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.

What was this work?

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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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