DOE: Design Of Experiment
Design Of Experiments
10 January 2022
This week, we went through the concept of the Design of Experiments and how it is conducted. A few questions that we asked ourselves were, "Why should I be concerned with experimentation?", "Is there a way to experiment on things more systematically and easily?"
After this week's practical, I should be able to:
1. Understand the concept of Design of Experiments.
2. Perform both FULL and FRACTIONAL design data analysis.
3. Make use of Excel to plot and put in my data collected.
Case Study #2
The above image is the Case study that I worked on for this blog!
FULL FACTORIAL DESIGN DATA ANALYSIS
To start off, I organized the data by arranging the values in the case study to "-" and "+" respectively before plotting the table.
When the table is completed I started to calculate the average values of the 3 different factors accordingly.
From the average values calculated, we than plotted a graph showing the effectiveness of the 3 different factors.
The effectiveness of the factors can be determined by the gradient of each line!
The image above shows the effectiveness graph of the 3 factors. From the graph, we can see that stirring speed (Factor C) has the steepest gradient followed by concentration (Factor A) and lastly temperature (Factor B). The line with the steepest gradient will suggest that it is the most effective factor, which in this case is the stirring speed.
RANKING OF EFFECTIVENESS
After determining the effectiveness of the factors, I moved on to calculate the interaction effects between Factors AB, AC and BC.
INTERACTION EFFECT (FULL FACTORIAL)
Using the same table used at the start, we calculated new average values based on the "low" and "high" variable.
The image above shows the results of the interaction between factors AB and AC. From the graph of AB, we can see that the gradient of the two graphs are only slightly different. This will suggest that the interaction between A and B is not very significant.
However, for the interaction between A and C, we can see that the two graphs have very different gradients! This would mean that A and C have a very significant interaction with each other!
The above image shows the interaction between A and B, and as you can see, the gradient of both graphs are really similar with very little difference. This will suggest that there is very little interaction between the two factors.
TAKE NOTE: If gradients of both lines are parallel with each other, no interaction will occur!!
Hence, for the Full Factorial Analysis, we can conclude that factor C, the stirring speed is the most important and effective factor that will significantly affect our results, followed by stirring speed, and lastly temperature.
FRACTIONAL FACTORIAL DESIGN DATA ANALYSIS
Next, we move on to our fractional factorial analysis where we select half of the 8 runs at the start that are orthogonal.
ORTHOGONAL: ALL FACTORS OCCUR (both low and high) / APPEAR THE SAME NUMBER OF TIMES
From the original table consisting of the 8 runs, I decided to choose runs 1, 2 7 and 8 as these runs provided me with an orthogonal analysis as both the "low" and "high" levels appeared in the table the same number of times!
With this data, we can now plot the graph...
As you can see from the image above, the graph that I obtained is different for Factor B but the same for Factors A and C when comparing with the Full Factorial graph.
Also, from the graph, the gradients of all 3 factors are quite large, but based on calculations, I have found out that factors B and C have the largest gradient compared to factor A. This suggests that factors B and C are both the most important and effective contributing factors to the results.
RANKING OF EFFECTIVENESS
B = C > A
The results that I have gotten from the fractional factorial analysis differs with only factor being different compared to the full factorial. But both factorial analysis states that Factor C is the most important and most effective in affecting the results.
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