LEGO Blocks - Design Of Experiments using Minitab
Final Version of our Lego Car
The problem that we are solving is identifying the set of factors that truly contribute to the distance that our Lego car travels.
The experiment was conducted in one of the study rooms at W.P. Carey where we setup the ramp as shown in the picture below, the ramp was perfectly positioned at 30 degrees(+/- 1) and set strong against the wall so that there was minimum vibration and that we could reduce as much noise factors as possible. The ramp was 31 inches long and 18inches high. We are a team of 4, therefore, we divided the experiment so that the operator changing the factors of the car was fixed, the operator loading the car in the ramp was fixed, one operator was taking the recordings on laptop and the last operator was responsible for accurately measuring the distance. The measuring tape was fixed on the floor with a tape to ensure consistency. All the measurements were taken on a single sitting to ensure that we reduced noise factors that could arise from resetting of the ramp as well as changing the operator and resetting the measuring tape and layout of experiments.
Just a side note on How to create Factorial Design in Minitab (Design of Experiment Study in Minitab)
Combination type 1: Long wheel base, with Spoiler, High Weight, short axle base(front), big wheel size(rear) and a small windshield
Combination type 2: Short Wheel base, without spoiler, low weight, short axle base(front), big wheel size(rear) and a small windshield.
Noise can be a major problem in result identification:
To block the noise in the experiment we ensured the following:
1. Fix the ramp to the wall and the floor – ensure it is sturdy
2. Fix the measuring tape to the floor
3. Conduct the entire experiment in one sitting in the same room in the same ramp position
4. One operator loads the car on the ramp
5. One operator responsible for changing combinations of the factors for DOE study
6. One operator records measurement on computer
7. One operator ensures accuracy in the measurement
8. The ramp angles were recalibrated after every 10 trials(128 + 16 total)
9. Measurement of each combination was taken twice, in a randomized order generated by minitab, to ensure accuracy in the measurement and to reduce noise factors
We conduct the experiment in two rounds:
a. Round 1: Experiment with 6 factors
b. Round 2: Experiment with 3 factors
Round 1: Experiment with 6 factors:
As mentioned above the first round of the experiment consisted of 6 factors analyzed. We have 6 factors and 2 replicates, therefore, totalling the number of times the experiment had to be run to 128. After running the experiment for 128 times and collecting the response variable measurement we identified the order of significance of the factors, to narrow down to smaller number of significant factors we repeat the above experiment, but with only the most significant 3 factors from this experiment. The Data and Graphs from this experiment will be discussed in detail in the following sections.
Round 2: Experiment with 3 factors:
The round 2 of the experiment consisted of 3 most significant factors which were studied in 2 replicates, therefore we had to run the experiment 23 * 2 = 16 times. This was like the previous experiment with 16 randomized combinations of the 3 most significant factors while keeping the other factors constant as per the previous experiment.
Results and Interpretations:
The results from the DOE study can be studied in terms of Data as well as interpreted by Graphs, we will analyze them both as follows for both Round 1 of the experiment and Round 2 of the experiment.
The table above shows the significant factors from the Round 1 of the experiment, based on this and combining it with the pareto chart, which we will explain in the next section of this report, we narrow down to 3 factors for our round 2 experiment.
The factors chosen for round 2 of the experiment are:
The regression equation from the round 2 of the experiment is as follows:
We can see from the above regression equation that weight has the highest impact on our response variable, followed by a two way interaction of weight and wheel size(rear)
Now we conduct a graphical analysis of the two experiments which includes pareto analysis, residual analysis, normal plot analysis, main effects analysis and the interaction effect analysis.
Graphical analysis of 1st Experiment(6 factors):
The normal plot of the standardized effects shows us the most significant factors in Red square blocks, the farther they are from the line the more significant they are.
The interaction plot when thoroughly studied shows us that the two way interaction of axle base(front) and weight of the car, gives us the highest distance(response variable), that is the combination of high weight and short axle base(front). Also, from the Squares that are in red we can see that the basis for our decision to choose the levels for the factors that remain constant in the 2nd round of DOE study.
The normal plot of the standardised effect shows the same conclusion that factor A, which is weight, is the most significant factor in our DOE study and has the most significant impact on the distance our lego car travels
The normal probability plot seems to violate the assumption that residuals are normally distributed, and shows outliers. Therefore we explore the other residual plots to check for problems with the model. The possible cause of this could be the outliers as seen from the histogram, which otherwise is normally distributed. The versus fit plot is evenly distributed verifying that the residuals are randomly distributed and have constant variance, and the versus order is randomly distributed above and below the centerline which verifies our assumption that the residuals are independent from one another.
The main effects plot for the 3 factors shows us that all the factors seem to positively affect the distance(y) when they increase from low to high. The factor that is most significantly affecting the distance is the weight when at a high level.
On analyzing the interaction plot above we can see that the combination of Big rear wheel size and high weight gives us the best two way combination and the highest effect on the response variable (y), which is the distance.
Additional Data (Appendix): ANOVA TABLE (EXPERIMENT ROUND 1)
Appendix: ANOVA TABLE FOR EXPERIMENT ROUND 2(3-Factor)
A special thanks to my team mates for their contribution to this