Six Sigma Project Assignment Parts 1 and 2

Define:
1.   Identify and define a particular paper airplane design.
2.   The key metric is flight time (how long the plane flies before it hits the floor). Fly the plane ten times and measure how long it takes for each of the ten flights. Use a stop watch and collect data in terms of seconds. Do not round the data to even seconds.
3.   Using the collected data, establish the current process capability. For example, what is the average flight time? What is the standard deviation? You can do this in Minitab with Stat>Basic Stats>Descriptive Statistics.
4.   Assuming a fictional fare that you can charge per flight second, calculate your current revenues projection assuming 500 flights per year. Use some creativity. Compare this to a target flight time (longer than you demonstrated in your capability study). Identify how much revenue you are currently missing because you are not currently achieving the target flight time. Do not try to change your design at this time.
Measure:
1.   Identify design or other such factors that might be preventing longer flight times. You might use such tools as a cause-and-effect diagram. Choose a couple factors that you might want to experiment with in order to increase flight times. Don’t experiment just yet.
2.   Evaluate your current ability to measure flight time. You might do this by using multiple people measure the same flights and compare results. How well do multiple people reproduce the same measurement? Who is most correct?
Feel free to collaborate in the study hall for this assignment, but you must collect your own data and run your own Minitab analysis. Feel free to discuss factors that impact flight time. Feel free to discuss how to best evaluate measurement ability.
Part two of this assignment will come next week.

Part 2
Analyze:
1. Choose one continuously variable factor to experiment with. For example, you might choose “length of airplane” as a factor to experiment with. I will use this example factor in the remaining description, but you simply substitute the experimental factor that you choose. Collect data for flight times versus airplane length. Create a scatter plot (X-Y plot) to visually detect if there is a relationship between length of plan and time of flight. In Minitab you can create this scatter plot as follows: Graph>scatter plot>simple>ok> click on time of flight as the Y variable and length of plane as the X variable > click on the column with your time of flight data as the Y variable and the column with the length of plan as the X variable.

Click ok and you will get a plot that looks like this:

You can visually assess if there is a relationship. In this example, it appears that shorter planes fly longer.
2. You can fit a regression line by choosing the option “with regression” instead of “simple”.

In order to determine if the apparent regression relationship is statistically significant, you need to run a regression analysis as follows: Stat>Regression>Fitted line plot> click on the column with your time of flight data as the Response (Y) variable and the column with the length of plan as the Predictor (X) variable. You will get the scatter plot with the regression line as follows:

You also need to go to the session window to check the p-value:

In this example the p-value is 0.007. For regression analysis, the p-value determines the significance of the regression relationship. If the p-value is 0.05 or less, then you conclude that the relationship is significant and is not simply a coincidence. If the p-value is greater than 0.05, then you conclude that whatever relationship that may seem apparent in the scatter plot might well be simply a coincidence and that the relationship is not statistically significant.
In Excel, you can create a scatter chart by highlighting the two columns of data and then clicking insert>scatter chart. If you then click on the data dots, you can right click and add trendline, which will be the regression line (usually linear).

To get the regression analysis, you click data>data analysis>regression> highlighting the Time flight data for Y and the length of plane data for X. The results will be as follows:

The p-value is the Significance F value.
Improve:
Based your Analyze phase work, choose and implement an improvement to your airplane. Fly the improved plane ten times. Compare the improved plane results with the baseline results determined in the Define phase. Is the improved phase average flight time longer than the baseline average flight time? This can be statistically assessed with a two sample t-test. In Minitab: Stat>basic stat> 2-sample t>click samples in different columns>put baseline data in first cell and new data in second cell>click ok. You get something like the following in the session window:
Two-Sample T-Test and CI: time of flight, new

Two-sample T for time of flight vs new

N   Mean StDev SE Mean
time of flight 5   7.30   1.72     0.77
new             5 10.20   1.30     0.58

Difference = mu (time of flight) – mu (new)
Estimate for difference: -2.900
95% CI for difference: (-5.180, -0.620)
T-Test of difference = 0 (vs not =): T-Value = -3.01 P-Value = 0.020 DF = 7

The p-value determines the significance of the difference in mean values. If the p-value is 0.05 or less, then you conclude that the difference in means is significant and is not simply a coincidence. If the p-value is greater than 0.05, then you conclude the observed difference in means may simply be a coincidence and that there may be no real long term difference.
In Excel: Data>data analysis>t-test: two sample assuming unequal variances>ok. Highlight the baseline and new data respectively and entering the number 0 into the cell designated “hypothesized mean difference”, click ok. You get the following where the p-value is for two-tail:

Control:
Using your fictional fare, determine how much increased revenue can be associated with your improved plane.
Six Sigma is deployed using the Define-Measure-Analyze-Improve-Control (DMAIC) project management framework. Identify an actual Six Sigma project and write one paragraph covering each of the DMAIC phases.

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