Design of Experiment

Welcome back to another entry of my Blog! Today's blog entry will be about the design of experiment.

Design of experiment or DOE for short is a statistics-based approach to designing experiments, it is a methodology to obtain knowledge of a complex, multi-variable process with the fewest trials possible.

Although DOE can be quite complicated, here are the fundamentals of DOE.

• Response variable (Dependant variable) - Outcome that is measured for a given experiment

• Factor (Independent Variable) - A variable that is varied to see its effect on the response variable

• Level - A specific condition of the factor for which we want to measure

• Treatment - A specific combination of factor levels

Formulae for the number of experiments:

N = No. of Experiments

r = No. of Replicates

l = No. of Levels

n = No. of Factors

Full and fractional factorial design

There are 2 types of factorial designs, fractional factorial, and full factorial. Fractional factorial design is more efficient and resource-efficient but risks missing out on information while Full factorial is more tedious and extensive but ensures accountability of all information.

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

Here is the link to the respective Case Study Excel Sheet: CPDD DOE Case Study - Ethan.xlsx

No. of experiments = 8(2)^3 = 64

Here are the tabulated results for the Full Factorial design:

Here are the graphical depictions of the relationship between factors A, B and C and Mass of bullets:

Relationship between factors and distance traveled: Factor A: When the diameter of the bowl increases from 10cm to 15cm, the mass of the bullets decrease from 1.75 to 1.5975g Factor B: When microwaving time increases from 4 minutes to 6 minutes, the mass of bullet decreases from 2.09g to 1.25g Factor C: When the power of the microwave increases from 75% to 100%, the mass of bullet decreases from 2.70g to 0.6425g

From the data above, factor C (Microwave Power) has the steepest gradient and is the most significant factor. Followed by factor B (Microwaving time) and factor A (Diameter of Bowl) which has the gentlest gradient and is the least significant factor.

Interaction of factors:

Interaction effect of A x B

The gradients of line +B and line -B are different as one increases while the other decreases. However, they are not intersecting so there is no significant interaction effect between A and B.

Interaction effect of A x C

The gradients of line +C and line -C are the same and do not intersect. Thus, there is no significant interaction effect between A and C.

Interaction effect of B x C

The gradients of line +C and line -C are the same and do not intersect. Thus, there is no significant interaction effect between B and C.

In conclusion for Full factorial design, there is no interaction amongst any of the factors. Next, we have the results of the fractional factorial design. :)

Here are the tabulated results for the Fractional Factorial design:

Here are the graphical depictions of the relationship between mass of bullet and factros A, B and C:

Relationship between factors and distance traveled:

Factor A: When the diameter of the bowl increases from 10cm to 15cm, the mass of the bullets decrease from 2.05g to 1.94g Factor B: When microwaving time increases from 4 minutes to 6 minutes, the mass of bullet decreases from 2.15g to 1.835g Factor C: When the power of the microwave increases from 75% to 100%, the mass of bullet decreases from 3.46g to 0.53g

From the data above, factor C (Microwave Power) has the steepest gradient and is the most significant factor. Followed by factor B (Microwaving time) and finally factor A (Diameter of bowl) which has the gentlest gradient and is the least significant factor.

Interaction of factors:

Interaction effect of A x B

The gradients of line +B and line -B are the different (One is positive while the other is negative). Additionally, both lines are intersecting. Thus, there is significant interaction effects between A and B.

Interaction effect of A x C

The gradients of line +C and line -C are different as one increases while the other decreases. However, they are not intersecting so there is no significant interaction effect between A and C.

Interaction effect of B x C

The gradients of line +C and line -C are different as one increases while the other decreases. However, they are not intersecting so there is no significant interaction effect between B and C.

In conclusion for Fractional factorial design, there is no interaction amongst any of the factors except A x B.

Reflection:

This practical was the most fun and productive practicals I have taken part in so far. I was able to implement my newfound knowledge of design of experiment factorial designs in the experiment. This practical helped us utilise our data analysis skills and had us practice our knowledge on factorial design in a controlled environment. The pre-practical task aided us in practicing the factorial skills before the practical, helping us be more efficient during the practical and data tabulation.

Throughout the process of data analysis, we face a small setback where one of the catapults given to our group was significantly less accurate than the other despite having similar settings. To combat this issue, we decided to just use 1 catapult. We used masking tape to mark positions on the floor that were used to place the sand tray, this helped us remember which spot was used for which combination of factors. We used a small ruler to smoothen out the sand to make observations of the projectile landing spot easier while using a long ruler to measure the distance of projectile traveled.

Luckily for us, we did not have any major hiccups and the runs went quite smoothly. We also managed to work while and delegate work with our temporary groupmate Tristan. This was a a very efficient practical session as we managed to complete the practical with successful end results while also getting 2nd in the final 'competition'.

Here is a video of a successful run during the practical: