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Implementing ISO 17025 Measurement Uncertainty Requirements
in Software
Matt Nicholas
Staff Software Engineer
Calibration Division
Fluke Corporation
Abstract
ISO/DIS 17025, "General Requirements for the Competence of Testing and
Calibration Laboratories, states that "calibration certificates shall
contain the measurement results including the measurement uncertainty".
What is meant by that? Is it simply a Test Uncertainty Ratio (TUR)
calculation, or are there other factors involved? Using the "Guide to the
Expression of Uncertainty in Measurement", it certainly is more than a TUR
calculation. This paper describes the implementation of the measurement
uncertainty calculation in an automated calibration software package.
Compliance with ISO/DIS 17025 is discussed.
1. Introduction
There is an increasing need to determine measurement uncertainties in a
calibration environment.
This need is based on the requirement to comply with the certain standards
documents, such as ISO 17025.
It is no longer sufficient to calculate the traditional test uncertainty
ratio (T.U.R.), per MIL STD 45662. The T.U.R. is usually calculated as:
T.U.R. = (Test Tolerance) / (Accuracy of Standard)
The T.U.R. calculation is thus based on the stated accuracy of the
measurement standard, but does not represent the total measurement
uncertainty because it does not encompass empirical information based on a
sequence of actual measurements, nor does it incorporate measurement
uncertainty information based on the resolution of the Unit Under Test
(UUT) or other components of the measurement system and aspects of the
measurement environment.
This paper discusses the implementation of the measurement uncertainty
calculation in MET/CAL V6.0 automated calibration software.
As many MET/CAL users are aware, MET/CAL is a software product produced by
Fluke Corporation.
MET/CAL was first released in 1989 as an MS-DOS-based product. The
initial release of MET/CAL coincided with the introduction of the Fluke
5700A calibrator.
Subsequently, MET/CAL was ported to the Windows environment (V4.0), and
integrated with Fluke's MET/TRACK asset management software (V5.0).
The current version of MET/CAL (V6.0, August 1999) is a suite of 32-bit
applications with over 50 built-in instrument drivers to support
calibration standards manufactured by Fluke, Hewlett Packard, Keithley,
and other manufacturers. In addition, MET/CAL includes approximately 2000
precompiled calibration verification procedures which cover a wide variety
of UUTs.
It is important to note that MET/CAL has always strived to maintain upward
compatibility of procedures. This requirement meant that the measurement
uncertainty calculation had to be implemented in such a way that existing
procedures would continue to work, and, in fact, would automatically
calculate plausible values for measurement uncertainty, with no additional
information provided by the procedure itself.
In a software-based automated calibration system the requirement to
determine measurement uncertainty presents some specific challenges and
problems:
(1) Automation The user would like the system to be as automated as
possible. Ideally, the calibration procedure writer should not be
required to analyze each specific test in a calibration verification
procedure and manually provide uncertainty information.
(2) Flexibility The procedure writer should have the ability to override
defaults in the measurement uncertainty calculation at all levels.
The overriding of defaults should be supported at the procedure level,
and, where appropriate, at the workstation level and at the site level.
(3) Compatibility It should be possible to continue to use existing
calibration verification procedures and perform a reasonable
measurement uncertainty calculation, in most cases, without procedure
modification.
This consideration is of particular importance for MET/CAL, because the
product dates back to 1989, and many users have large installed bases
of existing calibration procedures.
2. Calculating Measurement Uncertainty
2.1 Basic Calculation
At the top level, the measurement uncertainty calculation is simply:
Expanded Uncertainty = (Standard Uncertainty) * K
where K is the coverage factor.
The Standard Uncertainty is:
Standard Uncertainty = RSS(U1, U2, U3, ..., U10)
where "RSS" refers to the normal root-sum-square" calculation.
The terms U1, U2, ..., U10 are uncertainty components.
MET/CAL software attempts to determine U1 and U2 automatically.
U1 is the Normalized System Accuracy, i.e., it is based on the
accuracy of the calibration standard.
U2 is an uncertainty component based on two inputs:
(1) A sequence of actual measurements.
(2) The resolution of the UUT (Unit Under Test).
U3, U4, U5, U6, U7, U8, U9, and U10 are optional uncertainty
components which may be directly specified by the procedure writer.
If specified, they are included in the RSS calculation. If not
specified, they default to zero and do not affect the RSS
calculation. Values persist in a procedure until changed or reset.
2.2 Determining U1, the Normalized System Accuracy
In each test step in a MET/CAL calibration procedure there is a
measurement standard and a UUT.
For example, the measurement standard might be a Fluke 5700A multi-
function calibrator, and the UUT might be a Fluke 77 DMM.
In most cases, the specification of a test in the calibration
procedure includes information about the test sufficient for MET/CAL
to automatically program the measurement standard. The information
is also used to look up the accuracy of the standard in an external
accuracy file.
MET/CAL has always supported external accuracy files. Prior to
V6.0, however, the accuracy file information was used only to
determine the T.U.R. It is now used to determine both the T.U.R.
and the measurement uncertainty.
The Normalized System Accuracy is calculated as:
Normalized System Accuracy = System Accuracy / Confidence
where:
System Accuracy is typically looked up in a MET/CAL accuracy file.
The Confidence is a statistical measure of the confidence associated
with the specifications given for a calibration standard.
In normal operation, the Confidence is also looked up automatically,
in the header portion of the external accuracy file.
Typical Confidence values are 2 sigma, 2.58 sigma, and 3 sigma.
Note that the parameter called Confidence in this document is
described in various technical documents as a "coverage factor". It
is not the same coverage factor, however, used to determine the
Expanded Uncertainty from the Standard Uncertainty.
2.3 Determining U2
The second uncertainty component, U2, is typically based on a
sequence of actual measurements, and on the resolution of the Unit
Under Test (UUT). The calculation is:
U2 = RSS(S1, S2)
where S1 is based on the sequence of measurements, and S2 is based
on the resolution of the UUT.
2.3.1 Determining S1
S1 is based on a sequence of measurements at a particular test
point, and is calculated as:
S1 = (SDEV / (N ^ 0.5)) * F
where:
(1) N is the number of measurements.
(2) SDEV is the standard deviation of the measurements.
(3) F is a factor based on the Student's T distribution and
the number of degrees of freedom.
Unless overridden or disabled, the value of F is determined
per Table G.2 of Annex G of the document ANSI/NCSL Z540-2-
1997. The values of F used by MET/CAL are exactly half the
values shown in the 95.45% column of Table G.2.
Approximate values for F are given in the following table:
N F
---------- ---
10 or more 1
9 1.2
8 1.2
7 1.3
6 1.3
4 1.7
3 2.3
2 7.0
2.3.2 Determining S2
S2 is based on the resolution of the UUT.
The reason it is necessary to include the S2 component in the
calculation of the second uncertainty component, U2, is that
in cases where the accuracy of the standard is much greater
than the accuracy of the UUT there is a high probability that
a sequence of measurements at a particular test point will all
yield the identical value. In this case the calculated
standard deviation of the measurements will be zero, and S1
will therefore also be zero. However, a standard deviation of
zero does not indicate the measurements are all absolutely the
same, it only indicates that within the resolution of the UUT
the measurements are the same.
For example, if the real value of an applied signal is
fluctuating, but always with +/- 0.5 count as shown on the
display of a DMM, a sequence of identical measurements would
be recorded, with no account being taken of the fluctuation of
the real signal.
Including S2, therefore, prevents the inappropriate estimate
of U2 as zero in such cases.
S2 is calculated as:
S2 = (UUT_RES * 0.5) / (3 ^ 0.5)
i.e., S2 is half the resolution of the UUT divided by the
square root of 3.
The square root of 3 term comes from assuming a rectangular
distribution of probabilities of values within a range defined
by half the resolution of the UUT.
The resolution of the UUT is, by default, determined
indirectly, from information given in the procedure.
It is typically based on the specified NOMINAL value, although
there are other sources of information when the NOMINAL value
is not directly specified by the procedure writer.
For example, suppose a DC Volts verification test is done at
1V. If the procedure writer specifies that the NOMINAL value
is "1.00V", MET/CAL infers from the format of the NOMINAL
specification that the resolution of the UUT is 0.01V.
2.4 Determining U3, U4, ..., U10
As previously stated, the calculation of the standard uncertainty
is:
Standard Uncertainty = RSS(U1, U2, U3, ..., U10)
where U3, U4, ..., U10 are optional uncertainty components which can
be directly specified to augment the measurement uncertainty
calculation.
U3, U4, ..., U10 can be directly specified in a MET/CAL calibration
procedure. The specification may apply to a single test, a sequence
of tests, or to the entire procedure. The default value for each of
these components is zero. Thus, in the absence of a procedure
specification to assign non-zero values to one or more of these
optional uncertainty components, they make no contribution to the
RSS (root sum square) calculation, and therefore no contribution to
the measurement uncertainty.
Recall also that the Expanded Uncertainty is calculated as:
Expanded Uncertainty = (Standard Uncertainty) * K
where K is the coverage factor.
Thus, a specification of U3, U4, ..., and/or U10 affects both the
Standard Uncertainty and the Expanded Uncertainty.
It is up to the metrologist or procedure writer to decide when it is
appropriate to assign values to the optional uncertainty components
U1, U2, ..., U10. In general, these optional uncertainty components
are intended for Type B uncertainties. These uncertainties are not
directly based on the sequence of measured values, the accuracy of
the main calibration standard, or the resolution of the UUT, because
those uncertainty components are incorporated in U1 and U2, which
are, typically, automatically calculated by MET/CAL. As stated in
ANSI/NCSL Z540-2-1997, information used to determine Type B
uncertainties includes:
- previous measurement data
- knowledge of relevant behavior and properties of materials
and instruments
- manufacturer's specifications
- calibration certificates
- uncertainties assigned to reference data taken from
handbooks
In practice, sources of additional, optional uncertainty components
may include:
- test leads
- terminators
- attenuators
- power splitters
- thermocouples
- other signal conditioners
- environmental factors (temperature, humidity)
In some cases it may be appropriate to leave all optional
uncertainty components unassigned (i.e., set to zero). For example,
if you are using a Fluke 5720 to calibrate a Fluke 10 DMM, the
resolution of the UUT may well dominate the measurement uncertainty
calculation, and any uncertainty contribution from, say, test leads,
will probably be negligible. On the other hand, if you are using,
for example, an HP 3458A to measure a precision resistor,
uncertainty due to test leads and temperature fluctuations in the
calibration lab may be important.
3. Parameter Control
The measurement uncertainty calculation performed my MET/CAL is
described in detail above. Most parameters used in the measurement
uncertainty calculation can be overridden at the procedure level.
When a parameter is specified at the procedure level, the
specification remains in effect for the duration of the procedure,
unless subsequently modified or reset to the default.
In some cases, parameter values can also be set at the workstation
level (in a MET/CAL initialization file), or at the site level (in a
database table).
When a measurement uncertainty parameter is overridden in a
procedure, the parameter value can be obtained in a number of ways:
(1) A literal value can be specified directly.
(2) The value can be calculated using the "MATH" function of the
MET/CAL procedure language.
(3) The operator can be prompted to enter the value, or to enter
information used to calculate the value.
(4) The value can be determined by a separate, user-written program,
invoked automatically by MET/CAL.
This section provides additional information about the measurement
uncertainty parameters.
Parameter Summary
The following table lists the measurement uncertainty parameters
which can be directly specified at the procedure level:
Number of Measurements
Confidence
Coverage Factor
Expanded Uncertainty
F (normally based on Student's T)
Flag to enable or disable use of Student's T to determine F
"Measure Only" Flag
S1 = (SDEV / (N ^ 0.5)) * F
S2 = ((UUT Resolution) * 0.5) / (3 ^ 0.5)
Standard Uncertainty
System Accuracy
U1 = Normalized System Accuracy
U2 = RSS(S1, S2)
U3 to U10 (optional uncertainty components)
UUT Resolution
3.1 Specifying the Number of Measurements
The number of measurements, N, may be specified, in order of
increasing precedence, at the site level, the workstation level, or
the procedure level. A procedure level specification may apply to
one test, a sequence of tests, or an entire procedure.
The specified value of N indicates how many times each test step is
repeated. The process of repeating a particular test step is
necessary to accumulate a sequence of measurements on which to base
the standard deviation calculation.
Legal values for N range from 0 to 1000.
Setting N to zero disables the measurement uncertainty calculation.
Although it is legal to set N to 1, notice that this means that the
standard deviation is, in effect, zero. This, in turn, means that
the second uncertainty component, U2, becomes just S2, so the entire
uncertainty component is then based only on the UUT resolution.
In general, it is therefore not advisable to set the number of
measurements to 1. However, there may be some cases where it is
acceptable to do so.
One such case involves the pre-calculation of S1 or U2, which
may then be directly specified at the procedure level.
A second case where setting N to 1 may be acceptable is when the
accuracy of the standard is sufficiently greater than the resolution
of the UUT so that any practical sequence of measurements is very
likely to result in a standard deviation of zero (i.e., where all
measurements are the same).
The procedure writer or metrologist should carefully consider the
tradeoffs involved in setting the number of measurements. Large
values of N increase confidence in the standard deviation
calculation, but also slow down execution of the procedure.
In a closed-loop procedure (where both the standard and the UUT are
remotely controlled), the normal measurement plus settling time is
multiplied by N.
In a manual procedure, the operator will be prompted N times to
enter the measured value. This can be both slow and tedious.
3.2 Specifying the Confidence
The Confidence is a statistical measure of the confidence associated
with the specifications given for a calibration standard.
The Confidence must be specified as a sigma value, not as a
percentage. For example, if the specifications for a calibration
standard are stated as having a 99% confidence, the Confidence
should be set to 2.58, which is the equivalent sigma value.
In cases where the confidence associated with the specification of a
calibration standard is unknown, you may wish to use 1.73 (that is,
3 ^ 0.5). This is a conservative choice based on the assumption of
a rectangular distribution.
The Confidence is used to calculate Normalized System Accuracy. The
Confidence parameter is often referred to as a coverage factor.
Recall that:
Standard Uncertainty = RSS(U1, U2, ..., U10)
where U1 is the Normalized System Accuracy, calculated as:
Normalized System Accuracy = (System Accuracy) / Confidence
The System Accuracy is the accuracy of the calibration standard, and
is usually determined by looking up the value in a MET/CAL accuracy
file.
If the value specified in the accuracy file is incorrect for a
particular test or procedure, or no accuracy file is available, the
Confidence can be directly specified at the procedure level or in an
initialization file.
MET/CAL includes approximately 50 different calibration standards.
An accuracy file for each standard is included with the software.
It is not uncommon to find that the manufacturer did not indicate a
confidence value associated with the specifications for an
instrument. In such cases an attempt was made to contact the
manufacturer (e.g., HP, Keithley, ...), and used the Confidence
value provided. In cases where it was not possible to obtain a
Confidence value from the instrument manufacturer a default value of
2 sigma was used. This value can easily be modified by a customer,
however.
MET/CAL allows the procedure writer to create and use alternate
accuracy files. In such cases, the Confidence should be specified
in the accuracy file header.
MET/CAL also allows the procedure writer to specify the accuracy of
the standard directly, on a per-test basis, in the procedure. When
this is done, it is necessary to directly specify the Confidence at
the procedure level, unless it is acceptable to allow the Confidence
to default to 2 sigma.
3.3 Specifying the Coverage Factor
The Coverage Factor is used to calculate the Expanded Uncertainty
as:
Expanded Uncertainty = (Coverage Factor) * (Standard Uncertainty)
By convention, the value typically used for the Coverage Factor is
2, and MET/CAL V6.0 is shipped with the coverage factor set to 2 in
the database.
The Coverage Factor may be specified, in order of increasing
precedence, at the site level, the workstation level, or the
procedure level. A procedure level specification may apply to one
test, a sequence of tests, or an entire procedure.
In V6.0, the Coverage Factor is one of three quantities which may be
written to the results.
There is no provision in V6.0 for automatically determining the
coverage factor as a function of the number of degrees of freedom.
3.4 Specifying the Expanded Uncertainty
If measurement uncertainty is enabled, MET/CAL normally calculates
the Expanded Uncertainty as:
Expanded Uncertainty = (Standard Uncertainty) * K
where K is the coverage factor.
However, it is possible to directly specify the Expanded Uncertainty
at the procedure level. Such a specification overrides the built-in
calculation of expanded uncertainty.
Setting the Expanded Uncertainty directly is appropriate when
MET/CAL's built-in measurement uncertainty calculation does not
yield correct results for a particular test, and where the procedure
writer has externally determined the uncertainty.
Directly specifying the Expanded Uncertainty in this way removes any
dependency on the measured values, number of measurements, UUT
resolution, confidence value, and Student's T distribution, for the
affected tests. The dependency is removed only for the Expanded
Uncertainty, however, not for the Standard Uncertainty, which will
still be calculated in the normal way, unless its calculation is
also overridden.
In general, in cases where the procedure writer has calculated the
measurement uncertainty externally, it will usually make more sense
to override the Standard Uncertainty, and, possibly, the Coverage
Factor, and allow MET/CAL to continue to calculate the Expanded
Uncertainty as the product of the two.
3.5 Specifying the F Factor
F is a factor based on the Student's T distribution and the number
of degrees of freedom.
Recall that the basic measurement uncertainty calculation is:
Standard Uncertainty = RSS(U1, U2, U3, ..., U10)
where
U2 = RSS(S1, S2)
and where
S1 = (SDEV / (N ^ 0.5)) * F
SDEV is the standard deviation of the measurements, N is the number
of measurements, and S2 is based on the resolution of the UUT.
As mentioned previously, unless overridden or disabled, the value of
F is determined per Table G.2 of Annex G of the document ANSI/NCSL
Z540-2-1997.
Note that MET/CAL uses the simplifying assumption that the number of
degrees of freedom is one less than the number of measurements. If
this assumption is not acceptable, it may be possible for the
metrologist or procedure writer to directly calculate F and override
MET/CAL's built-in determination of F (see below).
The value of F can be directly specified in the initialization file
or at the procedure level. Such a specification overrides the
built-in calculation of F. An initialization file specification,
unless overridden at the procedure level, applies to all tests in
all procedures run on the workstation.
3.5.1 Disabling F
Some metrologists believe that the calculation of S1 should be
simply:
S1 = (SDEV / (N ^ 0.5))
To support this mode, a special flag parameter is provided to
force F, in effect, to be 1.0 in all cases.
To disable the use of F in the calculation of S1, set the
special flag (called "USE_ST") to "no". This can be
at the database, workstation, or procedure level.
By default (as distributed) MET/CAL V6.0 disables the use of
F. In other words, the factor F is set to 1 and it is
presumed that the Coverage Factor, typically set to 2, and
used to determine the Expanded Uncertainty based on the
Standard Uncertainty, is sufficient to incorporate the
confidence in the standard deviation of the measured values as
a function of the number of measurements. When the number of
measurements is 10 or more, F is close to 1 in any case, and
so this presumption would appear to be justified.
For smaller values of N, on the other hand, the Student's T-
based F value can be significant (for example, F is 6.985 when
N is 2), and the decision as to whether it's appropriate to
set F to 1 unconditionally has to be based on the judgement of
the metrologist. Based on comments from various European and
American sources, it was determined that the best approach for
MET/CAL is to provide the option and allow each site to decide
how to implement this aspect of the uncertainty calculation.
3.6 Specifying the "Measure Only" Flag
"Measure Only" is a flag parameter which can be set to "Yes" or
"No".
If it is "Yes", MET/CAL meter drivers do not re-set up the meter on
the second and subsequent measurements of a sequence of
measurements.
This can speed up execution of certain meter-based procedures when
the number of measurements is greater than 1.
It is up to the metrologist and procedure writer to determine
whether the increased speed compromises the measurement uncertainty
calculation. Re-setting up the meter prior to each measurement
will, if nothing else, slow down the procedure and may slightly
increase the chance of seeing significant deviations from one
measurement to the next.
The Measure Only flag may be specified in the initialization file or
at the procedure level.
By default, "Measure Only" is set to "no", i.e., in a sequence of
measurements where the calibration standard is a meter, the meter
will be fully reprogrammed prior to each measurement.
3.7 Specifying the S1 Parameter
Recall that the basic measurement uncertainty calculation is:
Standard Uncertainty = RSS(U1, U2, ..., U10)
where U2 is calculated as:
U2 = RSS(S1, S2)
and where S1 is normally calculated as:
S1 = (SDEV / (N ^ 0.5)) * F
In other words, S1 is normally based on the standard deviation of a
series of measurements, for some number of measurements greater than
1.
However, it is possible to override the normal calculation of S1 at
the procedure level and directly assign its value.
If the calculation of S1 is overridden for one or more tests, this
removes any dependency on the number of measurements in the
measurement uncertainty calculation for those tests. The procedure
writer should, in that case, set the number of measurements to 1,
unless it is specifically expected that the measurement result be
reported as an average of values rather than as a single
measurement.
3.8 Specifying the S2 Parameter
Recall that the basic measurement uncertainty calculation is:
Standard Uncertainty = RSS(U1, U2, ..., U10)
where U2 is calculated as:
U2 = RSS(S1, S2)
and where S2 is normally calculated as:
S2 = ((UUT Resolution) * 0.5) / (3 ^ 0.5)
In other words, S2 is normally a function of the UUT resolution.
However, it is possible to override the normal calculation of S2 at
the procedure level and directly assign its value.
If the calculation of S2 is overridden for one or more tests, this
removes any dependency on the UUT resolution in the measurement
uncertainty calculation for those tests.
3.9 Specifying the Standard Uncertainty
Normally,
Standard Uncertainty = RSS(U1, U2, ..., U10)
However, it is possible to override the normal calculation of
Standard Uncertainty at the procedure level and directly assign its
value.
Overriding the normal calculation of Standard Uncertainty is
appropriate only where the procedure writer has externally
determined the measurement uncertainty associated with a test.
Directly specifying the value of the Standard Uncertainty in this
way removes any dependency on the measured values, number of
measurements, UUT resolution, confidence value, and Student's T
distribution, for those tests.
The only subsequent calculation performed using the specified
Standard Uncertainty is:
Expanded Uncertainty = (Standard Uncertainty) * K
where K is the coverage factor.
3.10 Specifying the System Accuracy
The basic measurement uncertainty calculation is:
Standard Uncertainty = RSS(U1, U2, ..., U10)
where U1 is the Normalized System Accuracy, calculated as:
U1 = (System Accuracy) / Confidence
System Accuracy is represented in absolute units (e.g., 0.1 V), and
Confidence is expressed as a sigma value (e.g., 2.58 sigma).
Normally the System Accuracy is looked up in a MET/CAL accuracy
file. The accuracy file used is typically selected automatically,
based on the instrument (the calibration standard), and the
calibration interval specified for the particular configured
standard in use.
The procedure writer may override the normal accuracy file selection
and directly specify the use of an alternate accuracy file.
It is also possible, at the procedure level, to directly specify the
System Accuracy for the measurement uncertainty calculation.
It is important to understand that direct specification of the
System Accuracy in this way does not affect the T.U.R. calculation,
which will continue to be based on accuracy file lookup.
An alternative approach, which can be used in closed-loop
procedures, is to use the "ACC" procedure statement to directly
specify the system accuracy in a way which affects both the T.U.R.
and the measurement uncertainty.
Direct specification of System Accuracy is particularly useful in
cases where MET/CAL's built-in accuracy file lookup is not adequate
to determine the accuracy of a standard. For example, counter
accuracies typically cannot be represented as:
(percentage of NOMINAL) + floor
and therefore the standard accuracy file lookup does not work for
these devices.
The procedure writer may wish to directly specify the System
Accuracy in these cases in order to allow the measurement
uncertainty calculation to proceed.
3.11 Specifying the U1 Parameter
The basic measurement uncertainty calculation is:
Standard Uncertainty = RSS(U1, U2, ..., U10)
where U1 is the Normalized System Accuracy, calculated as:
U1 = (System Accuracy) / Confidence
However, it is possible to override the normal determination of U1
and directly assign its value.
When U1 is directly specified the calculated measurement uncertainty
no longer depends on the System Accuracy or Confidence, both of
which are usually based on accuracy file lookup.
3.12 Specifying the U2 Parameter
The basic measurement uncertainty calculation is:
Standard Uncertainty = RSS(U1, U2, ..., U10)
where U2 is calculated as:
U2 = RSS(S1, S2)
and where S1 is normally calculated as:
S1 = (SDEV / (N ^ 0.5)) * F
and where S2 is normally calculated as:
S2 = ((UUT Resolution) * 0.5) / (3 ^ 0.5)
However, it is possible to override the normal determination of U2
and directly assign its value.
When U2 is directly specified the calculated measurement uncertainty
no longer depends on the measured values, the number of
measurements, the Student's T distribution, or the UUT Resolution.
Directly specifying U2 is appropriate in cases where the procedure
writer or metrologist has determined that MET/CAL should calculate
measurement uncertainty using the usual RSS (root sum square)
calculation, including the normalized system accuracy component,
and, possibly, optional uncertainty components U3, U4, ..., U10, but
where the usual (empirical) determination of uncertainty component
U2 based on the standard deviation of the measured values and the
resolution of the UUT (Unit Under Test) is incorrect or
inappropriate.
3.13 Specifying Optional Uncertainty Components (U3, U4, ..., U10)
The optional uncertainty components U3, U4, ..., U10 default to zero
if not directly specified at the procedure level.
Zero or more optional components may be specified on a per-test
basis.
Values persist within a procedure until changed or reset.
Refer to the section "Determining U3, U4, ..., U10" above for
addition information.
3.14 Specifying the UUT Resolution
The basic measurement uncertainty calculation is:
Standard Uncertainty = RSS(U1, U2, ..., U10)
where U2 is calculated as:
U2 = RSS(S1, S2)
and where S1 is normally calculated as:
S1 = (SDEV / (N ^ 0.5)) * F
and where S2 is normally calculated as:
S2 = ((UUT Resolution) * 0.5) / (3 ^ 0.5)
Unless overridden, MET/CAL attempts to infer the UUT's resolution
based on information in the procedure. (Actually, MET/CAL has
always done this, but prior to V6.0 the inferred information was
used only to control the formatting of certain result quantities.)
In V6.0, the UUT Resolution is needed to determine the measurement
uncertainty.
If the automatically determined UUT resolution is incorrect or
inadequate, the procedure writer may directly specify the UUT
resolution.
The UUT Resolution is expressed in absolute units (Volts, Amps,
etc.)
The details of how MET/CAL attempts to infer the UUT Resolution from
procedural information are not given here. However, the procedure
writer must be cognizant of the fact that MET/CAL cannot always
reliably infer the UUT resolution, especially in cases where the
Nominal value of the test, or the test tolerance, are not statically
known but, rather, are prompted for or calculated at run time.
In such cases the UUT Resolution should be directly specified at the
procedure level. The specification may apply to a single test, a
group of related tests, or to the entire procedure.
4. Flow Control
In the MET/CAL procedure language a test is a sequence of one or more
procedure statements which determine a single result at a particular test
point.
In "closed-loop" procedures, where the Unit Under Test (UUT) can be
remotely controlled, full automation requires that the test will typically
consist of several discrete parts:
(a) Set up the calibration standard.
(b) Set up the UUT.
(c) Read the measured value.
(d) Compare the measured value to the expected value and generate a
test result.
Depending on the particular test and the particular instruments involved,
it may or may not be necessary to prompt the operator to make certain
connections as part of the test.
The measurement uncertainty calculation requires that some or all of the
parts of such a test be repeated automatically, once for each measurement
in the measurement sequence.
The question arises, then, as to how many of the procedure statements in
the test step should be repeated on the second and subsequent
measurements?
In some cases, such as when the operator is prompted to make a connection,
it is clear that requiring that the connection be broken and re-made for
each measurement in the sequence would be annoying to the operator, and
probably pointless.
In other cases, such as the decision whether to re-set up the calibration
standard for each measurement, it's a judgement call. There may be some
merit, from the measurement uncertainty point of view, in repeating as
much as possible of the entire measurement step. On the other hand, doing
so slows down procedure execution.
To provide full flexibility, a new procedure statement, "TARGET", has been
added to the MET/CAL procedure language. The procedure writer may insert
a TARGET statement at any desired point in a test. This causes execution
of the second and subsequent measurements to commence at the first
procedure statement after the TARGET statement.
For compatibility with existing compiled procedures, however, MET/CAL also
applies certain built-in rules to determine how much of a multi-statement
test to re-execute on the second and subsequent measurements when there's
no TARGET statement in the test.
Some statement types, like operator prompts to make connections are, by
default, not repeated. Other statement types, like low-level IEEE-488 or
serial commands to set up and query the UUT are, by default, repeated each
time.
5. Conclusion
The implementation of the measurement uncertainty calculation in MET/CAL
V6.0 had two main goals:
(1) To define built-in calculations which correctly calculate the
measurement uncertainty in most cases.
The measurement uncertainty calculation can be done for many
procedures without any required procedure modification.
(2) To provide a flexible implementation which allows the procedure
writer to override some or all of the built-in calculation, and to
include optional uncertainty components as needed.
Our plan for subsequent versions of MET/CAL is to listen carefully to
customer feedback on the measurement uncertainty implementation and add
additional capability as needed when cases arise where the measurement
uncertainty cannot be calculated in a satisfactory manner, or where it can
be done manually, but further automation is feasible.
Comments, questions, and suggestions from interested readers are most
welcome. I can be reached via email at:
[email protected]
6. References
(1) DIS 17025 "General Requirements for the Competence of Testing and
Calibration Laboratories".
(2) ANSI/NCSL Z540-2-1997 "U.S." Guide to the Expression of Uncertainty in
Measurement".
(3) EAL-R2 "Expression of the Uncertainty of Measurement in Calibration".
Note: The most recent version of this document is designated "EA-4/02".
(4) EAL-R2-S1 "Supplement 1 to EAL-R2 Expression of the Uncertainty of
Measurement in Calibration".
(5) "Guidelines on the Evaluation and Expression of the Measurement
Uncertainty", Singapore Institute of Standards and Industrial Research,
First Published July 1995.
(6) Calibration Philosophy in Practice, 2nd Edition, Fluke Corporation,
ISBN 0-9638650-0-5.
(7) Mr. Ray Kletke, Fluke Standards Lab.
(8) Mr. David Deaver, Fluke Standards Lab.
(9) "Software and Hardware Considerations for Automated Calibration
Systems", Peter Dack, Wavetek Calibration Division.