Design of Experiment
Hi everyone :D in this blog, I will be documenting my learning process of Design of Experiment (DOE) with the use of a case study and also with a learning reflection.
For starters the meaning of DOE refers to the statistical based approach to design experiments. It helps obtain knowledge for a complex, multivariable process with as little trials as needed.
To carry out DOE, we need the following variables:
Response (Dependent) Variable: Measured outcome
Factor (Independent Variable): Factor that is changed to see how it affects the response variable
Level: Refers to the level of the factor in a specific condition of the factor for which we wish to measure
Treatment: Specific combo of factor levels
Based on this case study, we can state the following:
For Full Factorial Design, 8 runs will be conducted as there are 3 factors present therefore, 23= 8.
For Fractional Factorial Design, 4 runs will be conducted
In table form, this is how the data looks like:
Full Factorial Design
In excel, this is how the table will look like:
To find out which factor has the most significance, we have to plot the graph based on the average values of the upper and lower limits of each factor. The values have been calculated by excel.
Based on the values above, plot the graph:
Using excel, obtain the trendline for all 3 factors:
Factor A: y=0.4375x + 0.895
Factor B: y = -0.3525x + 2.08
Factor C: y = -0.7475x + 2.6725
Based on the gradients of the 3 factors, it can be concluded that Factor C has the largest significance as it has the largest gradient (ignoring the “-” in front) of 0.7475 followed by Factor A which has a gradient of 0.4375 and lastly Factor B which has the least significance at at gradient of 0.3525.
To simplify it: C > A > B
Interaction between Factors
Moving on, as we all know, during the experiment, factors will interact with each other. In fact, 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.
To find out which factors interact with each other, we have to plot the graph again.
Interaction D (A x B)
These are the data obtained:
Using the data obtained, plot the graph:
Through the graph above, gradients of both lines are different, one being positive and the other being negative. Therefore, this means that there is significant interaction between A and B.
Interaction E (A x C)
Data obtained:
Plot the graph:
From this graph, it can be concluded that since the difference between the gradients of both lines is small, there is a small interaction between A and C.
Interaction F (B x C)
Data obtained:
Plot the graph:
Through the graph, we can see that the gradients of both lines are vastly different from each other and are both negative. Hence, this means that there is significant interaction between Factor B and C.
Fractional Factorial Design
Firstly we have to decide which of the runs to use. In this case, I will be using Runs 1,2,5 and 7. While deciding, it is important to make sure that there is an equal distribution of high and low factors.
In table form, this is how it looks like:
Based on this graph, we can conclude that Factors A and B have the highest and same significance as they have their gradients have the same value of 0.815. Factor C has the lowest gradient as it has the smallest gradient value of 0.635.
This is the link of everything I’ve done (Full and Fractional): DOE Case study excel.xlsx
Learning Reflection:
At first, when I saw DOE, I didn’t think it would be that hard(in terms of understanding), the only thing I had in mind was that it would be tedious as we had to conduct many runs for an experiment. In fact, I thought that it was going to be boring. However, after the practical session, it definitely somewhat changed my mind. In fact, it was really fun doing the group challenge where we got to ‘knock’ our lecturers down 🤡 .
During the practical, we were tasked with shooting a ball with the use of a catapult. However, there were obviously changes made to the variables. These included that the 2 different balls of different masses were used (projectile weight), the length of the catapult (Arm’s Length) is also different and the stop angle at which the catapult is set is also different.
Before conducting the experiment, we had to measure the respective variables so that we know the range of them from low to high. This was what we recorded. (We decided on the values for the low and high of the stop angle.
And with that, we conducted our experiment. However, while conducting the experiment, I realised that our results may not be the best and reliable as the distance between the catapult and the sandpit wasn’t specified meaning that we couldn’t really gauge where the ball is ‘rightfully’ supposed to land (basically we had no safety net and were somewhat conducting the experiment randomly). In fact, from what I remember, for other groups the distance between their catapult and the sandpit was at least 1m or more. However, ours was probably less than half a metre even. To add on to our uncertainty, during the practical, Mr Chua even told us to make sure that our values didn’t exceed 2m. Even though it may seem like we didn't have much to worry about, all the values that we obtained were less than 1.2m with the most being 115.5m. This then made me worry as I thought that the distance was too small. Additionally, due to not knowing what the group challenge was about, my group and I weren’t sure if our values were good enough or not.
These were the results we obtained:
Full Factorial:
Fractional (Runs 2,3,5 and 8):
Credits to firzanah and kelvin ^^
Heres some photos of us conducting the experiment:
When it came to the group challenge it was obviously a little scary at first since we didn’t know what we were doing. But turns out, we were knocking our lecturers down with the help of the catapult we used just now. It was then when I finally understood why Mr Chua said that our data had to be less than 2m. Some of the targets were really far and would not be easy to reach. My group went first (which made it scary as more than half the class was watching). To our surprise, we managed to hit 3 out of 4 of the targets (2 of them being the harder ones) even though it was a pity that we couldn’t hit one but its still better than nothing 😁✌️.
Here are some videos of us in the group challenge:
(lower the volume while watching pls 🙏
This practical session was a really fun one which helped wrapped up my learning of DOE in an enjoyable way :D
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