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uncertainties can and should be used to adjust Equation 5.3. So Equation 5.3 provides a minimum
value for design stage uncertainty. In later sections of this chapter, we move towards more thorough
uncertainty analyses.
Example 5.1
Consider the force measuring instrument described by the following catalog data. Provide an estimate
of the uncertainty attributable to this instrument and the instrument design-stage uncertainty.
Resolution:
0.25 N
Range:
0 to 100 N
Linearity error:
within 0.20 N over range
Hysteresis error: within 0.30 N over range
KNOWN Catalog specifications
ASSUMPTIONS Instrument uncertainty at 95% level; normal distribution
FIND u c , u d
SOLUTION We follow the procedure outlined in Figure 5.2. An estimate of the instrument
uncertainty depends on the uncertainty assigned to each of the contributing elemental errors of
linearity, e 1 , and hysteresis, e 2 , respectively assigned as
u 1 ¼ 0:20 N u 2 ¼ 0:30 N
Then using Equation 5.2 with K ¼ 2 yields
u c ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
ð0:20Þ
2 þ ð0:30Þ
2
q
¼ 0:36 N
The instrument resolution is given as 0.25 N, from which we assume u 0 ¼ 0:125 N. From Equation
5.3, the design-stage uncertainty of this instrument would be
u d ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u 2
0 þ u 2
c
q
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð0:36Þ
2 þ ð0:125Þ
2
q
¼ Æ0:38 N ð95%Þ
COMMENT The design-stage uncertainty for this instrument is simply an estimate based on the
‘‘experience’’ on hand, in this case the manufacturer’s specifications. Additional information might
justify modifying these numbers or including additional known elemental errors into the analysis.
Example 5.2
A voltmeter is used to measure the electrical output signal from a pressure transducer. The nominal
pressure is expected to be about 3 psi (3 lb/in.
2
¼ 0.2 bar). Estimate the design-stage uncertainty
in this combination. The following information is available:
166 Chapter 5 Uncertainty Analysis
14:36:25 Page 166
uncertainties can and should be used to adjust Equation 5.3. So Equation 5.3 provides a minimum
value for design stage uncertainty. In later sections of this chapter, we move towards more thorough
uncertainty analyses.
Example 5.1
Consider the force measuring instrument described by the following catalog data. Provide an estimate
of the uncertainty attributable to this instrument and the instrument design-stage uncertainty.
Resolution:
0.25 N
Range:
0 to 100 N
Linearity error:
within 0.20 N over range
Hysteresis error: within 0.30 N over range
KNOWN Catalog specifications
ASSUMPTIONS Instrument uncertainty at 95% level; normal distribution
FIND u c , u d
SOLUTION We follow the procedure outlined in Figure 5.2. An estimate of the instrument
uncertainty depends on the uncertainty assigned to each of the contributing elemental errors of
linearity, e 1 , and hysteresis, e 2 , respectively assigned as
u 1 ¼ 0:20 N u 2 ¼ 0:30 N
Then using Equation 5.2 with K ¼ 2 yields
u c ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
ð0:20Þ
2 þ ð0:30Þ
2
q
¼ 0:36 N
The instrument resolution is given as 0.25 N, from which we assume u 0 ¼ 0:125 N. From Equation
5.3, the design-stage uncertainty of this instrument would be
u d ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u 2
0 þ u 2
c
q
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð0:36Þ
2 þ ð0:125Þ
2
q
¼ Æ0:38 N ð95%Þ
COMMENT The design-stage uncertainty for this instrument is simply an estimate based on the
‘‘experience’’ on hand, in this case the manufacturer’s specifications. Additional information might
justify modifying these numbers or including additional known elemental errors into the analysis.
Example 5.2
A voltmeter is used to measure the electrical output signal from a pressure transducer. The nominal
pressure is expected to be about 3 psi (3 lb/in.
2
¼ 0.2 bar). Estimate the design-stage uncertainty
in this combination. The following information is available:
166 Chapter 5 Uncertainty Analysis