For Our Six Sigma Project, We Had To Fly Paper Airplanes Ten

For Our Six Sigma Project We Had To Fly Paper Airplanes Ten Times And

For our Six Sigma project, we had to fly paper airplanes ten times and collect the data in seconds: 1.50, 1.75, 1.25, 2.00, 2.50, 2.25, 2.25, 2.00, 2.75, 2.00. The following questions are part of the homework: 1. 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. 2. 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. Henry performed a two-tailed test for an experiment in which N=24. He could not find his table of t critical values, but he remembered the tcv at df=13. He decided to compare his tobt with this tcv. Is he more likely to make a Type I or a Type II error in this situation?

Paper For Above instruction

The analysis of a Six Sigma process involving paper airplane flights provides a practical example for understanding process capability, revenue projection, and hypothesis testing errors. This paper will systematically address each aspect, beginning with calculation of process capability, proceeding to revenue projection based on hypothetical flight tariffs, and finally explaining the implications of Henry's approach in hypothesis testing terms.

Process Capability Analysis

Process capability quantifies how well a stable process meets specified performance standards. For the paper airplane flights, the collected data are: 1.50, 1.75, 1.25, 2.00, 2.50, 2.25, 2.25, 2.00, 2.75, 2.00 seconds. The first step involves calculating the mean (average) flight time:

Mean (μ): (1.50 + 1.75 + 1.25 + 2.00 + 2.50 + 2.25 + 2.25 + 2.00 + 2.75 + 2.00) / 10 = 20.5 / 10 = 2.05 seconds.

The standard deviation (σ) is calculated using the formula:

σ = sqrt( Σ (xi - μ)^2 / (n - 1) ). Conducting this calculation yields a sample standard deviation of approximately 0.58 seconds, indicating the variability in flight times.

Next, process capability indices such as Cp and Cpk are computed assuming target or specification limits. Suppose the upper limit is based on the maximum observed flight time (2.75 seconds), and the lower limit is the minimum (1.25 seconds). With the mean and standard deviation, the Cp and Cpk values can be derived, which quantify how the process performs relative to these limits.

The process capability index Cp is calculated as:

Cp = (USL - LSL) / (6 × σ) = (2.75 - 1.25) / (6 × 0.58) ≈ 1.5 / 3.48 ≈ 0.86.

Since Cp less than 1 indicates a process not capable of consistently producing within limits, further analysis through Cpk considers the process mean's position relative to the limits. In this case, the process appears slightly centered but with room for improvement, highlighting the need for process stabilization.

Revenue Projection Based on Flight Data

Assuming a fictional fare rate of $0.10 per second per flight, the average flight time of 2.05 seconds translates to a revenue of $0.205 per flight. Projecting this over 500 flights annually results in:

$0.205 × 500 = $102.50 per year.

If a target flight time is set at 2.50 seconds, the revenue per flight increases to $0.25, accumulating to:

$0.25 × 500 = $125 per year, which is $22.50 more than the current projection. This comparison highlights the revenue opportunity that could be achieved by extending flight times closer to the target, assuming demand remains constant and customer preferences align with longer flights.

This analysis illustrates how process improvements or strategic targets could enhance organizational revenue, even in simplified scenarios involving paper airplanes.

Implications of Henry's Hypothesis Test Approach

In the context of hypothesis testing, Henry's scenario involves a two-tailed test with a sample size of N=24. He looks up the t-critical value (tcv) for degrees of freedom (df=13), which is lower than his actual degrees of freedom but uses it as a reference. He compares his obtained t-statistic (t_observed) with this tcv.

When the critical value is based on a lower degree of freedom than the actual, Henry's comparison effectively results in a more lenient critical threshold because tcv decreases as df decreases for a fixed significance level. As a result, he is more inclined to reject the null hypothesis than if he had used the correct critical value corresponding to N-1 degrees of freedom. This underestimation of the critical value increases the likelihood of a Type I error—the incorrect rejection of a true null hypothesis.

Therefore, in his situation, Henry is more likely to commit a Type I error due to comparing his test statistic against a less conservative critical value derived from a lower degrees of freedom approximation, which inflates the risk of false positives in his hypothesis testing framework.

Conclusion

This exercise demonstrates the importance of accurate statistical calculations and proper hypothesis testing in process analysis. Understanding process capability provides insight into current process performance, while revenue projections based on process improvements show potential financial benefits. Lastly, recognizing the implications of errors in hypothesis testing underlines the importance of correct critical value selection to avoid misleading conclusions. These analytical skills are essential for effective management and continuous improvement in any operational context, including seemingly simple projects like paper airplane flights.

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