Uncertainty Pre不确定度计算

Kamaleldin Ibrahim Ismail 01/10/2002 8
Uncertainty in Measurement
COVERAGE FACTORS
The precise value of the coverage factor needed depends on the number of measurements made, (actually the number of degrees of statistical freedom).
Kamaleldin Ibrahim Ismail 01/10/2002 2
Uncertainty in Measurement
This is not the same as ERROR.
An error can be corrected and eliminated, at least in principle; UNCERTAINTY is an intrinsic property which may be reducible but never to zero.
For a large (infinite) number of measurements: 95% Confidence is represented by the S.D. X 1.96
99% Confidence is represented by S.D. X 2.58
Kamaleldin Ibrahim Ismail 01/10/2002 9
95% Confidence is approximated by the S.D. X 2
99% Confidence is approximated by S.D. X 3
Kamaleldin Ibrahim Ismail 01/10/2002 10
Uncertainty in Measurement
COVERAGE FACTORS
Often you have to do the calculation the other way around since calibration certificates often quote confidence intervals and may not give the coverage factor used. You will need to derive the standard deviation so you will have to guess what coverage factor is appropriate. In this case it is best to assume 1.96 for 95% confidence and 2.58 for 99% confidence since this will ensure you do not underestimate the standard uncertainty.
Kamaleldin Ibrahim Ismail 01/10/2002 3
Uncertainty in Measurement
It is not the same as
IN-HOUSE REPRODUCIBILITY or REPEATABILITY.
These only measure the variations that actually occur within your own laboratory.
Kamaleldin Ibrahim Ismail 01/10/2002 7
Uncertainty in Measurement
COVERAGE FACTORS
• The standard uncertainty is the standard deviation. • For a normal distribution one standard deviation
cm3 5.00cm3 5.00 - 0.01cm3 5.00 + 0.01cm3
Figure 2.3 Normal distribution illustrated by random pipetting error
Kamaleldin Ibrahim Ismail 01/10/2002
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Uncertainty in Measurement
Kamaleldin Ibrahim Ismail 01/10/2002 16
Uncertainty in Measurement
This then means that the uncertainty in the reading resulting from the resolution of the meter display is represented by a rectangular probability distribution of half width 0.0005 units so the standard uncertainty in the meter reading resulting from the readability of the meter is 0.0005 / 3 = ± 0.00029.
Kamaleldin Ibrahim Ismail 01/10/2002 6
Uncertainty in Measurement
Standard uncertainty of a measurement is defined by ISO as the standard deviation, i.e. approximately 68% confidence interval for Gaussian data.
Uncertainty in Measurement
COVERAGE FACTORS
In practice it is usual to approximate this coverage factor to a slightly larger value. This allows to some extent for the fact that we always have a finite number of measurements.
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Uncertainty in Measurement
Suppose we have a digital voltmeter which reads to the nearest millivolt and it is reading 5.000 volts. As the voltage applied increases we would expect the meter to change to reading 5.001 volts when the actual voltage passes 5.0005 volts. A similar situation will apply on a decreasing voltage. This means that when the meter reads exactly 5.000 volts the true voltage may be anywhere between 4.9995 volts and 5.0005 volts. Since the meter is digital and provides no information across the interval between changes on the digital display we must assume that, when the meter reads 5.000 volts, the true voltage is equally likely to be anywhere in the interval 4.9995 volts to 5.0005 volts.
Worst case as in the case of a digital display or readout.
Kamaleldin Ibrahim Ismail 01/10/2002 14
Uncertainty in Measurement
a
1/2a
Probability of Capacity
e.g. confidence interval quoted, coverage factor specified.
Kamaleldin Ibrahim Ismail 01/10/2002
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Uncertainty in Measurement
Mean
Probability of Volume
Standard Deviation
The rectangular distribution applies in the case of:A tolerance being quoted, e.g. 1000 +/-5ppm, at least 95% pure. Where no information is available to justify an alternative distribution.
Kamaleldபைடு நூலகம்n Ibrahim Ismail 01/10/2002 5
Uncertainty in Measurement
As a result, a proper estimate of uncertainty advises the laboratory, and in particular its clients, how much agreement might reasonably be expected between different laboratories making the same measurement.
Uncertainty in Measurement
Kamaleldin Ibrahim Ismail 01/10/2002
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The variations in the result of a measurement which can be attributed to the properties of the measurement system and the properties of the quantity being measured.
Kamaleldin Ibrahim Ismail 01/10/2002 11
Uncertainty in Measurement
The Gaussian distribution applies in the case of:Specific information that an uncertainty derived from a standard deviation is being quoted.
represents a 68% confidence interval approximately.
• A 95%, or occasionally a 99%, confidence interval
is normally what is quoted for an uncertainty.
• This is derived by multiplication of the standard uncertainty by a COVERAGE FACTOR.
0
-0.03cm3 5.00cm3 +0.03cm3
Capacity of Pipette
5.00 - a/3 ½
Figure 2.1 Rectangular distribution for calibration of a 5cm3 bulb pipette
5.00 +a/3 ½
Kamaleldin Ibrahim Ismail 01/10/2002
Kamaleldin Ibrahim Ismail 01/10/2002 4
Uncertainty in Measurement
A real estimate of uncertainty is a global estimate, i.e. it reflects the spread in data which might be expected if the same samples were tested, by the same method, in any laboratory with equipment calibrated to the same accuracy as that in your laboratory.