DOE

Hello, on this page, I will describe

1.  the definition of Design of Experiments (DOE) and its importance 

2. Case study

3. Reflection on the DOE practical

1.  the definition of Design of Experiments (DOE) and its importance 

A statistics-based approach to designing experiments. 

A methodology to obtain knowledge of a complex, multi-variable process with the fewest trials possible. 

Optimization of the experimental process itself. 

The backbone of any product design as well as any process/ product improvement efforts.

 

To Determine the total number of experiments (N) that the process engineer needs to carry out, they use a formula:

N=rl^n

where N is the number of experiments to carry out

           r is the number of replicates

           l is the number of levels

           n is the number of factors

In Product design, it is infeasible to run all the experiments after determining N. Hence, it will be more realistic to shorten the number of runs by performing fractional factorial design. The advantages of using this rather than the full factorial design are:

it still provides sufficient information to determine the factor effect.

more efficient.

more resource effective.

However, you risk missing information.

2. Case study

ž  Document and describe how you performed the FULL FACTORIAL data analysis to solve the case study.

›      Determine the effect of single factors and their ranking.

Step 1: First I input the values of the bullet as per the run order

Step 2: Obtain the values of both + (HIGH) and - (LOW) values

Step 3: Select an appropriate line chart and input the + (HIGH) and - (LOW) values for each factor 

Effect of single factor

Factor A: When the diameter of the bowl increases from 10cm to 15cm, the mass of bullets decreases from 1.6g to 1.4265g.

Factor B: When the microwaving time increases from 4min to 6min, the mass of bullets decreases as well from 2.03g to 1.0475g.

Factor C: When the power setting increases from 75% to 100%, the mass of the bullets decreases as well from 2.5g to 0.575g.

The Determination of Ranking of the factors: 

C, B, A where C is the most significant factor and A the least significant. 

›      Determine the interaction effects.

Analysis between AxB

The gradients of both lines are different, where High B is (-ve) and Low B is (+ve). hence there is no interaction between A and B.

Analysis between AxC

The gradients of both lines are different, where High C is (+ve) and Low C is (-ve). hence there is an interaction between A and C but it is not that significant.

Analysis between BxC

The gradients of both lines are the same, where High C is (-ve) and Low C is (-ve). hence there is an interaction between B and C but it is not that significant.

›      Include all tables and graphs both as pictures and as excel file (hyperlink to google drive or OneDrive)

Blog Full Factorial.xlsx

›      Include the conclusion of the data analysis for full factorial data analysis

In conclusion,  Power (C) has the most significant effect on the yield of popcorn, followed by microwaving time (B), then the diameter of the bowl (A) to contain the popcorn.

 This is because, although all the factors have an effect on the mass of the bullets, the power setting of the microwave (C) is the most significant as there is a more significant or drastic decrease, than (B) and (A), in the mass of the bullets left behind after increasing power. 

Factor (A) which is the diameter of the bowl to hold the popcorn is the least significant as even though you increase the diameter, the decrease in the bullet's mass is not that significant, meaning your popcorn yield won't change a lot even if you increase the diameter.

Looking at the interactions, BxC has the most significant interaction, followed by AxC then AxB

So if you want to yield more popcorn, you should increase the power setting and microwaving time. 

ž  Document and describe how you performed the FRACTIONAL FACTORIAL data analysis by selecting 4 experiment from the full factorial data that are orthogonal to solve the case study.

›      Determine the effect of single factors and their ranking.

Effect of single factors

Factor A: When the diameter of the bowl increases from 10cm to 15cm, the mass of bullets left increases from 1.52g to 1.805g.

Factor B: When the microwaving time increases from 4min to 6min, the mass of bullets left decreases from 2.02g to 1.305g

Factor C: When the power setting increases from 75% to 100%, the mass of bullets left decreases from 2.79g to 0.53g.

The Rank of factors

C, B, A where C is the most significant factor in the yield of popcorn and A is the least significant.

›      Include all tables and graphs both as pictures and as excel file (hyperlink to google drive or OneDrive)

Blog Full Factorial.xlsx

›      Include the conclusion of the data analysis for fractional factorial data analysis.

In conclusion, the Power setting is the most significant in increasing the yield of popcorn followed by microwaving time and then the diameter of the bowl to hold the popcorn.

So if you want to yield more popcorn, you will have to increase the power setting.

Therefore, using Fractional Factorial will give us the same significant factor and it is a much more faster and efficient way to experiment to find how significant the factors are on the outcome (response variable). However, as it said, there is a risk of missing information such as the diameter of the bowl. For Full Factorial, when we increase the diameter, there is an increase in the yield of popcorn. but when we use fractional factorial, the yield of popcorn decrease when the diameter increase. 

3. Reflection on the DOE practical

During the DOE practical, I was able to apply what I had learned in the tutorial lessons to the practical. The practical requires us to investigate the effect of the individual factors and identify the factor that has the most significant effect on the distance the projectile has landed by using full and fractional factorial. 

After performing the full and fractional factorial, I found that using DOE is very useful in many ways such as saving time and being efficient, and also lowering cost as fewer experiments were done using DOE analysis and method. 

My group found that Factor (C) which is the stop angle has the most significant effect on the distance of the projectile, followed by arm length (A) then projectile weight (B) when using the full factorial. But when using fractional factorial, the ranking of the most to the least significant is (C), (B), (A). This is due to the loss of information when performing fractional factorial, but the most significant factor is still (C).

During the challenge, we were tasked to come up with the best combination of C, B, and A and hit the target at a specific distance. it was a tough challenge as we tried and experiment with lots of combinations and only 1 combination hit the target. Depending on the data we collected, the Stop angle has the most effect followed by Arm length the weight on the full factorial analysis. So if we want to hit a target at a closer distance, my group chose a higher stop angle and longer arm length. 

In conclusion, through the tutorial and practical lessons, I find DOE to be very helpful and hope to implement it in my capstone project and internship in year 3.