TEST UNCERTAINTY & TEST UNCERTAINTY RATIO (TUR)
Samira A Khanam1, Edward Morse1
Department of Mechanical Engineering and Engineering Science
The University of North Carolina at Charlotte
Charlotte, NC 28223, USA
Measurement is a process to determine the
value or physical quantity of a measurand. The
measurand is the particular quantity subject to
measurement [1]. Each test of dimensional
measurement
contains
one
or
more
measurement steps. These steps contain
inaccuracies or errors. To describe these errors
the term “Uncertainty” is used. The ISO
International Vocabulary of Basic and General
Terms in Metrology (VIM) define uncertainties as
“a parameter, associated with the result of a
measurement that characterizes the dispersion
of the values that could be reasonably attributed
to the measurand (VIM 3.9).” In general,
different measurements may have different
uncertainty statements, even if they are
measured with the same instrument [2].
Elimination of uncertainty is not the focus for
measurement only the reduction of it is possible.
The most common dimensional measurand is
associated with the work piece. The example
can be the measurand when measuring the
diameter of the hole by using micrometer or any
other instrument. The uncertainty associated
with this kind of measurand is known as “Task
specific uncertainty”. The uncertainty associated
when testing a piece of equipment is a new
concept in this field. As a result this discussion
focuses on this new type of uncertainty which is
known as “Test uncertainty”. The example can
be to calibrate micrometer by using a gauge
block or to calibrate CMM by using a step
gauge. The uncertainty associated with this kind
of measurand which is the “error of the
instruments” is known as “Test Uncertainty”.
This is mentioned in ISO 23165 in which test
uncertainty is characterized for CMM.
As stated above error is associated with the
measurement process. The term error and the
uncertainty are not exactly same. Error is the
difference between the result and the true value.
In practice, no one can know the true value. So
the measured value is compared with the
reference value. The reference value gives a
point of reference with an uncertainty which is
commonly
accepted to compare an indicator. If calibrated
at NIST the true value is inside that reference
value. In [2] S.D Phillips et al states, “The
relationship between the measured or indicated
values and those of the reference values is a key
issue with regards to calibration…all calibration
must include the statement about the accuracy of
the instrument or artifact as required by
traceability.” We interpret this to mean test
uncertainty in this discussion. Any calibration
result showed the error or the deviation of the
measurand with respect to the reference value
and uncertainty associated with this error. There
are different kinds of measurand for different
kinds of measurement process. Consequently the
uncertainty will be different also. A clear
description of different kinds of uncertainty
associated with different kind of measurand is
explained in table-1.
TABLE 1.
Measurand/
Quantity
Activity
Uncertainty
(U)
Some
characteristics
of the work
piece
The length of
the artifact
Measuring a work piece to
conform to specific value
or tolerance
Task
specific U
Calibrating the material
standard size.
( Diameter of a sphere)
Calibrating an instrument
Calibration
U
The error of
the instrument
(E-value)
Test U
Table 2 is showing the uncertainty contributors
for different kinds of Uncertainty.
Example of “Task specific uncertainty” & “Test
uncertainty”
TABLE 2.
Contributor
Environment
1)Temperature
Task Specific
Uncertainty
Test Uncertainty
1) If instrument
does not
compensate with
temperature it has
effect on TSU
1) Any error
introduced by
the instrument is
not the part of
TU
2) The temp.
difference between
W/P and room
temp.
2) If artifact is
compensate
with
temperature of
instrument, then
it is part of
instrument, not
include in TU
Does not apply
( Part of the
instrument)
2)Work Piece
Reference ele
ment of
measurement
equipment
Resolution of the
main scale
( analogue or
digital)
Measurement
setup
( Probe
selection, tip
size etc.)
Form deviation of
tip,
Offset, extension
Usually
specified by std.
Poor setup may
influence TU.
Software and
calculations
Rounding/Quantific
ation
Sampling
Algorithms
Experience,
training, knowledge
( precision)
Surface roughness,
form deviation of
the w/p
Well defined in
the standard,
may be
eliminated
Reproducibility
Alignment,
Clamping fixturing,
Number of
measurement etc.
example: Due to the
measurement
process of w/p like
repeatability
Alignment,
Clamping
fixturing ,
number of
measurement
etc. example:
Instrument
repeatability
error is not the
part of TU, but
the repeatability
error for tester is
the part of TU.
Metrologist
Measurement
object , work
piece or
measuring
instrument
characteristics
Measuring
procedure
CMM (Test
equipment)
Task: To
measure
true
position of
the hole
FIGURE 1. CMM is measuring the true position
of the hole of a block (Task specific uncertainty)
CMM
(Instrument)
Step Gauge
(Test
equipment)
Form error of
artifact,
uncertainty for
the length of
artifact
FIGURE 2. CMM is calibrating by using a step
gauge (Test uncertainty)
Test uncertainty depends on significantly test
equipment, test procedure (which should be well
recognized) and the influence of the human
operator. When calculating the test uncertainty all
these factors should be reasonably estimated to
ensure that the result does not give any wrong
impression of uncertainty. Test uncertainty is only
the indication of the quality of the test, it is not the
machine performance. By defining the test, how
well test is performed, the influence of the
operator, selection and placement of test
instrument test uncertainty can be decreased and
consequently increasing the precision and
usefulness of the test.
Another topic, Test Uncertainty Ratio (TUR) is a
measure of the ability of a particular
measurement instrument and/or process to
evaluate conformance to specification. TUR is
the ratio between the tolerance or specification
and the uncertainty present in the test of this
tolerance or specification. Historically, the rule
of thumb for an appropriate ratio was that the
TUR must be at least 10:1. The higher the ratio,
the better the performance of the test. Currently,
a ratio of 4:1 or even 3:1 is considered
acceptable. This is due mostly to the better
performance of manufacturing equipment, and
the tighter and tighter specifications on
manufactured components. In many cases, test
equipment with an uncertainty small enough for
a 10:1 TUR does not exist, or is prohibitively
expensive for the application. There are two
main applications of the TUR: the first is in the
calibration of measuring instruments and
equipment, the second is in the inspection of
manufactured components. The focus of this
document is the second application – how do we
determine the Test Uncertainty Ratio for a part
that we need to measure using a particular
gage?
The list below gives some of the
important things to consider.
1. The uncertainty statement in the gage's
product literature might not be the
uncertainty needed to calculate TUR.
2. The result of the gage's most recent
calibration is almost certainly not the
uncertainty needed to calculate TUR.
3. The tolerance value on the part drawing is
– if interpreted correctly – going to be
needed to calculate TUR.
4. There will be more than one TUR
calculation for a part if there is more than
one tolerance that must be inspected.
To preview what will be covered in this paper,
the task-specific measurement uncertainty
must be estimated for the measurand in
question for each tolerance. This is the "1"
value. The range of allowable values for the
measurand in question (this is usually the
tolerance) must be known, and is compared to
"4".
TUR =
Tolerance for the measurand
Task ⋅ specific. uncertaint y
As is easily inferred from the equation above,
the TUR ratio compares the allowable variation
for the measurand (the numerator) with the
variability associated with finding the measurand
(the denominator).
LSL
USL
Specification
zone
Out of
Specification
Out of
Specification
Measur
ement
U
increas
Non
confor
mance
zone
U
Conform
ance
Zone
U
Non
confor
mance
zone
FIGURE 3. Relationship between Specification
Zone and Conformance Zone
One function of industrial measurement is to
determine whether a particular part measurand
(length, form, location, etc.) conforms to the
specification given on the part drawing or model.
The difference between the specification zone
and the conformance zone for a measurand is
explained with the aid of FIGURE 3, taken from
ISO 14253-1:1998(E). The upper horizontal line
of the figure shows the specification zone, which
is bounded by the lower specification limit (LSL)
and the upper specification limit (USL). If the
"true value" of the measurand is within the
specification zone, then the specification is
satisfied, otherwise the measurand is out of
specification. However, we can never know the
"true value" of the measurand. In order to state
whether we believe that the measurand is in or
out of specification, we have to acknowledge the
existence of uncertainty in the measurement
process. This is shown in the lower horizontal
line in FIGURE 3. If the measurand is in
conformance zone, we are suitably confident
that the true value is in specification. Similarly, if
the measurand is in the non-conformance zone,
we are confident that the true value is out of
specification. For the uncertainty region shown
between conformance and non-conformance,
we need to apply the "Decision rules." A
decision rule is a method – agreed on by two
parties – to decide whether to accept or reject a
part when the measurement value lies in this
uncertainty region.
One common decision rule used in industry is
"Simple Acceptance and Rejection Using an
N:1 Decision Rule" as defined in ASME
B89.7.3.1-2001. Using this decision rule, the
measured value is compared directly to the
specification zone (i.e. the conformance zone
and the specification zone are identical). This
rule has the effect of dividing the risk for
accepting bad parts and rejecting good parts
between the supplier and customer. In order to
limit this risk, the requirement of N:1 is placed on
the test uncertainty ratio (N is often 4, as
mentioned already). In FIGURE 4 below, taken
from the B89.7.3.1 document, the acceptance
and rejection zones are shown to be identical to
the specification zones.
FIGURE 4. Schematic view of Simple
acceptance/rejection with a 4:1 uncertainty
requirement
The measurement uncertainty interval is of width
2U, where U is expanded uncertainty, and the
uncertainty interval is no larger than one-fourth
the product’s specification zone for N = 4. [B
89.7.3.1-2001] For the simple acceptance rule
with a 4:1 ratio means that the tolerance range
is at least 4 times the uncertainty interval.
REFERENCES
[1] http://www.measurementuncertainty.org/mu
/guide/uncertainty.html
[2] S.D Phillips et al. A Careful Consideration
of the Calibration Concept. Journal of
Research of the National Institute of
Standards and Technology. 2001; 106:371379.
[3] Adams M. A2LA Guide for the Estimation of
the Measurement Uncertainty in Testing.
American
Association
of
Laboratory
Accreditation Manual, 2002.
[4] http://en.wikipedia.org/wiki/Measurements.
[5] Guidance Uncertainty of Measurement
concept in European Standards.