Design of Experiment (DOE)

DOE is a methodology to obtain information about complex multivariable processes with the least trails possible. DOE is mainly used to improve product designs ie; Factors that have the greatest effect of the variable and seeing which is the most impacting

The formula used to calculate the number of experiments that need to be carried out:

N= Number of experiments

r= Number of replicates

l= Number of levels {There are 2 levels, high(+) and low(-).}

n=Number of factors

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:

Diameter of bowls to contain the corn, 10 cm and 15 cm
Microwaving time, 4 minutes and 6 minutes
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

Full Factorial Analysis

Link to excel file: Full Factorial Analysis

These data of + (HIGH) and - (LOW) were then used to plot a scatter which will allow us to see which factor has the most significance by looking at how steep each factor’s gradient is.

Looking at the graph, we can infer that when the diameter increases from 10cm to 15cm, the mass of the ‘bullets’ decreases from 1.58g to 1.43g. When the microwaving time increases from 4 min to 6 min, the mass of the ‘bullets’ decreases from 2.01g to 1.00g. When the power setting of the microwave increases from 75% to 100%, the mass of the ‘bullets’ decreases from 2.45g to 0.56g.

Hence, we can conclude that the most significant factor is the Power setting of the microwave (Factor C), followed by Microwave timing (Factor B) and then finally Diameter (Factor A).

Interaction effects

A against B

A against C

B against C

The gradients are different for both lines. Therefore, there is a significant interaction between A (Diameter) and B (Microwaving Time).

The gradients are different for both lines. Therefore, there is a significant interaction between A (Diameter) and C (Microwave Power).

The gradients are different for both lines. Therefore, there is a significant interaction between B (Microwaving Time) and C (Power Setting).

Conclusion

Looking at the effect of the individual factors, it can be seen that all the factors have a negative impact on the mass of the ‘bullets’ formed. To increase the popcorn yield, the mass of the ‘bullets’ have to decrease. Hence, to increase the yield, use a bowl with a larger diameter, have a longer microwaving time and a higher microwave power setting. (Basically Run 7)

Looking at the interaction effect between B & C, the mass of the ‘bullets’ will be lower when factor C is high. Factor B also decreases the mass of the ‘bullets’ when factor C is increased. Hence, I would choose factor B to be higher (longer microwaving time) and factor C to be higher (higher power setting) to increase the yield. However, when A is interacted with B or C, factor A has an increasing effect on the mass of the ‘bullets’ when factor B or C is high.

In conclusion, I would choose a bowl with a smaller diameter (factor A), a longer microwaving time (factor B) and a higher microwave power setting (factor C) so that the yield of my popcorn will increase. This is basically my run 7 with a Diameter of 10cm (-), 6 Minutes of microwaving time (+) and 100% Power setting of the microwave (+).

Fractional Factorial Data Analysis

For the fractional factorial data analysis, I will be choosing run order 1,2,3 and 6.The 4 runs allow each factor to be varied and each factor is investigated at both high and low levels the same number of times. Statistical Orthogonality is achieved.

Effects of individual factors

To determine the effects of the individual factors, I repeated the same steps as full factorial data analysis. First I determine the average mass of bullets formed for different levels. Then, I plotted a line graph with the level of factors as the x-axis and the mass of the bullets as the y-axis, with all 3 factors in one graph.

Link to excel file: Fractional Factorial Analysis

Similarly, the effects of each factor can be determined by their gradient. The gradient of the line for factor A is positive so factor A has a positive effect on the mass of bullets formedThe gradients of the lines for factor B and C are negative so both factor B and C have a negative effect on the mass of bullets formed.

When the diameter of bowls to contain the corn increases from 10 cm to 15 cm, the mass of bullets formed increases.When the microwaving time increases from 4 minutes to 6 minutes, the mass of bullets formed decreases.When the power setting of microwave increases from 75% to 100%, the mass of bullets formed decreases.

Factor C has the steepest gradient among the 3 factors so it causes the greatest change, hence has the largest effect on the dissolution time when the level has changed. Factor A has the gentlest gradient among the 3 factors so it causes the least change, hence has the least effect on the dissolution time when the level has changed. The gradient of factor B is between that of factor A and factor C. Going from most significant to least significant, Factor C (Power setting of microwave), B (Microwaving time) and A (Diameter of Bowls).

Conclusion

In conclusion, the data for fractional factorial analysis is slightly weird as when the diameter of the bowl increases, the mass of bullets increases which theoretically does not make sense as higher diameter gives a higher surface area so that more corn can become popcorn so the mass of the "bullets" should decrease instead. One thing i would change would be to increase the power setting on the microwave as it has the largest impact on the mass of ‘bullets’ formed.

Learning Reflection

For the design of the experiment tutorial and practical, I actually enjoyed and learned a lot. For the tutorial lesson, I learnt that in the industry, it is infeasible to run all treatments as the more factors we have the more runs we have to do. Thus, it is more realistic to restrict the number of runs a.k.a fractional factorial data analysis. However, although it is more effective and resource-effective, we risk missing information which can lead to inaccuracy.. A good fractional factorial data analysis consists of the equal amount of low and high level. After learning all these, I managed to finish my pre-experiment quickly. With the help of my lecturer, Dr Noel, I also learnt how to plot the graph on Excel.

During the experiment, I was surprised that when the length of the arm of the catapult increased, the distance travelled by the ball decreased, I thought it would have been the other way round where when the length of the arm of the catapult increases, the flying distance will increase due to greater a moment arm. During the group competition, we were so close to hitting 2 of the targets, 1 being 1 millimetre away and the other a centimetre away.😭😭😭😭😭😭😭😭😭😭😭😭

All in all, Design Of Experiment (DOE) practical was really interesting and fun. I learnt a lot. This is definitely top 3 of my favourite practicals.