Design of Experiments (DOE)
Week 12 & 13 (Tutorial)
For the tutorial sessions in week 12 and week 13, we were
introduced to the concept of Design of Experiments (DOE). DOE is a
statistics-based approach to designing experiments. It is a methodology to
obtain knowledge of a complex, multi-variable process with as little trial runs
as possible. It can be considered an optimisation of the experimental procedure
itself. DOE is basically the backbone of any product design as well as any efforts
to improve processes or products.
Fundamentals of DOE
- Response Variable (Dependent Variable)
Outcome that is measured for given experiment
- Factor (Independent Variable)
A factor is a variable that is deliberately
varied to see its effect on the response variable.
- Level
A level of a factor is the specific
condition of the factor for which we wish to measure
- Treatment
A treatment is a specific combination of
factor levels
Case Studies
For this activity, we did a case study to help us apply what
we had learnt about DOE. The group was split into two, with each pair taking on
one case study. As the CFO, I was assigned to Case Study 1.
The case study is indicated below in green.
What could be simpler than making microwave popcorn?
Unfortunately, as everyone who has ever
made popcorn knows, it’s nearly impossible to get every
kernel of corn to pop. Often considerable
number of inedible “bullets” (unpopped kernels) remain at
the bottom of the bag. What causes this
loss of popcorn yield?
In this case study,
three factors were identified:
1. Diameter of bowls to contain the
corn, 10 cm, and 15 cm
2. Microwaving time, 4 minutes, and
6 minutes
3. Power setting of microwave, 75% and 100%
8 runs were performed with 100 grams of corn used in every experiment
and the measured
variable is the number of “bullets” formed in grams and
data collected are shown below:
Factor A= diameter
Factor B= microwaving time
Factor C= power
Full Factorial Data Analysis
Step 1: Fill up the template with the information provided. Note that the order in which the cells are filled up should follow how each factor is varied for each run, and not the actual run order.
Step 2: The Excel sheet would have automatically calculated the average values for the different runs for each factor at each setting.
The calculated values are as follows:
Runs where A is +: 1, 4, 5, 6
Average = (3.5 + 1.2 + 0.7 + 0.3)/4 = 1.425
Runs where A is -: 2, 3, 7, 8
Average = (1.6 + 0.7 + 0.5 + 3.1)/4 = 1.475
Total effect = Difference = 1.425 – 1.475 = -0.05
Runs where B is +: 2, 4, 6, 7
Average = (1.6 + 1.2 + 0.3 + 0.5)/4 = 0.90
Runs where B is -: 1, 3, 5, 8
Average = (3.5 + 0.7 + 0.7 + 3.1)/4 = 2.00
Total effect = Difference = 0.9.0 – 2.00 = -1.10
Runs where C is +: 3, 5, 6, 7
Average = (0.7 + 0.7 + 0.3 + 0.5)/4 = 0.55
Runs where A is -: 1, 2, 4, 5
Average = (3.5 + 1.6 + 1.2 + 3.1)/4 = 2.35
Total effect = Difference = 0.55 – 2.35 = -1.80
Step 3: Plot the graph in the Excel spreadsheet. From the graph, we are able to determine which factors have a greater effect on the amount of unpopped kernels. In general, the steeper the gradient, the greater the effect.
1. Factor C (Power Setting of Microwave)
Factor C has the most significant effect on the amount of unpopped kernels in the popcorn. It has the steepest gradient, as seen in the graph.
When the power setting increases from 75% (-) to 100%(+), the mass of unpopped kernels drops from 2.35 g to 0.55 g, with a difference of 1.80 g.
2. Factor B (Microwaving Time)
Factor B has the second most significant effect on the amount of unpopped kernels in the popcorn. It has the second steepest gradient, as seen in the graph.
When the microwaving time increases from 4 min (-) to 6 min (+), the mass of unpopped kernels decreases from 2 g to 0.9 g, with a difference of 1.10 g.
3. Factor A (Diameter of Bowl)
Factor A has the least significant effect on the amount of unpopped kernels in the popcorn. It has the gentlest gradient, as seen in the graph.
When the diameter of the bowl increases from 10 cm (-) to 15 cm (+), the mass of unpopped kernels decreases slightly from 1.475 g to 1.425 g, with a difference of 0.05 g.
Next, we need to determine if there are any interaction effects between the factors. The three different interactions are as follows:
1. AxB
2. AxC
3. BxC
A x B (Diameter of
Bowl x Microwaving Time)
Step 2: Import data into Excel spreadsheet and us the data to plot a graph to see the interaction effects of factors A and B.
In conclusion, there is a significant interaction between
Factors A and B, as the gradients of both lines are different. One is positive
and the other is negative.
A x C (Diameter of
Bowl x Power Setting of Microwave)
In conclusion, there is a significant interaction between
Factors A and C, as the gradients of both lines are different. One is positive
and the other is negative.
B x C (Microwaving
Time x Power Setting of Microwave)
In conclusion, there is a significant interaction between
Factors A and B, as the gradients of both lines are negative and drastically
different.
Fractional Factorial Data Analysis
Fractional Factorial Design is the restricting of the number
of runs of an experiment as it is often unfeasible to carry out all the runs
required. In fractional factorial design, fewer than all possible treatments
are chosen to still provide sufficient information to determine the factor
effect. It is more efficient and resource-effective, though there is a risk of
missing information, especially if the runs to be conducted are not selected
carefully. This is because the fractional data analysis only considers the
experimental values of the runs selected and has a smaller pool of data. The
full factorial data analysis will give us a more accurate answer as there are
more runs being conducted, leading to a much wider pool of data.
To select a set of runs with an orthogonal design (good
statistical properties), the factors should all be varied at high and low
levels across all the runs, and the factors should be varied at their high and
low settings an equal number of times.
For this case study, the runs I have selected for the Fractional Factorial Data Analysis are Run 2, Run 3, Run 5, and Run 8. This selection allows me to vary all factors at the high and low levels the same number of times. This will mean that the experiment is balanced and orthogonal, with good statistical properties.
Step 1: Fill up the template with the information provided. Note that the order in which the cells are filled up should follow how each factor is varied for each run, and not the actual run order.
Step 2: The Excel sheet would have automatically calculated the average values for the different runs for each factor at each setting.
From the graph above, we
can rank the three factors according to their influence on the amount of
unpopped kernels:
1. Factor A (Diameter of
Bowl)
Factor
A has the most significant effect on the amount of unpopped kernels in the
popcorn. It has the steepest gradient, as seen in the graph.
When the power setting
increases from 10cm (-) to 15cm(+), the mass of unpopped kernels drops
from 1.28g to 0.25 g, with a difference of 1.03
g.
2. Factor B (Microwaving Time)
Factor
B has the second most significant effect on the amount of unpopped kernels in
the popcorn. It has the second steepest gradient, as seen in the graph.
When the microwaving time
increases from 4 min (-) to 6 min (+), the mass of unpopped kernels decreases
from 1.05 g to 0.475 g, with a difference of 0.575 g.
3. Factor C (Power Setting
of Microwave)
Factor
C has the least significant effect on the amount of unpopped kernels in the
popcorn. It has the gentlest gradient, as seen in the graph.
When the diameter of the bowl
increases from 75% (-) to 100% (+), the mass of unpopped kernels increases
slightly from 0.58 g to
0.95 g, with a difference of
0.37 g.
Link to Excel Sheet:
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