D-108

Estimation of Measurement Uncertainty

Section D — Laboratory Operations and Specifications Revision 0 11 pages

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1.0 Purpose

The objective of the measurement uncertainty process is to determine the overall uncertainty of
the measuring system. Guidance is provided for estimating uncertainty from all contributors

affecting a measurement. Process requirements are described, including responsibilities and
controls for estimation of uncertainty budgets. It is recognized that this estimation may be
performed in various ways as long as the results are statistically justifiable.

2.0 Scope

This procedure applies to all internally performed, quantitative measurements derived from
methods where known variability is inherent with equipment used. These uncertainty
measurements will be calculated for all methods that are ISO.17025 accredited.

3.0 Responsibility

3.1 QC Laboratory Management is responsible for calculating expanded uncertainty for
measurement systems used in testing and for documenting the results of such calculations
in an Uncertainty Budget

3.2 QC Laboratory Management is responsible for reporting changes in measurement
uncertainty and/or capability to the ISO 17025 accreditation agency.

3.3. QC Laboratory Management is responsible for ensuring that this procedure is accurate,
understood and implemented effectively. No changes may be made to this procedure
without the authorization of Laboratory Management.

4.0 Definitions

4.1 Uncertainty- a parameter associated with the result of a measurement that characterizes
the dispersion of values that could reasonably be attributed to the measurand. Sources of
uncertainty include incomplete definition of the measurand, sampling, matrix effects and
interferences, environmental conditions, uncertainties of masses and volumetric

equipment, reference values, approximations and assumptions incorporated in the
measurement procedure, and random variation.
4.2 Accuracy- the closeness of the agreement between a measured quantity value and a true

quantity value of a measurand.
4.3 Dispersion — the amount by which we can normally expect the measured values to spread
or be different from one another.

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4.4 Measurand- a quantity intended to be measured.

4.5 Measurement- the process of experimentally obtaining one or more quantity values that
can reasonably be attributed to a quantity.

4.6 Measurement Uncertainty- a non-negative parameter characterizing the dispersion of
the quantity values being attributed to a measurand, based on the information used. This
is a quantitative value. The dispersion relates to how well the measurement is made and
the accuracy and capability of the equipment in the measurement system.

4.7 Standard Uncertainty- uncertainty of the result of a measurement expressed as a
standard deviation.

4.8 Combined Standard Uncertainty- the standard uncertainty of the result of a
measurement when that result is obtained from the values of a number of other quantities.

4.9 Expanded Uncertainty- a quantity defining an interval about the result of a
measurement that may be expected to encompass a large fraction of the distribution of
values that could reasonably be attributed to the measurand.

4.10 Coverage Factor- Numerical factor used as a multiplier of the combined standard
uncertainty in order to obtain an expanded uncertainty.

4.11 Uncertainty Budget — a list of evaluated sources of uncertainty. It lists the sources and
their values. An uncertainty budget may also list items that have been assessed and
determined to have no impact on uncertainty.

4.12 Sensitivity Coefficient- a multiplier used to relate how the value of a measurement
variable (e.g. the concentration of a reference standard, the temperature in the laboratory,
or the tolerance of a pipet) is related to the final test result.

4.13 Repeatability- measurement precision under a set of repeatability conditions of
measurement. The repeatability conditions of measurement are those creating a set of

conditions that includes the same measurement procedure, same operators, same
measuring system, same operating conditions and same location, and replicate
measurements on the same or similar objects over a short period of time. The repeatability
is the variation in measurements obtained.

4.14 Reproducibility- measurement precision under reproducibility conditions of
measurement. The reproducibility conditions of measurement are those creating a set of
conditions that includes different locations, operators, measuring systems, and the same
measurements on the same or similar object.

4.15 Bias- systematic error in the measurement process.

4.16 Drift- systematic change in the measurement process over time.
4.17 Resolution- an evaluation of the smallest incremental change observed in you

measurement process of system.

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5.0 References

5.1 JCGM 100:2008 Free version of ISO/IEC Guide 98-32008- Guide to expression of
Uncertainty in Measurement (GUM).

5.2 ISO 17025 requirements for measurement uncertainty
6.0 Process Activities

6.1 Laboratory Management ensures that all types of accredited tests provided to customers

have a current uncertainty of measurement calculated on an Uncertainty Budget.
Laboratory Management also ensures that all uncertainty components which are of
significance in the given situation are considered using appropriate methods of analysis.

6.1.1 When using a well-recognized test method that specifies limits to the values of
the major sources of measurement uncertainty and specifies the form of
presentation of the calculated results, the laboratory is considered to have satisfied
the evaluation of measurement uncertainty by following the test method and

reporting instructions.
6.1.2 When the measurement uncertainty of a method has been established and verified,

there is no need to evaluate measurement uncertainty for each result if the
laboratory can demonstrate that the identified critical influencing factors are
under control.

6.2 Examples of uncertainty considerations are the environment, metrologist or technician,
measuring equipment, properties and condition of item being tested, software,
calculations, and physical characteristics of the material being tested.

6.3 When evaluating uncertainty for an instrument that has more than one parameter (e.g.,
voltage, current, resistance, etc.) and one or more ranges, the uncertainty must be
evaluated for each range and parameter that will be reported to a customer.

6.4 Laboratory Management determines the uncertainty requirements for each test within the
scope of accreditation.

6.5 There are several types of measurement uncertainty sources that can be calculated by
Type A methods including but not limited to:

6.5.1 The results of measurement assurance processes (control charts, etc.),
6.5.2 Results of Gage Repeatability and Reproducibility (Gage R & R) studies,

6.5.3 Data from experiments that were designed to evaluate a particular parameter or
condition (e.g. an HPLC assay evaluated at several different temperatures).

6.6 Type B method of evaluation includes any reasonable method except statistical
evaluation of your own measurements. The Type B evaluation is a standard uncertainty.
An example of an uncertainty source that is evaluated using a Type B method is the

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uncertainty of the purity of a standard used in the calibration of an instrument, which is
obtained from the standard’s certificate of analysis.

6.7 The following is an example demonstrating the use of the different methods:

6.7.1 If determining the uncertainty of the result of a length measurement, (which is
affected by temperature changes), using Type B methods, one would look up the
expansion coefficient of the material and multiply by the expected range of
temperatures. Using Type A methods, the technician would repeat actual

measurements at various temperatures. Both methods would then use those values
in the measurement uncertainty calculation.
6.8 When an instrument manufacturer identifies a factor in a specification as being a

contributor evaluated by Type A methods, this information is NOT a Type A contributor
for Ion Labs’ purposes, it is treated as a Type B contributor. This is a Type B contributor
because the relevant measurements have not been performed by Ion Labs’ personnel.

6.9 Uncertainty Budgets
6.9.1 An Uncertainty Budget is a listing of all known sources of uncertainty, their

magnitudes, how they were obtained and whether they were evaluated by Type A
methods or Type B methods. The goal of an uncertainty budget is to calculate
measurement uncertainty for a specific measurand using a specific measurement
system by a well-organized, structured approach.

6.9.2 There is no rule specifying how many contributors to uncertainty must be
considered, except that all known, significant contributors must be evaluated. Ifa
contributor was determined to have little significance, it may be omitted. Any

contributors that have been omitted will be documented with a justification in the
appropriate Uncertainty Budget.

6.9.3 Laboratory Management determines or creates the appropriate template for the
Uncertainty Budget. A review of the contributors listed on the Uncertainty Budget
is conducted by Laboratory Management to ensure that all significant contributors
are listed.

6.9.4 For each uncertainty contributor, Laboratory Management will determine
whether the Type A or Type B evaluation method will be used.

6.9.5 Laboratory Management or designated personnel performs Type A or Type B
evaluations and documents all measurements on the designated template. Other
resources (including external resources) may review the data at the discretion of
Laboratory Management.

6.9.6 Laboratory Management calculates the Expanded Uncertainty and updates the
associated documentation and/or template to ensure the Expanded Measurement

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Uncertainty is available for accredited test reports. Laboratory Management
reviews and approves the results of completed Uncertainty Budgets.

6.9.7 Uncertainty Budgets are updated when components contributing to the
uncertainty of measurement change, and Laboratory Management determines the
change is significant enough to warrant revising the budget. Examples of changes

that may require reevaluation include replaced standards or new equipment. The
revised Uncertainty Budget is reviewed and approved in the same manner as the
original.

6.9.8 Uncertainty Budgets are retained in accordance with the Record Retention Matrix.
7.0 Process Outputs

7.1 Outputs from the process include but are not limited to:

7.1.1 Completed and current Uncertainty budgets for each test in the scope of
accreditation.

7.1.2 A list of known and current calculated measurement capability.

8.0 Procedure
8.1 Specify the measurement process and equation.

8.1.1 Write down a clear statement of what is being measured, including the
relationship between the measureand and the input quantities (e.g. volumes,

reference standard concentrations, constants, etc.). A cause and effect diagram is
often useful to help clarify uncertainty sources and their interdependence.
8.1.2 For the measurement procedure under consideration, evaluate each step of the test

method to identify sources of uncertainty.
8.1.3 Identify the equipment, reagents, and standards that will be used.

8.1.4 Assess the desired range of measurement.

8.1.5 Evaluate any equations used to calculate the final result.
8.2 Identify which components of the measurement process may contribute to the uncertainty

of the test result (uncertainty budget).
8.2.1 It is usually convenient to start with the expression used to calculate the final

result from intermediate values. All the parameters in this expression may have
an uncertainty associated with their value.
8.2.2 It is often useful to consider a measurement procedure as a series of discrete
operations (or unit operations), each of which may be assessed separately to

obtain estimates of uncertainty associated with them. This is particularly useful
where similar measurement procedures share common unit operations.

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8.2.3 Elements of overall method performance, such as precision and bias measured
with respect to reference materials generally form the dominant contributions to
the uncertainty estimate. It is then necessary to evaluate other possible

contributions to check their significance, quantifying only those that are
significant.

8.2.4 Typical sources of uncertainty to consider are:
8.2.4.1] Sampling- effects such as random variations between samples and any
potential for bias in the sampling procedure form components of

uncertainty affecting the final result.
8.2.4.2 Sample Storage- The duration of storage as well as storage conditions

should be considered as these can affect the final result.
8.2.4.3 Instrument effects- may include, for example, a temperature controller
that may maintain a mean temperature which differs (within

specification) from its indicated set-point or an autosampler that is
subject to carryover effects.

8.2.4.4 Reagent purity- uncertainty in the purity of reagents and reference
standards should be considered.

8.2.4.5 Measurement conditions- for example, volumetric glassware may be
used at an ambient temperature different from that at which it was
calibrated.

8.2.4.6 Sample effects- the recovery of an analyte from a complex matrix, or
an instrument response, may be affected by the composition of the
matrix.

8.2.4.7 Computational effects- selection of the calibration model (e.g. using a
straight line calibration on a non-linear response, leads to higher
uncertainty. Truncation or rounding can lead to inaccuracies in the final
result. Since these are rarely predictable, an uncertainty allowance may

be appropriate.
8.2.4.8 Blank correction- there will be an uncertainty on the value of the blank

correction. This is particularly important in trace analysis (e.g. heavy
metals testing).
8.2.4.9 Operator effects- effects such as an operator reading a meter or scale

consistently high or low should be considered.
8.2.4.10 Random effects- random effects contribute to the uncertainty of all
determinations.

8.3. Characterize sources of uncertainty (Type A or Type B).

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8.3.1 Type A standard uncertainty is determined by performing statistical analysis of
repeated measurements obtained under defined measurement conditions.

8.3.1.1 The value used to quantify uncertainty for a Type A contributor is
typically the standard deviation of repeat measurements, which is
expressed in the same units as the quantity being measured.

8.3.1.2 The degrees of freedom, equal to n-1 where standard deviation is
calculated from n independent observations, should always be given

when Type A evaluation of uncertainty components are documented.
8.3.2 Type B standard uncertainty is that which has been determined using any method
other than statistical analysis. (e.g., using available information such as a

calibration report or manufacturer’s certificate of analysis).
8.4 Assign a probability distribution to each uncertainty component.

8.4.1 Potential probability distributions include:

8.4.1.1 Normal (Gaussian) — often used for Type A uncertainty components,
calibration results, and accuracy specifications.

8.4.1.2 Uniform (rectangular) — often used for resolution components and
environmental or physical influences.

8.4.1.3 Triangle
8.4.1.4 Log normal

8.4.1.5 Quadratic

8.4.1.6 U-shaped
8.5 Quantify the magnitude of uncertainty components. Various sources of information may
be used, including but not limited to, precision studies, the test method itself,

experimental results, manufacturer’s manuals and specifications, technical documents
and guides, published journal articles or studies.

8.6 Convert uncertainty components to standard uncertainty (u) corresponding to one
standard deviation. The method of conversion depends on the source and format of the
component.

8.6.1.1 Type A components are typically expressed in terms of one standard
deviation and do not require conversion.

8.6.1.2 Type B component with standard deviation or standard uncertainty
listed, but no coverage factor or confidence interval. In this case, the
standard deviation should be assumed to be one standard deviation. No
conversion is required.

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8.6.1.3. Type B component with normal distribution and confidence interval and
coverage factor given (e.g. “coverage factor k=2 at the 95% confidence
interval”). Divide the stated uncertainty by the listed coverage factor to

obtain the standard uncertainty.
8.6.1.4 Type B component with normal distribution and only confidence

interval given. Divide the stated uncertainty by a coverage factor
corresponding to the stated confidence interval.

8.6.1.4.1 68.27% confidence interval > no conversion required
8.6.1.4.2 90% confidence interval > divide by 1.645

8.6.1.4.3 95% confidence interval > divide by 1.960

8.6.1.4.4 95.45% confidence interval > divide by 2.000
8.6.1.4.5 99% confidence interval > divide by 2.576

8.6.1.5 Type B component stated in tolerance with unknown distribution.

8.6.1.5.1 Assume a uniform distribution and divide the tolerance by
v3.

8.6.1.5.2 This method allows quick and easy calculations that can be
used without having much knowledge on the source. It uses
good engineering principles to perform this method with
confidence. The downside of this method is that the resulting

uncertainty is typically large compared to what it might be
for full analysis and characterization of the instrument and
determination of the real standard deviation.

8.6.1.6 Type B component stated in tolerance with known distribution.
8.6.1.6.1 Divide the stated tolerance by a value corresponding to the

stated probability distribution.
e Normal distribution > divide by a value corresponding

to the stated confidence interval as listed in 8.6.1.4.
e Uniform distribution > divide by 73.

e U-shaped distribution > divide by V2.

e Triangular distribution > divide by V6. Instruments that
drift must not be characterized by the triangular
distribution.

e Quadratic distribution > divide by V5.

e Log-normal distribution > divide by 2.375.

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8.7 Convert Standard Uncertainties (u) to units that match the measurement result.

8.7.1 Sensitivity coefficients (c) are used to convert standard uncertainties into units
that match the measurement result.

8.7.2 Sensitivity coefficients show how the variables in an equation or function are
related to the calculated result.
8.7.3 In many cases, the sensitivity coefficient will be equal to one. However, this

should always be confirmed to ensure an accurate assessment of uncertainty.
8.7.4 Sensitivity coefficients are calculated using the following steps:

8.7.4.1 Identify the measurement function or equation.

8.7.4.2 Identify the variable of interest.
8.7.4.3 The sensitivity coefficient can be determined experimentally if the

measurement equation is unknown or by calculation if the measurement
equation is known.

8.7.4.4 Choose two values for your selected variable, and perform an experiment
or calculation to determine the result under both conditions with all other
variables constant.

8.7.4.5 Calculate the difference in the two results.
8.7.4.6 Calculate the difference in the two values of your selected variable.

8.7.4.7 Divide the difference in the results by the difference in the two values of
your selected variable. This is the selectivity coefficient.

8.7.5 An example of sensitivity coefficient calculation for gage block calibration is
given below:

8.7.5.1 The gage block is made of unknown material; therefore, its coefficient
of linear thermal expansion is unknown and we do not know the
measurement equation. The sensitivity coefficient must be determined

experimentally.
8.7.5.2 The variable of interest is temperature, and the result is the length of the
gage block.

8.7.5.3 At 20°C, the gage block measures 1.0 inches.

8.7.5.4 At 25°C, the gage block measures 1.0001 inches.
8.7.5.5 The difference in temperature is 5°C.

8.7.5.6 The difference in length is 0.0001 inches.

8.7.5.7 The sensitivity coefficient for temperature is:

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_ 0.0001in See fe
C= — a = 2x10TM°in/°C

8.7.6 After the sensitivity coefficient has been calculated, multiply the standard
uncertainty by the sensitivity coefficient to obtain the standard uncertainty in units
that match the result of the test method.

8.8 Combined Standard Uncertainty (uc)
8.8.1 Once the individual standard uncertainties (u) are determined, the values are

combined to yield the Combined Standard Uncertainty (uc). Uncertainty
components should be combined using the root-sum-square (RSS) method. It is
found by squaring each standard deviation, adding up the squares and taking the
square root of the result. The following equation is an example of Combined

Standard Uncertainty, if you had three uncertainties (ui, u2, and us).
ue = Jub + ug + ug

8.9 Expanded Uncertainty

8.9.1 When reporting a measurement in a test report or a specification, it is the
expanded uncertainty (U) that should be reported.

8.9.2 The expanded uncertainty is the combined standard uncertainty (uc) multiplied by
the coverage factor (k) to provide an uncertainty range that is believed to include

the true value of the measureand within a specific confidence interval. A coverage
factor of k=2 or k=1.960 is recommended.
8.9.3. The value of k is chosen to match the desired confidence interval.

8.9.3.1 68.27% confidence interval > no conversion required

8.9.3.2 90% confidence interval > multiply uc by 1.645

8.9.3.3. 95% confidence interval > multiply uc by 1.960
8.9.3.4 95.45% confidence interval > multiply uc by 2.000

8.9.3.5 99% confidence interval > multiply uc by 2.576

8.9.4 Then the expanded uncertainty can be calculated:
U=k xu,

8.9.5 When reporting the expanded measurement uncertainty, the report will provide
measurements along with the expanded uncertainty and indicate the coverage
factor and/or confidence interval.

8.9.6 The following is an example of reporting of expanded uncertainty following
GUM methods:

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Caffeine = 100 mg/tablet (U = + 0.5mg/tablet k=2)

8.10 Evaluating Estimates of Uncertainty

8.10.1 The predicted standard deviation of an experimental measurement, which has
been obtained by combining the various uncertainty components that characterize
the measurement, can be compared to the experimentally observed variability of
measurements to provide further confirmation of uncertainty estimates.

8.11 Reporting Measurement Uncertainty

8.11.1 Uncertainty Budgets are reported to the accreditation agency at the time of test
accreditation application.

8.11.2 Revised Uncertainty Budgets are reported to the accreditation agency after review
and approval by Laboratory Management.

8.11.3 Laboratory Management will ensure that revised testing measurement capability
information is communicated to customers as appropriate.

9.0 Revision History

| Rev | Date | Description of Changes | CCR # | By |
|-----|----------|------------------------|-------|----|
| 0 | 10/12/21 | New procedure. N/A J. Maignan | - | - |