Design of Experiments
Helloo welcome to my blog, today we will be working on a case study on DOE [Design of experiment]
What is DOE?
DOE is:
- A statistics-based approach to designing experiments
- A methodology to obtain knowledge of a complex, multi-variable process with the fewest trials possible
- An optimisation of the experimental process itself
- The backbone of any product design as well as any process/product improvement efforts
This then boils down to the fundamentals of DOE, They are:
- Response variable (Dependent variable)
- Factor (Independent variable)
- Level (High/Low values for a specific factor that we want to measure)
- Treatment (specific combination of factor levels)
How to determine the number of runs needed for an experiment?
To determine the number of runs for an experiment, we just have to use a simple formula of
Total number of experiments(N) = r2^n
r = number of replicates
n = number of factors
CASE STUDY
To allow a better understanding on what exactly is DOE, i will be walking you through on how to apply DOE in this case study.
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” (un-popped 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
experiments and the measured variable is the amount of “bullets” formed in
grams and data collected are shown below:
Factor A= diameter
Factor B= microwaving time
Factor C= power
To prove that DOE can be applied, i will be using both Full factorial and Fractional factorial methods in this case study.
Full Factorial method
First we must determine the number of experiments needed,number of replicates = 1
number of factors = 3
Number of experiments needed = (1)(2)^3 = 8
1. By filling in the excel template with the values we have
3. I then plot each factor from LOW to HIGH on the same graph
Analysis
From the values in step 2, we can conclude that
- When diameter increases from 10cm to 15cm, the mass of bullet decreases from 1.47g to 1.3225g
- When microwaving time increases from 4 minutes to 6 minutes, the mass of bullet decreases from 1.96g to 0.8375g
- when power increases from 70% to 100%, the mass of bullet decreases from 2.29g to 0.505g
How to read step 3 graph
The graph shows us the difference between each factor against the mass of bullets, AKA gradient = significance. Thus, a steeper gradient would mean the factor plays a big part in affecting the mass of bullet.
From the graph we can clearly see the rankings in which factor is the most significant. With #1 being the most significant to #3 being the least significant
- Power (steepest gradient)
- Microwaving time
- Diameter (most gentle gradient)
Interaction effects
Two factors are said to interact with one another if the effect of one factor on the response variable is different at different levels of the other factor. Thus we will be testing different factor interactions
Factor D: Diameter x microwaving time
The gradients of both lines are different with one being +ve and the other being -ve, However there is no intersection. Thus there is no interaction.
Factor E: Diameter x Power
Factor F: Microwaving time x Power
The gradients of both lines are the same (-ve), However there is no intersection. Thus there is no interaction.
Fractional factorial method
Fractional factorial method is a more efficient and resource-effective alternative compared to full factorial method, however the downside is that there is a risk of missing information
For fractional factorial method, i will be using runs 2,3,5 and 8
1. Filling in excel with the values we are using
3. I then plot each factor from LOW to HIGH on the same graph
Analysis
From the values in step 2, we can conclude that
- When diameter increases from 10cm to 15cm, the mass of bullet increases from 1.38g to 1.665g
- When microwaving time increases from 4 minutes to 6 minutes, the mass of bullet decreases from 1.88g to 1.165g
- when power increases from 70% to 100%, the mass of bullet decreases from 2.51g to 0.53g
step 3 graph
From the graph we can clearly see the rankings in which factor is the most significant. With #1 being the most significant to #3 being the least significant
- Power (steepest gradient)
- Microwaving time
- Diameter (most gentle gradient)
Interaction effects
Factor D: Diameter x microwaving time
The gradients of both lines are different with one being +ve and the other being -ve, there is also an intersection. Thus there is a significant interaction between Diameter and microwaving time
The gradients of both lines are different with one being +ve and the other being -ve, However there is no intersection. Thus there is no interaction.
Factor F: Microwaving time x Power
The gradients of both lines are the same (-ve), However there is no intersection. Thus there is no interaction.
LINK TO EXCEL
Reflection
After doing DOE for about 2 weeks, i now feel confident in applying DOE methods into experiments and i look forward to using this method of planning in the future, especially for my final year project (FYP).
When i first learnt about how to use DOE, it really changed my perspective towards conducting experiments because i have always disliked experimental analysis as it always makes me think a lot and we have to run the experiment at the maximum amount of times. For example, in a previous module Lab & Process skills (LPS), we had to use different parameters to test the effects they have on the extraction of coffee solubles from coffee beans. Because we have not learnt DOE officially, we had to conduct and analyse the experiment data manually which took a lot of time. However, after learning about DOE, it made collecting and analyzing data so much more tolerable. This is because we can calculate exactly how many runs we need for the experiment and know which experiments to run if we are short on resources or time.
However, learning how to use DOE was also not that easy for me because it took me a few days to actually understand the concept of it. when i first saw the many graphs that i needed to plot, i thought it was just going to be another tedious task. But after going back and forth from the slides and my answers, i realised that the graphs were not that hard to read and it easily tells me the relationships between each factor just by taking a quick look at the graphs.
At the end of this DOE experience, there is one thing that i am curious about and that is how many experiment runs can an experiment go to? This is because for a small experiment like the one we did for our practical session, we had 3 factors to test out and already had to conduct 64 experiment runs. What about real life DOE's? is it economically sustainable if there was a need to conduct more than a thousand runs? what exactly are the limits that you can apply DOE to? and is there a better method?
these are the questions that go through my mind and although i do not have the answers right now, i hope to be able to meet a challenge such as 'too many runs' and be able to learn from it.
Practical:
This practical in my opinion was the most enjoyable practical session out of all the other practical sessions. Firstly it was because it was our first time operating a catapult, although mini. but i still enjoyed it because we get to 'play' with a new toy. And secondly, we got to put what we learnt into the last challenge of the practical session.
At the last part of the practical session, we were tasked to hit targets at different distances with the allowance of changing the 3 factors. (arm length, stop angle, Density of ball).
The targets were our lecturers which made it more interesting because there were some friendly 'beef' going on which made us more determined to hit the targets. One of the targets was Mr Ting who teaches us POS. 
when we were given time to prepare our catapult settings, we used the data collected from the first part of the practical to see which distances we could reach, saving us time on testing. And at the moment of writing this reflection, i realised that i applied 'recall what you have done and learnt' subconsciously which was taught to us constantly in past POS & LPS modules. This is because our experiment went very smoothly and i strongly believe the reason for that was because we had done our pre-experiment properly and applied it to the practical session. Therefore i hope to be able to continue to apply this skill in not just future practical sessions, but onto other modules as well so that i can have a more meaningful learning experience.
Here is also a bonus clip of us hitting Dr Noel (the target) 👀
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