Blog 3: Design Of Experiments (DOE)

Introduction

Hi! It has really been a long time since I posted anything. Today I am going to be talking about Design Of Experiment aka DOE. Below are some of the content I will be covering today.

Content:

1. Theory (Fractional and Full Factorial Design)

2. Case Study

3. Practical + learning reflection

Theory of Design Of Experiments (DOE)

What is DOE?

• It is a statistics-based approach to designing experiments.

• A methodology to obtain knowledge of a complex, multi-

• It is basically using math to obtain the significance of the different factors with the least number of runs.

How to know how many experiments to run?

• The above equation governs how many experiments you would need to run

• N (total number of experiments)

• r (number of runs per experiment)

• n (total number of factors, exp temp, viscosity)

Full and Fractional Factorial Design

• Above is the table you are going to be using in your full and fractional design analysis.

• On the left, the picture basically shows the runs and which of the independent factors that were changed.

• This is very important especially for choosing the correct experiments for fractional factorial design.

How to choose the correct experiments for fractional factorial design?

• Above the picture shows the 8 runs being shown in a 3-dimensional space, all connected with each other.

1. All the runs chosen need to have equal number of +s and -s

2. The run need to be orthogonal to each other when display in a 3-dimensional space as shown above (For those vector and AMM2 people, dot product=0)

3. The columns cannot be directly opposite of one another (Will further elaborate in Learning Reflection)

Case Study

Hyperlink: Blog 3 Case Study.xlsx

Full Factorial Design:

Data Analysis for Full Factorial Design:

Graph for significance of factors:

Significance of factors:

• C>B>A. Factor C is the most significant as the gradient of the graph of C is the largest compared to A and B. This shows that a change in factor C will indicate a large change in the amount of bullets. Therefore, from the significance of main effects graph, it shows that the power setting has the most effect on the number of bullets.

• Factor A is the least significant as the gradient of A is the lowest among all the factors. This shows that a change in A will not bring about a large increase or decrease in the number of bullets. Therefore, the bowl diameter has little to no effect on the number of bullets remaining.

Interaction effect of the factors in Full Factorial Design:

Interaction effect (AxB):

Data analysis of AxB:

Conclusion:

• The gradient of the two lines are different by only a small margin. Therefore, there is interaction between factor A and B, but the interaction is small. Thus, there is little interaction between bowl diameter and microwaving time.

Interaction effect (AxC):

Data analysis of AxC:

Conclusion:

• The gradient of the two lines are different by only a small margin. Therefore, there is interaction between factor A and C, but the interaction is small. Thus, there is little interaction between bowl diameter and power setting.

Interaction effect (BxC):

Data analysis of BxC:

Conclusion:

• The gradients of both lines are negative and are of different values. This indicates a interaction between factor B and C. Since the gradients of the lines are quite far apart from one another, there is a significant interaction between factor B and C. Therefore, there is a significant interaction between microwaving time and power setting.

Fractional factorial design:

Data analysis:

Conclusion:

• C>B>A. Factor C is the most significant as the gradient of the graph of C is the largest compared to A and B. This shows that a change in factor C will indicate a large change in the amount of bullets. Therefore, from the significance of main effects graph, it shows that the power setting has the most effect on the number of bullets.

  • Although the order of factors from most significant to least significant is the same for full factorial design, on the fractional factorial graph, factor A has an large positive gradient while for the full factorial design graph, factor A is seen to have a small negative gradient. Thus, this shows that fractional factorial design is less accurate than a full factorial design due to fractional factorial design having a smaller dataset.

Learning Reflection

• For me, when I was first introduced to DOE, I was not really exposed to excel and the graphing ability of excel so it took a long time to get the hang of it through playing around with the full and fractional factorial graphs. Through the practicals and activities, I have begun to appreciate the use of DOE as it could be very useful in both my internship and Final Year Project (FYP). An example of DOE being used in my internship is that when I have to do an experiment, I can use the equation at the start of this blog to help me determine how many runs I should carry out. In addition, if my supervisor asks me why do I carry out so little runs, I can simply refer back to DOE and explain my point of view.

• Another learning point is that when choosing runs to put through fractional factorial design, the columns must not directly opposite of one another. Below the picture is an example. As you can see column B is directly opposite of that of A.

• Now, you may be wondering why is that bad? let say I want to see the significance of factor C. It is good as I have 2 sets of data I can take from which is Run 1,4 and Run 2,3. However, it is bad for factor A and B.

• Let say I want to know the significance of A so B and C needs to be the same but as you can say from the table, there is no 2 runs that will give this result. I encountered this problem during our practical as I was the one doing the excel graphing. Luckily, I caught it before we had to redo anything.

• From this near-miss experience, I have learnt that I have to check my work properly and even though the runs chosen has already fulfilled the above 2 requirements, I will still have to account for the final requirement.

Hope you enjoy this blog! Look forward for my next blog! See you.