New uncertainty course part 2- july05.ppt

Measurement Uncertainty in
ISO17025
ISO 17025 5.4.6.1
A calibration laboratory or a testing laboratory performing
its own calibration, shall have and shall apply a
procedure to estimate the uncertainty of measurement
for all calibration and types of calibrations.
ISO 17025 5.4.6.2
Testing laboratories shall have and shall apply procedures
for estimating uncertainty of measurement. In certain
cases the nature of test methods may preclude rigorous ,
metrologically and statistical valid, calculation of
uncertainty………………..

Measurement Uncertainty in
ISO17025
ISO 17025 5.4.6.3
When estimating the uncertainty of measurement, all
uncertainty component which are of importance in the
given situation shall be taken into account using
appropriate method of analysis.
Measurement uncertainty is also mentioned elsewhere in
the ISO 17025 standard.

Measured
value
Error
Uncertainty at 95%
confidence level
Uncertainty and Error
True
value
+2 б
-
2
б
Measurement Uncertainty

Measurement Error
Measurement Error
• Error is the difference between the result of the
measurement and the true value of the quantity
measured.
• Error is a real physical quantity, its magnitude can not
be exactly known .
• Error is viewed is being of two kinds : random error and
systematic error .

Uncertainty
Uncertainty
Uncertainty is the range of values, usually centered on the
measured value, that contains the true value with stated
probability.
Confidence interval
Confidence interval
When uncertainty is defined as above, the confidence
interval is the range of values that corresponds to the
stated uncertainty.
Confidence level
Confidence level
It is the probability associated with a confidence interval.

• We would say “The true value can be expected to lie
within ± X units of the measured value with 95%
confidence . “
• Uncertainty is determined by an uncertainty analysis that
take into consideration the effect of systematic and
random errors in all the measurement processes.
Measurement
Uncertainty

Sources of Measurement
Uncertainty
• Incomplete definition of measured quantity.
• Non-representative sampling.
• Environmental conditions effects.
• Instruments resolution.
• Personal bias in reading analogue instruments.
• Inexact values of measurement standards and reference
materials.
• Approximations and assumptions in measurement
methods and procedures.
• Variations in repeated measurements.

Calculating Measurement
Uncertainty
Before Starting
• Basic knowledge of mathematics and statistics is
required to determine measurement uncertainty.
• Ensure that the process of determining uncertainty is
under statistical control.

Uncertainty
Steps for calculating measurement uncertainty
1. Identify the uncertainties in the measurement process.
2. Classify type of uncertainty (A or B).
3. Quantify (evaluate and calculate) individual uncertainty
by various methods.
4. Combine uncertainty by Root sum square (RSS
methods).
5. Assign appropriate K factor multiplier to combined
uncertainty to report expanded uncertainty
6. Document in an uncertainty budget.
7. Document in an uncertainty report.

Uncertainty
1.Identify the uncertainties in the measurement
process.
Determine contribution of factors affecting measurement.
• Environment
• Measuring Instruments.
• Operators.
• Measuring methods and procedures.
• Calculation methods.
• Other constrains

Uncertainty
2. Classify Type of uncertainty (A or B).
Uncertainty components are grouped into two major
categories depending on the source of data. The
categories are type A and type B uncertainties.
2.1 Type A uncertainty
Uncertainty of measurement evaluated by statistical
analysis of series of observations. In this case the
standard uncertainty is the experimental standard
deviation of the mean that follows from an averaging
procedure.

Uncertainty
2.1 Type A uncertainty.
Type A evaluation of standard uncertainty can be applied
when several independent observations have been
made for one measurement . When there is sufficient
resolution in the measurement process there will be an
observable scatter or spread in the values obtained.

Uncertainty
2.2 Type B uncertainty.
Type B evaluation of standard uncertainty is the evaluation
of the uncertainty by means other than the statistical
analysis of a series of observation.
it is based on experience and general knowledge. It is a
skill that can be learned with practice.

Uncertainty
2.2 Type B uncertainty.
Values of this type of uncertainty are driven at least from:
• Previous measurement data.
• Experience or general knowledge of the behavior of the
instrument.
• Manufacturer's specifications.
• Data in calibration certificates.
• Data in hand books.
• Environmental conditions effect.

Uncertainty
3. Evaluate and calculate individual uncertainty by
various methods.
• Compute a type A standard uncertainty for random sources
of error from series of measurements observations.
• Compute a standard uncertainty for each type B
component

Uncertainty
3.1 type A uncertainty evaluation.
Arithmetic mean or average:
x = ∑ x
Experimental variance S =
Experimental standard deviation S =
1
1
1
1
n -1
n -1
∑
∑ (x – x )
(x – x )
i
i
2
2
_
_
n
n
i=1
i=1
_
_
2
2
S
S
2
2
i
i
i=1
i=1
n
n

Uncertainty
3.1 Type A uncertainty evaluation
Experimental standard deviation of the mean:
S (x ) =
Standard uncertainty is the experimental standard deviation
of the mean
U (x ) = S (x )
S
S
n
n
_
_
_
_ _
_

Uncertainty
3.2 type B uncertainty evaluation.
• The standard uncertainty is calculated from known
characteristics of the distribution.
• There are 3 distributions that can be considered;
rectangular – triangle – normal.
• One can not combine normal and non normal
distributions when combining uncertainties.
• apply correction factors when combining normal and
non normal distributions.

Uncertainty
3.2 Type B uncertainty evaluation.
Normal distribution.
Gives the smallest standard deviation.
Rectangular distribution.
• Gives the largest standard deviation.
• It is used if only upper and lower limits values +a,-a of
the quantity are known.
• U(x) = 1/ √3 a
• It is often used when information is driven from
calibration certificate and manufacture’s specifications.
-
-
a
a +
+
a
a

Uncertainty
3.2 Type B uncertainty evaluation
Triangle distribution.
• It gives smaller standard deviation than the rectangular
distribution.
• It is often used in evaluation of noise and vibration.
• U(x) = 1/√ 6 a
-
-
a
a +
+
a
a

Uncertainty
Reference instrument uncertainty
The uncertainty assigned to the calibration of the reference
instrument will be stated on the certificate of calibration
with certain confidence level and coverage factor and it
has normal distribution.
U(x1) = Expanded uncertainty / K

Uncertainty
All uncertainty components (standard deviations) of type B
are combined by root sum square (RSS)
U (B) = √ U1 + U2 +………..
2
2 2
2

Uncertainty
4. Combined uncertainty
Combine type A and type B standard uncertainties into a
combined standard uncertainty by RSS.
Uc = √ U(A) +U(B)
This is the combined standard uncertainty of the
measurement, statistically one standard deviation
2
2 2
2

Uncertainty
5. Expanded uncertainty
• The uncertainty is expressed in more than one standard
deviation basis
• Expanded uncertainty , roughly equivalent to a
confidence interval .
• Expanded uncertainty provide high level of confidence.
• Expanded uncertainty should be calculated by
multiplying the combined uncertainty by a coverage
factor K.
Um = K Uc

Uncertainty
Coverage factor can be 1 or 2 or 3.
Assuming normal distribution
• For K = 1, the confidence level is 68%
• For K = 2, the confidence level is 95 %
• For K = 3, the confidence level is 99 %
Coverage factor 2 is often used for approximately 95%
confidence level ( 95,45%)

Vendor X (14 ppm)
Vendor Y (20 ppm)
Vendor Z (26 ppm)
Confidence
Level
85%
95%
99%
Specifications
Specifications
Same Performance, Different
Same Performance, Different
Specs
Specs

Uncertainty
Coverage factors derived from effective degree of freedom
• Effective degree of freedom is the reliability of the
standard uncertainty as an estimate of the standard
deviation of measurement.
• For normal distribution Veff = n -1 Type A
• For other distributions in type B assume Veff = ∞

Uncertainty
The coverage factor Kp is used when type A uncertainty is
large with respect to other components of combined
uncertainty and the number of observations n is small
(2 or less).
In this case the probability that the distribution is not
normal and the confidence level is less than 95% when
K = 2

Uncertainty
The coverage factor Kp with value more than 2 is obtained
from a table based on a t-distribution, evaluated for a
coverage probability of 95.45% .
If Veff is not an integer, truncate Veff to the next lower
integer
Veff 1 2 3 ………………….. 50 ∞
Kp 13.97 4.53 3.31 ………………… 2.05 2.00

Uncertainty
6. Uncertainty Budget
All results are tabulated to include all uncertainties
components , uncertainties values , probability
distributions, the correction factors, the combined
uncertainty and the expanded uncertainty,

Uncertainty
7. Uncertainty Reporting
The reported measured value and the uncertainty are
written in the calibration certificate as:
Y +/- U
With the following statement:
“The reported expanded uncertainty of measurement is
stated as the standard uncertainty of measurement
multiplied by the coverage factor K= 2 which for a normal
distribution corresponds to confidence level of 95 %”

Uncertainty
7. Uncertainty Reporting
In case of using Kp the following statement is used:
“The reported expanded uncertainty of measurement is
stated as the standard uncertainty of measurement
multiplied by the coverage factor Kp = xx which for
t- distribution corresponds to effective degree of freedom
Veff = y y with confidence level of 95 %”

New uncertainty course part 2- july05.ppt

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New uncertainty course part 2- july05.ppt