Design Of Experiments
Hello, this week we learned about design of experiments (DOE) and its importance and how to apply it. We learned that DOE is a versatile data gathering and analysis technique that can be applied to a wide range of experiments. It allows for the manipulation of many input elements in order to determine their impact on a desired outcome. DOE can identify crucial interactions that might be missed when experimenting with one component at a time by altering several inputs at the same time.
I am tasked to perform DOE on case 1 on factors affecting the number of inedible “bullets” (unpopped kernels) remaining. I used both full and fractional factorial design to obtain the results.
Full Factorial Design
Table of Data:
Only the average is inputted as only the average was given in the case study.
Calculation of Mean:
Graph:
A: When the diameter of bowls increases from 10cm to 15cm, the mass of bullets increases from 1.43g to 1.48g.
B: when the microwaving time increases from 4 to 6 minutes, the mass of bullets decreases from 2.00g to 0.9g.
C: when the power increases from 75% to 100% the the mass of bullets decreases from 2.35g to 0.55g.
The graph shows the power line has the steepest gradient followed by the microwaving time line and the diameter line indicating that the power has the biggest impact on the mass of bullets, then followed by microwaving tine, and lastly the diameter.
Interactions Between Factors
For FULL factorial design: (A x B)
At LOW B, (runs 1 and 5) Average of low A=(3.1+0.7)/2=1.9
At LOW B, (runs 2 and 6) 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, (runs 3 and 7) Average of low A=(1.6+0.5)/2=1.05
At HIGH B, runs 4 and 8) 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)
The gradient of both lines are different, -B line is positive and +B line is negative. This shows that there are significant interaction between factors A and B.
For FULL factorial design: (A x C)
At LOW C, (runs 1 and 3) Average of low A=(3.1+1.6)/2=2.35
At LOW C, (runs 2 and 4) Average of high A= (3.5+1.2)/2=2.35
At LOW C, total effect of A=(2.35-2.35)= 0 (no increase or decrease)
At HIGH C, (runs 5 and 7) Average of low A=(0.7+0.5)/2=0.6
At HIGH C, (runs 6 and 8) 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 gradients of both lines are only slightly different with very small margins. This indicates that there’s an interaction between A and B, but the interaction is very small. It could also be said that there is no interaction between factors A and B as the lines are almost parallel.
For FULL factorial design: (B x C)
At LOW C, (runs 1 and 2) Average of low B=(3.1+3.5)/2=3.2
At LOW C, (runs 3 and 4) Average of high B=(1.6+1.2)/2=1.4
At LOW C, total effect of B=(1.4-3.2)= -1.8 (decrease)
At HIGH C, (runs 5 and 6) Average of low B=(0.7+0.7)/2=0.7
At HIGH C, (runs 7 and 8) Average of high B=(0.5+0.3)/2=0.4
At HIGH C, total effect of B=(0.4-0.7)=-0.3 (decrease)
The gradients of both lines are negative and are different values. This shows that there are significant interaction between factors B and C.
From the fractional factorial design data, it seems that the strongest interaction is between BxC followed by AxB and finally AxC has the least interaction.
Fractional Factorial Design
For the fractional factorial design, I decided to use the results from runs 2, 3, 5, 8. This is because all factors (both low and high levels) occur the same number of times. It is an orthogonal design and has good statistical properties.
Table of Data:
Only the average is inputted as only the average was given in the case study.
Calculation of Mean:
Graph:
A: When the diameter of bowls increases from 10cm to 15cm, the mass of bullets increases from 1.15g to 1.9g.
B: when the microwaving time increases from 4 to 6 minutes, the mass of bullets decreases from 2.10g to 0.95g.
C: when the power increases from 75% to 100% the the mass of bullets decreases from 2.55g to 0.5g.
The graph shows the power line has the steepest gradient followed by the microwaving time line and the diameter line indicating that the power has the biggest impact on the mass of bullets, then followed by microwaving time, and lastly the diameter. The ranking of strongest factors for the fractional factorial design is the same as the full factorial design which shows that the runs chosen for the fractional factorial design were valid. Therefore, the fractional factorial design is a more efficient way to conduct the experiment as it requires a lesser number of total experiments which means lesser time and resources are required for the experiment while still providing the correct results.
No comments:
Post a Comment