STAT 495, Fall 2010
Homework Assignment #3
1. Because of expansion and contraction, the temperature of parts can have an effect on
the measurement process. Below are two scenarios for collecting data on the effects
of temperature on a measurement system. For each of the scenarios indicate whether
it is an observational study or an experiment. Explain briefly your choice. Which do
you think will give you a better understanding of the effects of temperature on the
measurement process?
a) Before a diameter measurement is made on an engine part, the part is chilled or
warmed to a specified temperature. There are 10 temperatures (in degrees
Celsius) used: –10, –5, 0, 5, 10, 15, 20, 25, 30, 35. Forty parts are measured, four
parts at each of the ten temperatures.
b) Whenever a diameter measurement is made on an engine part, the temperature of
the part is also taken. Forty parts are measured and their corresponding
temperatures are recorded.
2. A gauge R&R study was performed on black and white film test strips developed
using KODAK GBX chemicals for the manual processing of dental x-ray film.
Measurements were made using a densitometer and these measurements were used to
calculate a speed-value for the test strips. Ten test strips were prepared and
measured. There were three operators and each operator measured each strip 3 times.
Below are summaries, ranges and means, of the data.
Operator
A
B
C
Operator
A
B
C
2
1.41
0
1.41
Ranges of Repeat Measurements
Strip
3
4
5
6
7
0
0
1.41
0
0
2.82
2.82
1.41
1.41
1.41
0
0
0
2.82
1.41
1
2
Means of Repeat Measurements
Strip
3
4
5
6
7
381.97
381.97
380.56
376.33
375.86
376.80
1
1.41
1.41
1.41
377.27
375.86
377.27
378.68
379.15
378.68
377.74
375.39
375.86
378.68
378.21
378.68
374.45
374.92
374.92
8
1.41
1.41
1.41
9
0
2.82
1.41
10
1.41
1.41
1.41
8
9
10
376.33
376.33
375.39
373.04
372.57
372.10
373.51
372.57
372.57
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a) Using the formulas discussed in Lecture 8, compute the estimate of σ Repeat
and
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the estimate of σ Reprod
.
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b) Give the percentage of variation due to the densitometer and that due to the
operator.
c) According to the percentages calculated in b), where should improvement efforts
be focused – training the operators or purchasing a new densitometer?
d) The 90 individual values of speed for this gauge R&R study are given in the JMP
data table that accompanies this assignment. Open this table in JMP and use JMP
to produce a variability chart. From the JMP Starter go to Measure – Variability
Chart, or from the Graph pull down select Variability/Gauge Chart. Comment on
the variability chart. Does there appear to be more variation in the repeat
measurements for a part or between operators? Explain briefly.
e) Have JMP do a gauge study (from the red triangle pull down next to Variability
Gauge in the variability chart output select Gauge Studies – Gauge RR and click
on OK for the next two screens, Select model type Crossed, K sigma multiplier
6). Give the percentage of the Gauge RR variation due to the densitometer and
that due to the operator.
f) According to the percentages calculated by JMP, where should improvement
efforts be focused – training the operators or purchasing a new densitometer?
g) Are there differences in the percentages calculated by hand (using ranges) and by
JMP (using variances)? Are there differences in the conclusions on where
improvement efforts should be focused? Explain briefly.
h) JMP also calculates a variance component for the Part-to-Part variation. What
percentage of the total variation (Gauge RR and Part-to-Part) is attributable to the
Gauge RR? What does this value indicate about the measurement process?
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