E1C05 09/14/2010
14:36:29 Page 193
3. Similarly, spatial variations in the diameter along its length introduce scatter between the
statistical values for each cross section. Since this affects the overall mean diameter, its effect
must be accounted for. Label this error as a spatial error with random standard uncertainty,
s 3 . It can be estimated by the pooled statistical standard deviation of the mean values at each
measurement location (replication).
Example 5.15
The mean temperature in an oven is to be estimated by using the information obtained from a
temperature probe. The manufacturer states an uncertainty of Æ0.6
C (95%) for this probe.
Determine the oven temperature.
The measurement process is defined such that the probe is to be positioned at several strategic
locations within the oven. The measurement strategy is to make four measurements within each of two
equally spaced cross-sectional planes of the oven. The positions are chosen so that each measurement
location corresponds to the centroid of an area of value equal for all locations so that spatial variations
in temperature throughout the oven are accounted for. The measurement locations within the cubical
oven are shown in Figure 5.7. In this example, 10 measurements are made at each position, with the
results given in Table 5.4. Assume that a temperature readout device with a resolution of 0.1
C is used.
KNOWN Data of Table 5.4
FIND T
0
¼ T Æ u T 95%
ð
Þ
m = 2
m = 1
Plane B
m = 4
m = 5
m = 7
m = 8
Measurement
locations
Plane A
m = 6
m = 3
Figure 5.7 Measurement locations
for Example 5.15.
Table 5.4 Example 5.15: Oven Temperature Data, N ¼ 10
Location
T m
s Tm
Location
T m
s Tm
1
342.1
1.1
5
345.2
0.9
2
344.2
0.8
6
344.8
1.2
3
343.5
1.3
7
345.6
1.2
4
343.7
1.0
8
345.9
1.1
Note: T m ¼
1
N
X N
n¼1
T mn ; s Tm ¼
1
N À 1
X N
n¼1
T mn À T m
À
Á 2
"
# 1=2
5.8 Multiple-Measurement Uncertainty Analysis 193
14:36:29 Page 193
3. Similarly, spatial variations in the diameter along its length introduce scatter between the
statistical values for each cross section. Since this affects the overall mean diameter, its effect
must be accounted for. Label this error as a spatial error with random standard uncertainty,
s 3 . It can be estimated by the pooled statistical standard deviation of the mean values at each
measurement location (replication).
Example 5.15
The mean temperature in an oven is to be estimated by using the information obtained from a
temperature probe. The manufacturer states an uncertainty of Æ0.6
C (95%) for this probe.
Determine the oven temperature.
The measurement process is defined such that the probe is to be positioned at several strategic
locations within the oven. The measurement strategy is to make four measurements within each of two
equally spaced cross-sectional planes of the oven. The positions are chosen so that each measurement
location corresponds to the centroid of an area of value equal for all locations so that spatial variations
in temperature throughout the oven are accounted for. The measurement locations within the cubical
oven are shown in Figure 5.7. In this example, 10 measurements are made at each position, with the
results given in Table 5.4. Assume that a temperature readout device with a resolution of 0.1
C is used.
KNOWN Data of Table 5.4
FIND T
0
¼ T Æ u T 95%
ð
Þ
m = 2
m = 1
Plane B
m = 4
m = 5
m = 7
m = 8
Measurement
locations
Plane A
m = 6
m = 3
Figure 5.7 Measurement locations
for Example 5.15.
Table 5.4 Example 5.15: Oven Temperature Data, N ¼ 10
Location
T m
s Tm
Location
T m
s Tm
1
342.1
1.1
5
345.2
0.9
2
344.2
0.8
6
344.8
1.2
3
343.5
1.3
7
345.6
1.2
4
343.7
1.0
8
345.9
1.1
Note: T m ¼
1
N
X N
n¼1
T mn ; s Tm ¼
1
N À 1
X N
n¼1
T mn À T m
À
Á 2
"
# 1=2
5.8 Multiple-Measurement Uncertainty Analysis 193