Design of Experiment (DOE)

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Week 12 and 13 (Tutorial)

For the tutorials sessions in weeks 12 and 13, we were introduced to a concept called Design of Experiment, or DOE for short.

Background Information
DOE is a statistics-based approach to designing experiments. It acts as the backbone of any product design, as well as any process or product improvement effor. It allows us to obtain knowledge of a complex, multivariable process with the fewest trials possible through optimisation of the experimental process itself. This is achieved by first determining a set of factors which are most important to the system or process, and concluding through trial and error at what levels these factors must be kept to optimise the process or system performance. Its main benefit is that it provides a quick and cost-effective method to understand and optimize any manufacturing processes.

For the activity for this learning topic, we completed a case study which was designed to help us apply what we had learned about DOE. We were given two case studies to complete, and the group was split into two groups of two to complete both. As the CEO (team leader), I was assigned to Case Study 1.

My documentation for this activity can be found below:


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 a 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 amount of “bullets” formed in grams and data collected are shown below:
  • Factor A = Diameter of Bowl
  • Factor B = Microwaving Time
  • Factor C = Power Setting of Microwave
The different high and low settings of the three identified factors can be found below:
Figure 1: Runs with Factors at Different Settings


Full Factorial Data Analysis

The first part of the full factorial data analysis requires us to determine the effects of the individuals on the amount of unpopped kernels in the popcorn, as well as rank them according to how great of an effect they have on the amount of unpopped kernels in the popcorn.

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 will automatically calculate the average values of the different runs for each factor at each setting.





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 a graph in the Excel sheet. We can determine from the gradient of the slopes which effect has the greatest effect on the amount of unpopped kernels. In general, the steeper the gradient, the greater the effect of the factor on the amount of unpopped kernels.













From the graph above, we can rank the three factors according to their influence on the amount of unpopped kernels:

1. Factor C - Power Setting of Microwave (Most Significant)
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 (Least Significant)
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 have to determine if there are any interaction effects between the different factors. Two factors are said to interact with each other if the effect of one factor on the response variable is different at different levels of the other factor. The three interactions are:
  1. A × B (Diameter of Bowl × Microwaving Time)
  2. A × C (Diameter of Bowl × Power Setting of Microwave)
  3. B × C (Microwaving Time × Power Setting of Microwave)
A × B (Diameter of Bowl × Microwaving Time)
Step 1: Calculate the average effects of Factor A when Factor B is at its lowest and highest.
Step 2: Import the date into an Excel file, and plot a graph displaying 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 × C (Diameter of Bowl × Power Setting of Microwave)
Step 1: Calculate the average effects of Factor A when Factor C is at its lowest and highest.
Step 2: Import the date into an Excel file, and plot a graph displaying the interaction effects of Factors A and C.


















In conclusion, there is a small interaction between Factors A and C, as the gradients of both lines are positive and different by a little margin.


B × C (Microwaving Time × Power Setting of Microwave)
Step 1: Calculate the average effects of Factor A when Factor C is at its lowest and highest.
Step 2: Import the date into an Excel file, and plot a graph displaying the interaction effects of Factors B and C.


















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 refers to the restriction of the number of runs of a certain experiment, as it is often unfeasible and unrealistic to run all treatments of the experiment, which may require over a thousand runs. 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 1, Run 2, Run 3 and Run 6. 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 will automatically calculate the average values of the different runs for each factor at each setting.
Step 3: Plot a graph in the Excel sheet. We can determine from the gradient of the slopes which effect has the greatest effect on the amount of unpopped kernels. In general, the steeper the gradient, the greater the effect of the factor on the amount of unpopped kernels.














From the graph above, we can rank the three factors according to their influence on the amount of unpopped kernels:

1. Factor C - Power Setting of Microwave (Most Significant)
Factor C still 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 2.55 g to 0.50 g, with a difference of 2.05 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 2.10 g to 0.95 g, with a difference of 1.15 g.

3. Factor A: Diameter of Bowl (Least Significant)
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.
However, unlike in the full factorial data analysis, where Factor A would cause the amount of unpopped kernels to decrease as it increases, it has the opposite effect in the fractional data analysis.
In the full factorial data analysis, 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.
In the fractional data analysis, when the diameter of the bowl increases from 10 cm to 15 cm, the amount of unpopped kernels increases from 1.15 g to 1.90 g., with an increase of 0.75 g.

Since the runs selected for the Fractional Factorial Data Analysis gives similar results to that of the Full Factorial Data Analysis, they can be considered as good runs.

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