Introduction
Applying statistics is as much science as art, especially when we are forced to make trade-offs between qualitative and
quantitative aspects of analysis.
In this lab you will explore some concepts that engineers grapple with in the field of data analysis.
Objective
1. Construct confidence intervals suitable for design engineers to use in developing a medical device.
2. Consider the trade-off between certainty (a higher confidence) and the cost of data collection.
3. Develop an appreciation for the nuances of statistical application.
Notes
Tips for full scoring: SHOW ALL WORK, USE CORRECT NOTATION, COMPLETE ALL CALCULATIONS!
Lab Assignment
Part A. Variability in Flying Paper Planes
This part of assignment guides you through the steps of data collection and analysis. All team members must participate in
the data collection process (1)-(4) to qualify for full score. Note the collected data will also be used for your individual final
report at the end of the semester: the quality of your data impacts your final report. In general, a good quality data refers to
the one with minimal ‘unexpected' variance. In experimentation, people unwillingly and unknowingly invite multiple sources of variability that add to a variance. Having unexpected variance in your data twists your conclusions, and lowers the power of your statistical model. You will understand how this happens in Lecture 9 Regression Model. Thus, the primary goal of data collection is to minimize variance by identifying and eliminating unexpected sources of variability. In this regard, the current task is to measure air-time of three paper planes, repeated at least 30 times for each plane. The quality
of your work is evaluated by successfully minimizing variance, and by reasonable efforts to reduce it.
First, select three designs of paper planes from Appendix I and make them. You can find steps to make each design in the webpage address below
Appendix I.
(1) Before measurement, brainstorm with your team members to identify a list of potential sources that may impact the variance
of your measurements. Construct a Fish-Bone diagram to organize the list into proper categories.
(2) Discuss practical methods to prevent the sources from impacting your measurement. Describe at least three actions you will
take during your measurement to keep from the unexpected variability.
Next, find a place for uninterrupted flight and measure air-time. Repeat measurements at least 30 times for each design.
(3) Specify measurement environment, methods, devices, and individual roles. Also, attach a photograph of measurement.
(4) Attach the recorded data from Excel. It will have at least 30 rows of data fields with three columns, one for each design.
Finally, provide some descriptive and inferential statistics for your data. Show all steps if you manually get them. Show all
functions or screen-captured steps when you use Excel or other statistical software.
(5) Provide descriptive statistics for all three designs including mean, range, and standard deviation.
(6) Draw box plots for all three designs.
(7) Construct 95%-confidence intervals for means of all three designs.
Part B
Read the case study in Appendix II, "Neonatal Device Development: Engineering a Better Future One Baby at a Time."
After reading the case, answer the following questions, using the table of collected data entitled, "Measurements taken from Neonatal Ward."
(1) Develop a 99% confidence interval for Biparietal distance for neonatal infants based on the data available in the case for
babies who are 1-2kg, 2-3kg, and 3-4kg in weight.
Clearly indicate whether you are using Z or t table values. [Hints: One interval for each group; therefore, three total intervals;
is population standard deviation known?]
(2) Suppose you wanted to predict the baby's Biparietal distance with more precision.
The design team claims that it must have more precise and accurate estimates of this measure to ensure that the device fits
properly for each baby. In fact, they would like to have the half-interval, h, be less than 2% of the mean value (e.g., for the
1-2kg group, h= 1.4948).
How many babies would you need to sample in each group to have this be the case? Maintain 99%
confidence. [Hint: If your result is n<30, by CLT, we would need to round n up to 30 to maintain this confidence level. In other
words, you would always have sample size greater than 30. ]
Part C
Read the article in Appendix III entitled "Pocono Medical Center: Faster Lab Results Using Six Sigma and Lean" by T. Hayes,
Carmine J. Cerra, and Mary Williams. Turn in answers to the following questions:
(1) Describe the reasons why the Pocono Medical Center decided that a quality program was needed in the laboratory. What
was/were the goal(s) of the study?
(2) What was the "huge bottleneck"?
(3) A process map was used during the measuring phase to determine variability in processing times.
Which areas caused the most variability?
Why is a large amount of variability undesirable?
Submission Rules Submit in a PDF file.
Make sure the team Number is at the top of the document, as well as in the PDF file name.
Only one solution set per group. Your responses must be typed and organized. Any illegible answers will not receive points. Late labs will not be accepted.
The entire group will receive the same grade. Do not consult with anyone outside of your group, other than the Instructor for IE 424.
APPENDIX I
Paper Plane Designs
Figure 1 Arrow
Figure 2 Delta
Figure 3 Classic-Dart
Figure 4 Condor
Figure 5 Dragonfly
Figure 6 Canard
Figure 7 Bullet
Figure 8 Raptor
Figure 9 Spade
Figure 10 Interceptor
Figure 11 Bulldog
Figure 12 Trap-glider
Figure 13 Stealth-wing
Figure 14 Helicopter
Figure 15 Flying-ring0F1