DESIGN OF EXPERIMENT

Design Of Experiment (DOE)

Hello! Welcome back to another blog! This week, I had learned on Design of Experiment (DOE)

and how we can use a statistics-based approach to designing of experiment.

Tip for DOE:

For experiment with factors having different levels, e.g.,

L1: 2

L2: 3

L3: 3

N = L1 * L1 * L3

Documentation on Case Study

Link for Excel File: https://docs.google.com/spreadsheets/d/1SOgx5xY2TL9s6dQ29oShgyQBJVsVzQwK/edit?usp=sharing&ouid=107171668789834527235&rtpof=true&sd=true

Occupation: CEO, Case 1

Full Factorial Design

Step 1 & 2: Determining the effect of single factors and their ranking

Step 1: Filling up the Template 

I had typed in the average number of inedible bullets into the “AVE” column, which stands for average. As I do not have the different runs’ number of inedible bullets,

those cells will be left empty.

Step 2: Creating a Graph for Visualisation

By creating a new small table, I then created a graph, which can accurately show the effect of single factors. The slope with the steepest line, or the highest gradient

value, is the most influential factor.

CONCLUSION:

The 3 factors which are the most significant to the least significant is:

1. C: Power

2. B: Microwaving Time

3. A: Diameter of Bowl

This can be read from the graph, as the line with the steepest slope represents the most influential factor.

• Factor C, Power has the most significant effect on mass of bullets. The higher the power, the lower the mass of bullets remained at the bottom of the bag. At a higher microwave power, the chances of every kernel of corn to pop is higher. Therefore, with increasing power, the mass of bullets decreases. Factor C is therefore the most significant factor. The higher the power from 75% to 100%, the lower the mass of bullets by 1.8g.
• Factor B, Microwaving Time has the 2nd most significant effect on mass of bullets. The longer the microwaving time, the lower the mass of bullets remained at the bottom of the bag. A longer time spent in the microwave means that there will be more heat introduced longer to each kernel of corn, thus having more kernel of corn pop, and therefore lesser mass of bullets. Factor B is the second most significant factor. The longer the microwaving time from 4 minutes to 6 minutes, the lower the mass of bullets by 1.1g.
• Factor A, Diameter of bowl has the least significant effect on mass of bullets. The smaller the diameter of the bowl, the lower the mass of bullets remained at the bottom of the bag. The smaller the diameter of the bowl from 15cm to 10cm, the lower the mass of bullets by 0.05g.

Step 3 & 4: Determining the Interaction Effect

Step 3: Data Analysis for Full Factorial Design

When the diameter of the bowl decreases from 15cm to 10cm, the mass of indelible bullets reduces by 0.05g.

When microwaving time increases from 4 minutes to 6 minutes, the mass of indelible bullets reduces by 1.1g.

When power increases from 75% to 100%, the mass of indelible bullets reduces by 1.8g.

Step 4: Interaction effects between Factors

The 3 interaction factors are

• A x B (Diameter of Bowl x Microwaving Time)

• A x C (Diameter of Bowl x Power Setting of Microwave)

• B x C (Microwaving Time x Power Setting of Microwave)

• Data Analysis for (A x B)

At LOW B

Average of Low A: (3.1 + 0.7) / 2 = 1.9

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

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)

CONCLUSION: The gradient of both lines are different as one is positive, and one is negative. Therefore, there is a significant interaction between A and B.

• Data Analysis for (A x C)

At LOW C

Average of Low A: (3.1 + 1.6) / 2 = 2.35

Average of High A: (3.5 + 1.2) / 2 = 2.35

At LOW C, total effect of A: 2.35 - 2.35 = 0

At HIGH C

Average of Low A: (0.7 + 0.5) / 2 = 0.6

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)

CONCLUSION: The gradients of both lines are different by a little margin. Therefore, there is an interaction between A and C, but the interaction is small. 

• Data Analysis for (B x C)

At LOW C

Average of Low B: (3.1 + 3.5) / 2 = 3.3

Average of High C: (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

Average of High C: (0.5 + 0.3) / 2 = 0.4

At HIGH C, total effect of B: 0.4 - 0.7 = -0.3 (decrease)

CONCLUSION: The gradients of both lines are negative and have different values. Therefore, there is a significant interaction between B and C.

Fractional Factorial Design

The runs selected are:

• Run 1

• Run 2

• Run 3

• Run 6

The chosen runs have the factors occurring the same number of times. It has a good statistical property, and is said to be orthogonal.

Step 1: Determining the effect of single factors and their ranking.

Step 1: Filling up the Tables

Similar to step 1 of Full Factorial Design, I had started by making the graph for the 4 selected runs.

By creating a new small table, I then created a graph, which can accurately show the effect of single factors. The slope with the steepest line, or the

highest gradient value, is the most influential factor.

CONCLUSION: 

The 3 factors which are the most significant to the least significant is:

1. C: Power

2. B: Microwaving Time

3. A: Diameter of Bowl

This can be read from the graph, as the line with the steepest slope represents the most influential factor.

• Factor C, Power has the most significant effect on mass of bullets. The higher the power, the lower the mass of bullets remained at the bottom of the bag. At a higher microwave power, the chances of every kernel of corn to pop is higher. Therefore, with increasing power, the mass of bullets decreases. Factor C is therefore the most significant factor. The higher the power from 75% to 100%, the lower the mass of bullets by 2.05g.
• Factor B, Microwaving Time has the 2nd most significant effect on mass of bullets. The longer the microwaving time, the lower the mass of bullets remained at the bottom of the bag. A longer time spent in the microwave means that there will be more heat introduced longer to each kernel of corn, thus having more kernel of corn pop, and therefore lesser mass of bullets. Factor B is the second most significant factor. The longer the microwaving time from 4 minutes to 6 minutes, the lower the mass of bullets by 1.15g.
• Factor A, Diameter of bowl has the least significant effect on mass of bullets. The smaller the diameter of the bowl, the lower the mass of bullets remained at the bottom of the bag. The smaller the diameter of the bowl from 15cm to 10cm, the lower the mass of bullets by 0.75g.

CONCLUSION:

	Full Factorial Method	Fractional Factorial Method
Most Significant #1	C: Power	C: Power
Significant #2	B: Microwaving Time	B: Microwaving Time
Least Significant #3	A: Diameter of Bowl	A: Diameter of Bowl

Comparing the Full Factorial method and the Fraction Factorial method answers, I have made the following conclusion.

• Factor C, being concluded as the most significant factor for both methods, is concluded as the most significant factor for reducing mass of inedible bullets remaining at the bottom of the bag.

• Factor B, being concluded as the second most significant factor for both methods, is concluded as the second most significant factor for reducing mass of inedible bullets remaining at the bottom of the bag.

• Factor A, being concluded as the least significant factor for both methods, is concluded as the least significant factor for reducing mass of inedible bullets remaining at the bottom of the bag.

 

Therefore, the 4 runs selected (Run 1,2,3,7) can be considered as good runs since they do give the same findings as the Full Factorial method.