Design Of Experiment

Reflection:

In this week's blog entry, I learned about a way to do experimentation in an easy and systematic way through designing of experiments (DOE). DOE is a statistics-based approach to designing experiments, a methodology to obtain knowledge of a complex, multivariable process with the fewest trials possible, an optimisation of the experimental process itself and the backbone of any product design as well as any process/ product improvement efforts. Through this, we are able to study the effects of factors as they are set at various levels.

The task assigned was to perform a full and fractional factorial design data analysis on a case study about analysis of the loss of the popcorn yield due to unpopped kernels. 

Full Factorial Data Analysis:

Ranking from most significant to the least significant: C > B > A 

Factor C (power) has the most significant effect on the mass of bullets (unpopped kernels). The higher the power setting of microwave from 75 to 100%, the lighter the mass of the bullets by 1.8g hence lesser number of unpopped kernels at the bottom of the popcorn bag which causes to have lesser loss of popcorn yield.

  

Factor B (microwaving time) has the 2nd most significant effect. The longer the microwaving time from 4 to 6 minutes, the lighter the mass of the bullets by 1.1g hence lesser number of unpopped kernels at the bottom of the popcorn bag which causes to have lesser loss of popcorn yield.  

Factor A (diameter) has the least significant effect. The higher the diameter of bowls to contain the corn from 10 to 15cm,  the lighter the mass of the bullets by 0.05g hence lesser number of unpopped kernels at the bottom of the popcorn bag which causes to have lesser loss of popcorn yield.  

Conclusion: As factor C has the steepest gradient with a gradient of -1.8 followed by factor B with a gradient of -1.1 and lastly by factor A with a gradient of -0.05 which less steep, the ranking of effect on the mass of bullets are C > B > A.

A x B:

At LOW B, Average of low A=(3.1+0.7)/2=1.9 

At LOW B, 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

At HIGH B, Average of high A=(1.2+0.3)/2=0.7 

At HIGH B, total effect of A=(0.7-1.05)=-0.35 (decrease)

The gradient of both lines are different (one is + and the other is -). Therefore, there's a significant interaction between A and C.

A x C:

At LOW C, Average of low A=(3.1+1.6)/2=2.35

At LOW C, Average of high A=(3.5+1.2)/2=2.35 

At LOW C, total effect of A=(2.35-2.35)=0 (no change) 

At HIGH C, Average of low A=(0.7+0.5)/2=0.6 

At HIGH C, 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)

The gradient of both lines are different (one has no gradient and the other is -). However, the difference between the gradient of both lines are by a little margin of 0.1. Therefore, there is an interaction between A and C, but the interaction is small hence insignificant.

B x C:

At LOW C, Average of low B=(3.1+3.5)/2=3.3 

At LOW C, Average of high B=(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+0.5)/2=0.6 

At HIGH C, Average of high B=(0.5+0.3)/2=0.4 

At HIGH C, total effect of B=(0.4-0.6)=-0.2 (decrease)

The gradient of both lines are negative and of different values, -1.9 and -0.2. Therefore, there is a significant interaction between B and C.

Conclusion: From the gradients shown, the interaction effect between B x C have a more significant effect on mass of bullets (unpopped kernels) in the bag followed by A x B and then A x C. As C had the most significant effect on the mass of bullets, followed by B then A, the interaction effect between B x C would have the most influence on the loss of popcorn yield due to the bullets.

Fractional Factorial Data Analysis:

Calculating the Significance of Main Effects (Solving for Means)

Run Order	A	B	C	Bullets
2	-	+	-	1.6
6	+	+	-	1.2
4	-	-	+	0.7
5	+	-	+	0.7

4 runs chosen are 2,6,4,5. All factors occur the same number of times. This shows that it has good statistical properties and is said to be orthogonal.  

Factor A — Runs Where A is + : (1.2 +0.7)/2 = 0.95

Factor A — Runs Where A is - : (1.6 +0.7)/2 = 1.15

Total Effect = Difference = 0.95 - 1.15 =-0.2

Factor B — Runs Where B is + : (1.6+1.2)/2 = 1.4

Factor B — Runs Where B is - : (0.7 +0.7)/2 = 0.7

Total Effect = Difference = 1.4-0.7=0.7

Factor C — Runs Where C is + : (0.7+0.7)/2 = 0.7

Factor C — Runs Where C is - : (1.6 +1.2)/2 = 1.4

Total Effect = Difference = 0.7-1.4=-0.7

	A	B	C
-	1.15	0.7	1.4
+	0.95	1.4	0.7

Ranking from most significant to the least significant: C > A > B 

Factor C (power) has the most significant effect on the mass of bullets (unpopped kernels). The higher the power setting of microwave from 75 to 100%, the lighter the mass of the bullets by 0.7g hence lesser number of unpopped kernels at the bottom of the popcorn bag which causes to have lesser loss of popcorn yield.

 

Factor A (diameter) has the  2nd most significant effect. The higher the diameter of bowls to contain the corn from 10 to 15cm,  the lighter the mass of the bullets by 0.2g hence lesser number of unpopped kernels at the bottom of the popcorn bag which causes to have lesser loss of popcorn yield.  

 

Factor B (microwaving time) has the least significant effect. The longer the microwaving time from 4 to 6 minutes, the heavier the mass of the bullets by 0.7g hence more number of unpopped kernels at the bottom of the popcorn bag which causes to have more loss of popcorn yield.   

Conclusion: Factor C has the steepest gradient with a gradient of -0.7 followed by factor A with a gradient of -0.2 and lastly by factor B with a gradient of 0.7. Even though Factor C and B have the same gradient of 0.7, Factor C's gradient is negative indicating that the mass of bullets is lighter while Factor B's gradient is positive indicating that the mass of bullets is heavier. Thus, ranking of effect on the mass of bullets are C > B > A.

Using the analysis from the 8 runs in full factorial data analysis and 4 runs chosen in fractional factorial data analysis (2, 6, 4, 5), both does not returns the same findings of significant effect with mass of bullets as the full factorial data analysis ranking of significant effect are: C > B > A while the fractional factorial data analysis ranking of significant effect are: C > A > B. As the findings are inconsistent, the 4 runs chosen (2, 6, 4, 5) in Task 2 are not good runs and is not the right runs. 

Link for excel datasheet: Here