyable practical I have had. I think that this practical was definitely an essential as I got a better understanding on how to make use of DOE to conduct experiments and as well as to learn how to study the effects of the factors have on a certain variable. 

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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 number : 2122234

Link 🔗to excel for case study: CPDD DOE blog case study mavis.xlsx

Run order	A	B	C	Bullets (grams)
1	+	–	–	3.34
2	-	+	–	2.34
3	–	-	+	0.74
4	+	+	-	1.34
5	+	–	+	0.95
6	+	+	+	0.32
7	–	+	+	0.34
8	–	-	-	3.12

Full factorial data analysis:

I keyed in the values into the excel sheet, and plotted the graph

Ranking factors based on the significance they have on the mass of bullets.

1. Factor C, power 

2. Factor B, microwaving time

3. Factor A, diameter 

Based on the graph plotted, factor C has the most significant effect on the mass of bullets as it has the steepest gradient. It is then followed by factor B and A where A (diameter) has the least significance of the mass of bullets as it has the gentlest gradient. 

Interaction between factors:

Between A and B:

Since there is an intersection between the 2 lines, this shows that Factors A and B interacted quite significantly.

Between A and C:

Since there is an intersection of the 2 lines, this shows that there is interaction between Factors A and C. However, the interaction is not a significant one as the gradient is gentle. 

Between B and C:

Since there is both the gradients for the graphs are the same (negative gradient) and there is no intersection between the 2 lines, this shows that there is no interaction between factors B and C.

Fractional data analysis:

Only runs 2, 3, 5, 8 were chosen. 

Ranking factors based on the significance they have on the mass of bullets.

1. Factor C, power 

2. Factor B, microwaving time

3. Factor A, diameter 

Factor C, power, has the most significant effect on the mass of bullets as it has the steepest gradient. 

Since the results obtained from the fractional data analysis also showed that factor C is the most significant factor, this proves that there is no error in computing the results.