Blog 4 (Design Of Experiment)

Hello everyone! Welcome back to my blog. This time around, I am going to be documenting my experience on a CPDD practical that required us to use Design Of Experiment (DOE). It is a powerful technique used for discovering a set of factors which are most important to the process and then determine at what levels these factors must be kept to optimize the process performance. In the second part of the blog, I will attempt to solve a case study using the DOE technique.

PRACTICAL (DOE)

In this practical, we are required to investigate to effect of individual factors using DOE on a catapult. Afterwards, we needed to identify the factor that has the most significant effect on the response variable. Within our group, we are split up into two groups, one doing the Full Factorial Method, while the other one doing the Fractional Factorial Method.

Factors to be investigated are shown below:

Factors	LOW (-)	HIGH (+)
A. Arm Length	28 cm	33 cm
B. Projectile Weight	0.86 g	2 g
C. Stop Angle	55°	90°

To determine the effect of each factors, we measure the flying distance of the projectile. In total, there are 8 unique runs. In each unique run, there are 8 runs. Then, the average value of each unique run is calculated using a excel sheet.

Data Table for FULL FACTORIAL METHOD:

Data Table for FRACTIONAL FACTORIAL METHOD:

When comparing the two data tables, the values of the same unique run are different. The differences in the runs are around 10 cm even though the factor levels used are identical. Since we used two catapult to conduct the two methods, the strength of the elastic band on the catapults may differ, resulting in different flying distance of the projectile.

Data analysis: FULL FACTORIAL METHOD

When A (Arm Length) increases from 28 to 33 cm, the average distance travelled by the projectile decreases from 152.55 to 132.29 cm.

When B (Projectile Weight) increases from 0.86 to 2 g, the average distance travelled by the projectile decreases from 148.60 to 136.25 cm.

When C (Stop Angle) increases from 55° to 90°, the average distance travelled by the projectile decreases from 183.96 to 100.89 cm.

Factor C (Stop Angle) is the most significant factor that affect the flying distance of the projectile.

Data analysis: FRACTIONAL FACTORIAL METHOD

When A (Arm Length) increases from 28 to 33 cm, the average distance travelled by the projectile decreases from 143.26 to 127.50 cm.

When B (Projectile Weight) increases from 0.86 to 2 g, the average distance travelled by the projectile increases from 130.60 to 140.16 cm.

When C (Stop Angle) increases from 55° to 90°, the average distance travelled by the projectile decreases from 168.53 to 102.23 cm.

Factor C (Stop Angle) is the most significant factor that affect the flying distance of the projectile.

Group Challenge:

After we were done with investigating the effect of each factors and finding out the most significant factor, we needed use our collated data to try to overcome this challenge. The objective of this challenge is to knock down 4 targets positioned at different spots using the catapult. The catapult is to be positioned behind a demarcated line when the projectile is launched. Each group had 3 trial attempts for whole challenge and 2 actual attempts at each target. The video below will show the setup of the challenge.

My group only ended up hitting two targets. Despite this absolute failure, we were ranked second alongside another group. This meant we secured 8 marks for this group challenge.

Learning Reflection:

When we were first introduced to DOE in the tutorial lesson, it did not felt foreign to me. It was a technique that we have utilised since secondary school days during science experiments. However, we did not actually learn how DOE was carried out and why was it so critical in our experiments. In the tutorial lesson, we were able to uncover all that.

In our first example, we were given 3 factors with their respective high and low levels. We needed to find out the total number of experiments that is needed to be carried out. I did not know how to start. Afterwards, we were given the solution which uses an equation to solve it. It was very intriguing as I did not know such equation exist.

As everyone knows, the more factors you have, the more runs you have to conduct. Thus, it is very important to restrict the number factors and work out a value that would deem feasible to run all the treatments. Another option to decrease the number of runs is to use fractional factorial method. However, how does one select the runs to maintain good statistical information? We had to learn how to fractionalise by visualising a 3D box and select a design that would enable all factors to have the same number of high and low levels. Thus, this method would be able to allow fewer than all possible treatments to be chosen and still provide sufficient data to determine the effect of the factors. I felt that although fractional factorial method is very efficient and resource-effective, there are still possibilities that you will miss information which would affect the data. This would be why full factorial method and fractional factorial method would not be able to get the same data. However, when doing data analysis, their differences are minimal.

Moving onto interaction effect among the 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. Thus, it would be critical to find out the interaction between the factors to better optimise the DOE such as tuning a process to achieve consistent results.

Although understanding DOE was manageable, I would find executing it would be a bit challenging. We were given a pre-made response table for our pre-practical activity. We were required to fractionalise the runs given by an example and produce a graph using excel that showcases the effect of each factor. Plotting the graph proved to be tricky as I am not well-versed in microsoft excel. After getting assistance from my lecturer, I was able to successfully produce the graphs for full and fractional factorial.

Moving on to the practical, I felt that doing 96 runs in total was too excessive even though we were split into groups. It gets tiring when it gets repetitive. However, only through repetition we can get accurate and reliable data to do analysis and find out the most influential factor. During the group challenge, it really needed strategic planning and thinking. Due to the different distance of the targets, we needed to analyse our data and come out with the best combination of the factors. In addition, given 3 trial attempts, we decided to use them on the more difficult targets so that it will give us more room to adjust our catapult. In my opinion, this activity was enjoyable.

All in all, after experiencing the tutorial and the practical, it allowed me to understand DOE better. I realised its importance in product design as we are constantly required to test our prototype and find the best outcome through data analysis. Although DOE is a great technique, it also comes with weaknesses such as it is time-consuming. Regardless of fractional factorial method to halve the number of runs required, restricting the number of factors in our product would ultimately restrict the true potential of the product. Hopefully, I will be able to use DOE to create a successful product with my group in the near future.

CASE STUDY

The main objective of this case study is to find the most influential factor that causes the loss of popcorn yield. Three factors with their respective levels are identified:

Factors	LOW (-)	HIGH (+)
A - Diameter	10 cm	15 cm
B - Microwaving time	4 min	6 min
C - Power	75%	100%

8 runs were conducted with 100 grams of corn in every experiment and the measured variable is the amount of “bullets” formed in grams and data collected are shown below:

Run Order	A	B	C	Bullets (grams)
1	+	-	-	3.02
2	-	+	-	2.02
3	-	-	+	0.74
4	+	+	-	1.02
5	+	-	+	0.95
6	+	+	+	0.32
7	-	+	+	0.02
8	-	-	-	3.12

Effects of Single Factors

Full Factorial Method

The HIGH and LOW levels of each factor are totaled and averaged out separately. This is shown in the diagram below.

The average of the HIGH and LOW values of each factor are used to plot a graph. This graph allows us to visualise the significance of each factor by looking at the steepness of the gradients. The graph is shown below.

When A (Diameter) increases from 10 to 15 cm, the average mass of bullets decreases from 1.475 to 1.3275 g.

When B (Microwaving Time) increases from 4 to 6 min, the average mass of bullets decreases from 1.9575 to 0.845 g.

When C (Power Setting) increases from 75 to 100%, the average mass of bullets decreases from 2.295 to 0.5075 g.

Factor C (Power Setting) is the most significance factor, followed by Factor B (Microwaving Time) and Factor A (Diameter). This can be deduced from the steepness of the gradients. Factor C (Power Setting) has the steepest gradient while Factor A (Diameter) has the least steep graph.

Interaction Effects

The objective is to study the interaction effects among the factors. A pair of factors are selected and analysed by checking if the effect of one factor on the response variable is different at different levels of the other factor. E.g. the effect of diameter at high microwaving time is different as compared to that at low microwaving time. A graph is plotted and the gradients will determine the significance of the interaction effects.

A x B

The gradient of both lines are different (One is positive while the other one is negative). Therefore, there is a significant interaction between A (Diameter) and B (Microwaving Time).

A x C

The gradient of both lines are different (One is positive while the other one is negative). Therefore, there is a significant interaction between A (Diameter) and C (Power Setting).

B x C

The gradient of both lines are different. Both of them are negative, however, one is significantly steeper than the other. Therefore, is a significant interaction between B (Microwaving Time) and C (Power Setting).

Full Factorial Method: Conclusion

Factor C (Power Setting) is most significant factor, followed by Factor B (Microwaving time) and Factor A (Diameter). Furthermore, for interaction effects of the factors, A x B can be seen as to have the least significant interaction effect among the three interactions. Thus, it supports the fact that Factor A is least significant factor. Assuming the same amount of corn is used in every run, the larger the diameter of the bowl would mean that there will be a greater surface area on the top surface. However, I would think that the surface area exposed is inconsequential to the corn popping. As it is in a microwave where the corn is exposed to heat from everywhere.

Case Study - Full Factorial Method.xlsx

Fractional Factorial Method

Run 1, 2, 3 and 6 are chosen to be analysed since they would provide good statistical properties. Similar to Full Factorial Method, a graph will be used for data analysis.

When A (Diameter) increases from 10 to 15 cm, the average mass of bullets increases from 1.38 to 1.67 g.

When B (Microwaving Time) increases from 4 to 6 min, the average mass of bullets decreases from 1.88 to 1.17 g.

When C (Power Setting) increases from 75 to 100%, the average mass of bullets decreases from 2.52 to 0.53 g.

Factor C (Power Setting) is the most significance factor, followed by Factor B (Microwaving Time) and Factor A (Diameter). This can be deduced from the steepness of the gradients. Factor C (Power Setting) has the steepest gradient while Factor A (Diameter) has the least steep graph.

Fractional Factorial Method: Conclusion

From the data analysis, we still can deduce that Factor C is the most significant factor. This would proof that using this method would provide sufficient data to obtain the same analysis. However, there is a change in the gradient of factor A. In Full Factorial, the gradient of A is decreasing while in Fractional Factorial is increasing. This would also proof that this method is not fully reliable since we still risk missing some vital information.

Case Study - Fractional Factorial Method.xlsx