Design Of Experiments
What does it mean to compare the gradient of the lines plotted? -> A steeper gradient indicates that the factor is more significant in affecting the remaining bullets as the change between the high and low levels are greater while the other factors remain constant.
From the graph above, the effect of every Factor can be determined as well as the rankings of the significance of the factors can be identified.
4) Make conclusion on the effect of Factors
When A (Bowl Diameter) increases from 10cm to 15cm, the bullets remaining decreases from 1.48g to 1.43g.
When B (Microwaving Time) increases from 4 minutes to 6 minutes, the bullets remaining decreases from 2.00g to 0.90g.
When C (Power) increases from 75% to 100%, the bullets remaining decreases from 2.35g to 0.55g.
5) Rank the significance of the factors
Most Significant: C (Power)
Significant: B (Microwaving Time)
Least Significant: A (Bowl Diameter)
6) Explanation
As mentioned earlier, The way I analysed the results were based on the Calculations in the Full Factorial Excel, (See figure 1) I plotted the average values of the grams of bullets remaining for every High and Low factor into line graphs (See figure 2) and compared their gradients.
The difference between the average values of the grams of bullets remaining for every High and Low level of each factor shows the effect of the factor on the grams of bullets remaining which is also reflected by the slope of the graphs for each factor (Figure 2). I.e. If the difference between the average value of the grams of bullets remaining during the High level of a factor and the average value of the grams of bullets remaining during the Low level of a factor is large i.e. hence a steeper gradient for that factor’s graph, it can be deduced that the factor has a significant impact on the grams of bullets remaining.
Hence, based on Figure 1, the difference (effect) between the average value for the grams of bullets remaining at low Power and high Power is the largest -> [1.80 absolute value]. This can be seen also when the gradient of the graph for the grams of bullets remaining based on varying levels of Power (grey graph in Figure 2) is the steepest. Therefore, Power i.e. Factor C has the most significant impact on the grams of bullets remaining. When C (Power) increases from 75% to 100%, the bullets remaining decreases from 2.35g to 0.55g.
Followed by Microwaving time which has a lower impact than Power but more significant impact than Bowl Diameter which has the least significant impact on the grams of bullets remaining. This can be concluded because from Figure 1 the difference (effect) between the average value for the grams of bullets remaining at low level and high level Microwaving time is [1.10 absolute value], higher than that of the effect of the Bowl Diameter on the grams of bullets remaining [0.05 absolute value] but lesser than that of the Power’s effect. The gradient of the graph for the grams of bullets remaining based on varying levels of Microwaving time (orange graph in Figure 2) is more steeper than that of the Bowl Diameter graph but less steep compared to the Power graph. When B (Microwaving Time) increases from 4 minutes to 6 minutes, the bullets remaining decreases from 2.00g to 0.90g. When A (Bowl Diameter) increases from 10cm to 15cm, the bullets remaining decreases from 1.48g to 1.43g.
(A) First, determine the effect of AxB by:
From the table above, the average of low A and high A, for both high B and low B, is calculated from which the total effects of the factor can be determined. Hence, a graph can be plotted to find out if there is any interaction between A & B by comparing the gradients of the 2 lines plotted.
(B) Determine the effect of AxC
Conclusion from graph:
(C) Determine the effect of BxC
1) Select 50% of the number of runs done for full factorial
In this case, the fractional factorial is done by reducing the number of runs used from 8 to 4. With the data, then determine the most significant factor.
Below shows the 4 runs I have selected to ensure that the design is balanced and it will achieve statistical orthogonality. Thus, yielding good statistical properties and results.
2) After identifying the 4 runs, calculate the average values as shown below
3) Plot a graph using the mean values
This is to determine the significance of a factor on the bullets remaining, by comparing the gradient of the lines plotted. A steeper gradient indicates that the factor is more significant in affecting the remaining bullets as the change between the high and low levels are greater while the other factors remain constant.
4) Conclude the effect of every factor from the graph
When A (Bowl Diameter) increases from 10cm to 15cm, the bullets remaining increases from 1.15g to 1.90g.
When B (Microwaving Time) increases from 4 minutes to 6 minutes, the bullets remaining decreases from 2.10g to 0.95g.
When C (Power) increases from 75% to 100%, the bullets remaining decreases from 2.55g to 0.5g.
5) Conclude the ranking of the factors from the graph
Most Significant: C (Power)
Significant: B (Microwaving Time)
Least Significant: A (Bowl Diameter)
The way I
analysed the results was the same as how I did for FULL factorial except that now, I
had to modify the Full Factorial Excel to ensure it is applicable for a
Fractional Factorial Excel i.e. I deleted the 4 runs I wasn’t doing such that
only the 4 runs I selected from Task 1 were being examined -> Run 1, 2,3, 6. For the Calculation formulas I changed the average of 4 to 2 since now there
would only be 2 runs for each level of every factor i.e. 2 runs for when the
factor is at a high level and similarly for when the factor is at a low.
Based on the
Calculations in the Excel, (See figure 2) I plotted the average values of the
time taken for dissolution to happen for every High and Low factor into line
graphs (See figure 3) and compared their gradients.
The difference between the average values of the grams of bullets remaining for every High and Low level of each factor shows the effect of the factor on the grams of bullets remaining which is also reflected by the slope of the graphs for each factor (Figure 3).
Hence, based on Figure 2 and Figure 3, the difference (effect) between the average value for the grams of bullets remaining at low level temperature and high level Power is the largest -> [2.05 absolute value]. This can be seen also when the gradient of the graph for the grams of bullets remaining based on varying levels of Power (Grey graph in Figure 3) is the steepest. Therefore, Power i.e. Factor C has the most significant impact on the grams of bullets remaining. When C (Power) increases from 75% to 100%, the bullets remaining decreases from 2.55g to 0.5g.
Followed by Microwaving time which has a lower impact than Power but more significant impact than Bowl Diameter which has the least significant impact on the grams of bullets remaining. This can be concluded because from Figure 3 the difference (effect) between the average value for the grams of bullets remaining at low and high level Microwaving time is [1.15 absolute value], higher than that of the effect of the Bowl Diameter on the grams of bullets remaining [0.75 absolute value] but lesser than that of the Power’s effect. The gradient of the graph for the time taken for grams of bullets remaining based on varying levels of Microwaving time (orange graph in Figure 3) is more steeper than that of the Bowl Diameter graph but less steep compared to the Power graph. When A (Bowl Diameter) increases from 10cm to 15cm, the bullets remaining increases from 1.15g to 1.90g. When B (Microwaving Time) increases from 4 minutes to 6 minutes, the bullets remaining decreases from 2.10g to 0.95g.
In conclusion, the most significant factor remains to be C (Power) as it has the steepest gradient, indicating the most change in Bullets remaining when level is adjusted from low to high, followed by B (Microwaving Time), then A (Bowl Diameter) least significant. However, an observation made is that there is a change in gradient for A. Initially, gradient of A was of a very small negative value. Then, it became positive slope.
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Overall Conclusion
Comparing the full factorial design and fractional factorial design, there isn't much difference as the results remained relatively similar.
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