DESIGN OF EXPERIMENTS
Design of Experiments
CASE STUDY
Link: DOE Case Study
where,
Factor A: Diameter of bowl (cm)
Factor B: Microwaving time (mins)
Factor C: Power (%)
Admin no.: 2135474
a. Full Factorial Data Analysis (Case Study)
For Full Factorial data analysis, two factors are said to interact with each other if the effect of one factor on the response variable is different at different levels of the other factor.
Taking the interaction effect of A x B as an example, the effect of diameter of bowls, at low microwaving time, 0.415 (increase), is different from the effect of diameter of bowls at high microwaving time, -0.71 (decrease).
Effect of each factors
When microwaving time increases from 4 mins to 6 mins, the mass of bullets formed decreases from 2.14 g to 1.385 g.
When power increases from 75% to 100%, the mass of bullets formed decreases from 2.84 g to 0.6875 g.
From the interaction effect of A x B, the gradient of both lines are different. At low B, gradient is positive. At high B, gradient is negative. Hence there is significant interaction between factors A & B.
From the interaction effect of Bx C, the gradients of both lines are negative and are of different values. Hence, there is significant interaction between factors B & C.
Conclusion:
From the Full Factorial data analysis, Factor B is the most significant followed by A and C. Since B produces more significant interaction with the other two factors, hence, it is the most significant factor.
b. Fractional Factorial data analysis (Case Study)
For Fractional Factorial data analysis, I selected runs 2, 3, 4 and 5 as all the factors, both high and low, occur the same number of times and is said to be orthogonal.
When diameter of bowl increases from 10 cm to 15 cm, the mass of bullets formed decreases from 0.87 g to 0.6725 g.
When microwaving time increases from 4 mins to 6 mins, the mass of bullets formed increases from 0.42 g to 1.12 g.
When power increases from 75% to 100%, the mass of bullets formed decreases from 1.12 g to 0.4225 g.
Conclusion:
From the Fractional Factorial data analysis, factor C is the most significant factor because it has the largest difference in values from the lowest to highest followed by factor B and factor A which is the least significant factor.
PRACTICAL
Link: Practical Excel Sheet
In this practical, my team and I were tasked to investigate the launch of projectile using a catapult. The three factors identified which affects the distance the projectile travelled are:
1. Arm length (cm)
2. Projectile weight (g)
3. Stop angle (°)
64 runs were carried out during the practical and the measured variable is the distance the projectile travelled. The independent variables are as follows:
Factor A: Arm length (cm)
Factor B: Projectile weight (g)
Factor C: Stop Angle (°)
a. Full Factorial data analysis (Practical)
From the interaction effect of A x B, the gradient of both lines are negative and are of different values. Hence there is significant interaction between factors A & B.
From the interaction effect of A x C, the gradient of both lines are different. At low C, gradient is negative. At high C, gradient is positive. Hence there is significant interaction between factors A & C.
From the interaction effect of B x C, the gradient of both lines are different. At low C, gradient is negative. At high C, gradient is positive. Hence there is significant interaction between factors A & B. However, as both lines are almost parallel, the interaction is small.
b. Fractional Factorial data analysis (Practical)
For Fractional Factorial data analysis, the team selected runs 1, 2, 3 and 4 as all the factors, both high and low, occur the same number of times and is said to be orthogonal.
When arm length increases from 22.5 cm to 28 cm, the projectile distance decreases from 171.7 cm to 137.4 cm.
When projectile weight increases from 0.87 g to 2.01 g, the projectile distance increases from 134.4 cm to 174.7 cm.
When stop angle increases from 60° to 90°, the projectile distance decreases from 208.3 cm to 100.85 cm.
Conclusion:
From the Fractional Factorial data analysis, factor C is the most significant factor because it has the largest difference in values from the lowest to highest followed by factor B and factor A which is the least significant factor.
