IE 361 Exam 1 (Corrected)
Spring 2011
I have neither given nor received unauthorized assistance on this exam.
________________________________________________________
Name
Date
1
Below are 25 True-False Questions, worth 2 points each. Write one of "T" or "F" in front of
each.
_____ 1. Modern quality assurance is fundamentally process-oriented.
_____ 2. If a production process is made to be consistent/physically stable, then it will of necessity
produce good/functional product.
_____ 3. Most effective process improvement analysis is based on data mined from large generalpurpose databases.
_____ 4. Shapes of histograms can provide clues to physical origins and thus clues about the
operation of processes that generated the data being summarized.
_____ 5. Complicated multi-step production processes are most effectively monitored through
"end-of-the-line" inspection where a whole final product can be inspected, and causes of
problems can thus be easily diagnosed.
_____ 6. A bell-shaped histogram of consecutively-produced widget diameters is evidence that a
production process is operating consistently over time, so nothing more can be revealed by
plotting a run chart.
_____ 7. A Pareto diagram is used to focus attention on the biggest causes of process problems.
_____ 8. Without effective measurement systems, it is impossible to know whether a business or
production process is performing well.
_____ 9. Without appropriate routine collection and analysis of process data, it is impossible to
know whether a business or production process is performing well.
_____ 10. Measurement variation will typically inflate one's perception of process variation (based
on the measurement of a sample of parts produced by a process).
_____ 11. When measurement is destructive, there is no possibility of evaluating the size of pure
repeatability variation.
_____ 12. The width of a confidence interval for a standard deviation,  , tells one about the size
of  .
_____ 13. In order to compare biases of two measurement devices, one needs at least two
"standards" (items with known values of measurands).
_____ 14. Measurement device A is known to be linear, but is not known to be properly calibrated.
I wish to know if device B is linear. That can be determined using A and B only if standards
are available.
_____ 15. A gauge R&R study typically reveals which of several operators produces the most
accurate measurements.
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_____ 16. If widget diameters have actual standard deviation .01 mm and measurement has
standard deviation .01 mm , then measured diameters can be expected to exhibit a standard
deviation of .02 mm .
_____ 17. In an R&R context, limitations on the amount of information available on  reproducibility
related to a relatively small number of operators being included in the study can be
overcome by use of a large number of parts.
_____ 18. If a gauge capability ratio (or precision to tolerance ratio) is at least 1.00, the gauge in
question is probably adequate for checking conformance to the engineering specifications
under study.
_____ 19. Industry standard range-based gauge R&R analyses fail to produce appropriate
estimates for  reproducibility and lack associated confidence interval methods.
_____ 20. Measurement precision can often be improved by finding an equation to use in
replacing raw measurements with transformed or adjusted measurements.
_____ 21. In a go/no-go R&R study, it is theoretically impossible for two operators to each be
perfectly consistent in their go/no-go calls for a part, and yet have different probabilities of
calling "go."
_____ 22. Repeatability variance in a go/no-go R&R study is unlike that in a measurement R&R
study, because it is assumed to vary "cell-to-cell." (If the part or operator changes, it
typically changes.)
_____ 23. If there is no reproducibility variance in a go/no-go R&R study, then all operators
must be individually perfectly consistent in their go/no-go calls.
_____ 24. Confidence limits .1  .02 for the difference in two "go" call rates for a fixed part by
two different operators in a go/no-go study, p1  p2 , indicates that there is no clear different
in the call rates.
_____ 25. In the estimation of p1  p2 based on pˆ1  .2, pˆ 2  .3, and n1  n2  10 , approximate
95% confidence limits are .1  .41 .
The next 5 pages each have a 10 point "work out" problem on them (numbered W1,
W2,W3,W4, and W5.). Answer all 5.
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W1. Two operators made m  10 go/no-go calls on each of I  5 parts. The table below provides
their "go" call rates. Make and interpret an appropriate 95% confidence interval for comparing
overall (across all parts) "go" call rates for the two operators.
Part
1
2
3
4
5
Operator #1 "go" Call Rate
.2
.1
.8
.4
.9
Operator #2 "go" Call Rate
.2
.3
.9
.4
1.0
Interval:
Interpretation:
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W2. 20 students each measured the size of a single Styrofoam packing peanut once. Their
measurements produced a sample standard deviation of .014 in . Subsequently, a single student
who missed class measured that same peanut 10 times. That person's measurements produced a
standard deviation of .006 in . It is sensible here to say that the 20 measurements were observations
2
2
each having (theoretical) variance  reproducibility
  repeatability
and that the 10 measurements were
2
.
observations each having (theoretical) variance  repeatability
This scenario is not exactly like any discussed in class, the modules, or the revision of V&J. But its
basic structure is like one you've encountered, and a statistical method from class can be used to
make approximate 95% confidence limits for  reproducibility . Do this.
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W3. Below is a JMP report from a data set collected to relate temperature to resistance of a carbon
resistor. The report is for a fit of the model
y   0  1 x   2 x 2  3 x3  
to the x  temperature (K) and y  resistance () data pairs from the study. Plotted is the curve
fit by least squares and 99.5% prediction limits for ynew at each value of x . (Simple linear
regression corresponding to the simpler model y   0  1 x   is clearly not appropriate here, but
this cubic modeling seems to be sensible.)
Consider the future use of this resistor to measure temperature.
What are 95% confidence limits for the repeatability standard deviation of measured resistance at a
given temperature for this resistor?
What are 99.5% confidence limits for the actual temperature if a resistance of 13.0  is observed
for this carbon resistor. (Indicate on the JMP report how you obtained the interval.)
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W4. Two digital calipers are used to measure a gauge block "known" to be a 2.000 in gauge block.
Summary statistics for the two sets of measurements are below.
Caliper #1
n1  5
y1  2.0012 in
s1  .0005 in
Caliper #2
n2  10
y2  1.9998 in
s2  .0008 in
Give 95% confidence limits for the Caliper #1 bias for measuring 2.000 in.
Give 95% confidence limits for comparing Caliper #1 and Caliper #2 biases for measuring 2.000 in.
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W5. Here are some summary statistics from a standard gauge R&R study involving 5 operators and
10 parts where every operator measures each part 4 times
SSOperator  10, SSOperator  Part  6, and SSE  20
(units of sums of squares are lb 2 ).
Find an estimate of  R&R .
Approximate degrees of freedom for ̂ R&R are ˆ  36.96 . Use this fact and your value from above
to give approximate 95% confidence limits for  R&R .
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