Design of Experiments

      Full factorial data analysis

      To use the full factorial data analysis to solve the case study, we identified the dependent variable as the flying distance of the projectile and the independent variables as the three factors that affect the flight distance of the ball. The three factors are:

      Factor A: Arm length

      Factor B: Projectile weight 

      Factor C: Stop angle     

      Each factor has 2 levels, low and high. We ran tests with each of the factors in different combinations, each run was done eight times and the average distance was taken in the end.

      Then, we tabulated the average distances when each of the factors were high and when each of the factors were low. We took the average of that to find the significance of each factor.

• When arm length increases from low to high, the flying distance of  projectile decreases from 96.20 cm to 77.35 cm
•       When the projectile weight increases from low to high, the flying distance of  projectile increases from 90.16 cm to 83.39 cm
• When the stop angle increases from low to high, the flying distance of  projectile decreases from 88.96 cm to 84.59 cm

    Hyperlink: DOE practical full factorial analysis.xlsx

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 effect between Factors A and B:

Interaction between A and B for full factorial:

Interaction between A and C for Full factorial:

Interaction between B and C for Full factorial:

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

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.

Fractional factorial data analysis

      To perform the fractional factorial data analysis, we took four runs, 2, 3, 5 and 8. They have the equal number of highs and lows for each factor and are thus statistically orthogonal. 

      Then, we tabulated the average distances when each of the factors were high and when each of the factors were low. We took the average of that to find the significance of each factor.

• 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

    Hyperlink: DOE practical fractional factorial analysis.xlsx

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 stop angle. Then the least significant factor, projectile weight, with the most gentle gradient.

   

    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.

            Reflection

      After this practical, I have a better understanding on the methods to design an experiment. To maximise the effectiveness of the session, I had to make use of metacognition and recall what I have learned in CP5202 Lab Process Skills 2 practical 3. In that practical, we also had to make use of design of experiment and discover which factor is the most significant in affecting the leaching of coffee solubles.

      By doing so, my team and I had a better understanding of the procedures and we were able to finish all eight runs the fastest.

      However, that was not without any challenges. Life is never fair as pitfalls can suddenly appear and land you into a cesspit. This was no different.

      Firstly, we faced troubles with the projectile flight distance. Our first few runs had the ball flying from one end of the lab to another, which made it very difficult for us to take values. This forced us to improvise and adapt. With the help of a man with a lackluster childhood, we decided to charge the trebuchet only down two gear teeth. This gave us a maximum ball flight distance of 118 cm, allowing us to take the values easily and quickly.

      Secondly, one of our trebuchets exploded while we were loading it. This costed us both manpower and experimental efficiency as one member had to leave and repair the trebuchet and doing the runs with only one was terribly slow. After half an hour of pain, the guy we sent fixed it and we were able to proceed with our usual speed.

      Lastly, we realised that our maximum ball flight distance of 118 cm was too short for the challenge at the end.

            From the picture, we can see that the furthest target was 196 cm away from the start line and                  that we were at a serious disadvantage. However, we improvised and using the factor                            combination that achieved the greatest projectile distance and adjusted the charge for the                        trebuchet by varying the number of gear teeth we push the arm down by. With this                                    improvisation, we were able to hit the furthest target and that was enough for us.

      In conclusion, the skills will be very important to me in the future as I will most likely make use of it in my internship and in the workforce. Knowing how to design an experiement and get to the results with the least number of steps would make me a very efficient worker and someone worth keeping around. 

      This practical has also taught me how to adapt when challenges suddenly appear out of left field in life. The entire session was flled with many ups and downs that challenged my team and I to near collapse, and we would have actually collapsed if we did not adapt.

      This was an extremely enjoyable and equally important, 8/10.

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	+	–	–	3.43
2	-	+	–	2.43
3	–	-	+	0.74
4	+	+	-	1.43
5	+	–	+	0.95
6	+	+	+	0.32
7	–	+	+	0.43
8	–	-	-	3.12

Full factroial analysis:

Taking the average bullet mass for each of the levels for each factor,

From the graph, we can see that factor c, power, has the most significant effect on the mass of bullets as it has the steepest graph. This is followed by factor b, microwaving time. The least significant factor is factor A, diameter, as its graph is the most gentle.

From the interaction graphs, each of the factors have a rather significant interaction with each other. Factors A and C have the least interaction as the gradient of their interaction graphs are the closest. Factors B and C have the most interaction with the greatest gradient difference between their interaction graphs.

Fractional factorial analysis:

To perform the fractional factorial data analysis, runs, 3, 4, 5 and 6 were used. This is because they have the equal number of highs and lows for each factor and were thus statistically orthogonal. 

From the graph, we can see that factor c, power, and factor b, microwaving time, have the most significant effect on the mass of bullets as they have the steepest graph. Both factors c and b have equal significance as thier gradients are the same in different directions. The least significant factor is factor A, diameter, as its graph is the most gentle.

Hyperlink for case study spreadsheet: DOE blog Case Study (1).xlsx