# Quality and Six Sigma Tools

NOTE: For questions having solution boxes, work needs to be entered in the appropriate
box to receive full or partial credit.
1. Identify two Quality gurus whose work during WWII contributed to the Allies’ victory.
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2. A subgroup size of 19 is to be used to run an Xbar chart of the difference between
each Johnson Controls thermostat coming off the thermostat assembly line and the
true temperature. Let the true mean of this difference be µ and the true variance be
s2. In terms of these symbols, what is the expected value, variance, and approximate
sampling distribution of the subgroup sample mean?
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3. Do an FMEA of the process of receiving a walk-in patient complaining of flu-like symptoms
at the Urgent Care unit of the University of Chicago Medical Center. Identify
four Failure Modes. Use your judgment to assign Severity, Occurrence, and Detection
ranks to your Failure Modes. A flowchart need not be given.
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4. Let the quality metric be the number of minutes that a Delta Airlines flight is late
pushing off the gate at Mitchell airport. On Tuesday, Delta flights 1 through 4 out of
Mitchell were 3, 2, 5, and 3 minutes late pushing back, respectively.
(a) Using a subgroup size of 2, create a Stage I s chart with probability limits. In
doing so, replace the 0.001 and 0.999 ?2 quantiles on page 105 in Ryan with those
for 0.05 and 0.95, respectively. What is the chance that your s chart will give
signal on the next subgroup even though the variance has not changed?
Use the boxes on this and the next page to answer this question.
si, ˆsX computations
Quantiles (from calculator or approximation formulas)
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Control limits formula
Control limits computations
Tabular form of chart Chart
Chance chart will give signal?
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(b) Also using a subgroup size of 2, create a Stage I X¯ chart with 1.5 sigma limits.
x¯i, si, x¯¯, ˆs computations
Control limits formula
Control limits calculations
Tabular form of chart Chart
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(c) Define the term “statistical control.” Then, use this definition and the charts you
drew in questions (a) and (b) above, to argue why this process is or is not in
statistical control.
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(d) The next day, you begin Stage II monitoring with a subgroup size of 2 and observe
the first six flights pushing back 2, 2, 3, 5, 6, and 10 minutes late. Flights are
scheduled to leave every half hour starting at 7am. Use Stage I’s ˆµ and the
statistical method given in Ryan to estimate when the mean of this process shifted.
Regardless of which of these subgroup means plot outside the control limits, use
the time of the last subgroup for T.
Function value at first trial time point
Function value at second trial time point
Computation of t
ˆshift
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