ISO/TS 15530-2:2026

Technical
Specification
ISO/TS 15530-2
First edition
Geometrical product specifications
2026-03
(GPS) — Coordinate measuring
machines (CMM): Technique for
determining the uncertainty of
measurement —
Part 2:
Use of multiple workpiece
orientations and calibrated simple
standards
Spécification géométrique des produits (GPS) — Machines
à mesurer tridimensionnelles (MMT) : Technique pour la
détermination de l'incertitude de mesure —
Partie 2: Utilisation de plusieurs orientations de la pièce et
d'étalons simples étalonnés
Reference number
© ISO 2026
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ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols . 2
5 Requirements for uncertainty assessment . 3
6 Principle of measurement and uncertainty assessment. 3
7 Procedure . 4
7.1 Measurements . .4
7.1.1 General .4
7.1.2 Multiple measurements on the workpiece .5
7.1.3 Measurements of standards of length.8
7.1.4 Measurements for probe qualification error assessment .10
7.2 Evaluation of the measurement value . 12
7.2.1 Calculation of measurement value y without error correction . 12
corr
7.2.2 Calculation of the bias corrected measurement value y . 12
corr
7.3 Evaluation of the measurement uncertainty . 13
8 Special considerations . 14
8.1 Geometrical deviation measurement .14
8.1.1 General .14
8.1.2 Full information case. 15
8.1.3 Lesser information case . 15
8.2 Tolerances .16
8.3 Calibration .16
8.3.1 Requirements for traceability .16
8.3.2 Avoidance of unknown biases and other uncertainty underestimates . .16
8.3.3 Calculation of the expanded measurement uncertainty .16
Annex A (normative) Formulae . 17
Annex B (informative) Examples for calibration/test use .26
Annex C (informative) Application for lot inspection in conformance verification . 41
Annex D (normative) Calculation of the coverage factor k using the effective degrees of freedom .43
Annex E (informative) Guidance of the undetected uncertainty contributors .45
Annex F (informative) Relation to the GPS matrix model .48
Bibliography .49

iii
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out through
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with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are described
in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the different types
of ISO document should be noted. This document was drafted in accordance with the editorial rules of the
ISO/IEC Directives, Part 2 (see www.iso.org/directives).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
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rights in respect thereof. As of the date of publication of this document, ISO had not received notice of (a)
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Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 213, Dimensional and geometrical product
specifications and verification.
A list of all parts in the ISO 15530 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.

iv
Introduction
This document is a geometrical product specification (GPS). It influences chain link G of the chain of
standards on size, distance, form, orientation, location and run-out in the general GPS matrix (see Annex F).
The ISO GPS matrix model given in ISO 14638 gives an overview of the ISO GPS system of which this
document is a part. The fundamental rules of ISO GPS given in ISO 8015 apply to this document and the
default decision rules given in ISO 14253-1 apply to specifications made in accordance with this document,
unless otherwise indicated.
For more detailed information on the relation of this document to the GPS matrix model, see Annex F.
Coordinate measuring systems (CMS) have become essential for verifying geometrical specifications
in industry. According to the ISO 9000 series of standards, in a quality management system, the relevant
measuring equipment is required to be calibrated against certified equipment having a known and valid
relationship to internationally or nationally recognized standards, in order to establish traceability.
According to ISO/IEC Guide 99, the International vocabulary of basic and general terms in metrology (VIM), a
calibration comprises – besides the establishment of the relationship between the measured and the correct
values of a quantity – the uncertainty evaluation in the final results (measurands) of the measurement task.
However, evaluating the uncertainty for the numerous measurement tasks a CMS performs is often very
complex. In these cases, the risk of an unrealistic estimation of task-related uncertainty is likely to arise.
The aim of this document is to provide a method and related procedures for the evaluation of the measurement
uncertainty of specific measuring tasks using CMS. The method applies to Cartesian coordinate measuring
machines (CMM) equipped with tactile probing systems. This method can possibly be applied to other CMS,
however the difference in CMS kinematics and appropriate error model must be considered. This is not a
trivial effort to investigate what measurement orientations can randomize systematic errors using that
CMS. This document is a Technical Specification, and as such, feedback is sought regarding its usage and
performance within its scope (i.e., on contact Cartesian CMM). It is expected that various investigations will
take place on other types of CMS. As these investigations can occur (perhaps with adaptations of the method
to the particular CMS technology, e.g., kinematics), feedback is welcome regarding these other technologies
as well.
A possible application of the method described in this document is the calibration of workpieces. The
workpiece and the related calibration results can be utilized as "calibrated workpieces" in ISO 15530-3. The
calibration values and their calibration uncertainties are derived by this document.
Another possible application is the conformity verification of workpieces against their geometrical
specifications in accordance with ISO 14253-1 or ISO/TR 14253-6. The method described in this document
provides the values and uncertainties of the specified geometrical characteristics, which are used as the test
values and guardbanding.
Another possible application is the estimation of the task-specific measurement uncertainty (see
ISO/TS 15530-1) within the PUMA method in ISO 14253-2, whereby a CMM user can compare different
measurement conditions, e.g. fewer measurement repetitions.

v
Technical Specification ISO/TS 15530-2:2026(en)
Geometrical product specifications (GPS) — Coordinate
measuring machines (CMM): Technique for determining the
uncertainty of measurement —
Part 2:
Use of multiple workpiece orientations and calibrated simple
standards
1 Scope
This document describes a procedure for the evaluation of the uncertainty of measurements made with
tactile Cartesian coordinate measuring machines (CMM).
The measurement uncertainty evaluated in accordance with this document indicates the performance of
the individual measurement operation, which is not the measuring capability nor test uncertainty when
verifying the performance of the CMM against its maximum permissible errors (MPE).
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 1101, Geometrical product specifications (GPS) — Geometrical tolerancing — Tolerances of form,
orientation, location and run-out
ISO 10360-1, Geometrical Product Specifications (GPS) — Acceptance and reverification tests for coordinate
measuring machines (CMM) — Part 1: Vocabulary
ISO/TS 15530-1, Geometrical product specifications (GPS) — Coordinate measuring machines (CMM): Technique
for determining the uncertainty of measurement — Part 1: Overview and metrological characteristics
ISO/IEC Guide 99, International vocabulary of metrology — Basic and general concepts and associated terms
(VIM)
ISO/IEC Guide 98-3, Uncertainty of measurement — Part 3: Guide to the expression of uncertainty in
measurement (GUM:1995)
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 1101, ISO 10360-1, ISO/TS 15530-1,
ISO/IEC Guide 99, ISO/IEC Guide 98-3 and the following apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/

3.1
nominal sampling pattern
measurement points in an agreed upon pattern extracted from the workpiece and used to associate one or
more characteristics of interest
Note 1 to entry: The nominal sampling patterns are essential parts of the measurand definitions, and their designation
is to be stated clearly e.g. in the measurement protocols.
3.2
undetected uncertainty contribution
uncertainty contribution not detected by the described usage of multiple workpiece orientations and
calibrated simple standards
Note 1 to entry: Undetected uncertainty contributors are discussed in Annex E.
4 Symbols
For the purpose of this document, the symbols given in Table 1 apply.
Table 1 — Symbols
Symbol Definition
u(y ) standard uncertainty of the final corrected result of the measurement
result
U(y ) expanded uncertainty of the final corrected result of the measurement
result
k coverage factor for calibration use
i index for the current measurement in a series of repeated measurements
j index for the current workpiece orientation, or, index for the probe stylus
h index for the measurement point ID in the nominal sampling pattern, or, index for the length standard
n number of repeated measurements of the workpiece in a single orientation, where W stands for
WR
workpiece and R stands for repeated measurements
n number of workpiece orientations, where W stands for workpiece and O stands for orientations
WO
of the workpiece
n number of repeated measurements of a length standard in a single orientation, where L stands
LR
for length standard and R stands for repeated measurements
n number of length standard orientations, where L stands for length standard and O stands orien-
LO
tations of the length standard
n number of length standard(s) measured in a single orientation, where L stands for length standard
LN
and N stands for the number of length standard(s)
n number of repeated measurements of a probe verification standard with a single stylus, where P
PR
stands for probe stylus and R stands for repeated measurements
n number of probe styli orientations to be used, where P stands for probe stylus and O stands for
PO
orientation of the probe stylus
n number of measurement points in a nominal sampling pattern, where M stands for measurement
MP
and P stands for points
y measured value; workpiece orientation j (1 ≦ j ≦ n ), repetition i (1 ≦ i ≦ n )
ij WO WR
y measured value at the h-th point on the workpiece (1 ≦ h ≦ n ); workpiece orientation j (1 ≦ j ≦
ijh MP
n ), repetition i (1 ≦ i ≦ n )
WO WR
W
measured value for the calibration/test; workpiece orientation j (1 ≦ j ≦ n ), repetition i (1 ≦
ij OW
i ≦ n )
WR
y calibration/test result value of the feature
result
y raw measurement result, not corrected for the bias
W raw measurement value for the calibration/test
y measurement result corrected for the bias
corr
E average scale error of the CMM in the region of interest
S
TTaabblle 1 e 1 ((ccoonnttiinnueuedd))
Symbol Definition
L measured value of the length standard; orientation j (1 ≦ j ≦ n ), repetition i (1 ≦ i ≦ n )
Meas.ij LO LR
L measured value of the h-th length standard (1 ≦ h ≦ n ); orientation j (1 ≦ j ≦ n ), repetition i
Meas.ijh LN LO
(1 ≦ i ≦ n )
LR
u standard uncertainty attributed to the scale error
S
E average error of the probe size qualification
D
D measured value of the diameter of the probe verification standard; stylus j (1 ≦ j ≦ n ), repetition
Meas.ij PO
i (1 ≦ i ≦ n )
PR
u standard uncertainty attributed to the probe size error
D
E average error of the probe location qualification
PrbLoc
D diameter of the minimum circumscribed sphere enclosing the centres of the least-square spheres
MCS.i
of the probe verification standard measured with the n probe styli; repetition i (1 ≦ i ≦ n )
PO PR
u standard uncertainty attributed to the probe location error
PrbLoc
u (y) standard uncertainty attributed to the repeatability of the workpiece measurement
WR
u (y) standard uncertainty attributed to the randomized systematic errors of the CMM geometry and
WO
environment
u (y) standard uncertainty attributed to the interaction between the error of the CMM geometry and
WO×dist
environment, and the measurement points in the nominal sampling pattern on the feature element
u standard uncertainty attributed to temperature-related effects
temp
u uncertainty contributor which is undetected by the method described in this document, and have
UUC
been evaluated by other appropriate methods
5 Requirements for uncertainty assessment
The method requires that the measurement for each geometrical feature is performed with the nominal
sampling pattern of the measurement points on the surface of the geometrical feature. Defining the number
of the measurement points and the sampling scheme are parts of measurement strategy design, therefore,
they shall be selected to be suitable for the test purpose. This document specifies neither the default number
of measurement points on the surface of the geometrical feature nor the default sampling pattern.
The number of points and their pattern (defined outside the scope of this document) are sources of
measurement uncertainty, but those uncertainty components are not detected in this method and are
discussed in Annex E.
Likewise, the specification of the association, e.g., Gaussian or Chebyshev, is a part of the test protocol design,
therefore, it is out of the scope of this document even though it can be a source of undetected measurement
uncertainty. This document does not specify the association to be used. The initializations, conditions, and
preliminary procedures applied – or that will apply – to the actual measurement of the workpiece shall be
retained during the measurements to evaluate the uncertainty as described in this document.
NOTE 1 An example of a condition is whether and how the CMM compensates its geometry errors.
NOTE 2 Examples of preliminary procedures are the probe configuration and qualification.
6 Principle of measurement and uncertainty assessment
Essentially, a CMM measures single-point coordinates. The dimensions and geometrical deviations of the
features are computed from the set of measurement points sampled by the CMM. Therefore, the uncertainty
in the measured value of the dimensions or geometrical deviations is derived from the uncertainty of each
single point coordinates. This is a combination of various uncertainty contributors, which are difficult to
evaluate individually because of the complexity of a CMM measurement task.
In practice, combined uncertainties of measurements are dominated by random errors and systematic
errors. When a workpiece is measured on a CMM in one orientation, the measured coordinates of a single

point in the workpiece coordinate system include random and systematic errors. The errors derived from
the contributors are propagated to the machine coordinates of the CMM. The contributions of these factors
to the measurement uncertainty propagate and are categorized into components, such as the items listed in
an uncertainty budget.
If a measurement is made in a fixed orientation and environment, then, the measurement result is biased by
systematic errors. Even if the measurement is repeated and the measurement results are averaged, the bias
incurred by the orientation and environment is neither eliminated nor reduced. To eliminate or reduce the
effect of the bias and to evaluate the magnitude of it, extra independent measurements are necessary (see
Annex E.3).
Proper experimental design can help reduce the impact of unknown systematic errors by randomizing them.
One effective approach is to use multiple measurement techniques. Different instruments or environmental
conditions introduce unique systematic errors. When combined, these errors vary across measurements,
making them appear more like random errors. This approach mitigates the influence of systematic bias and
improves the accuracy of the results.
In the procedure of this document, a workpiece is measured in different orientations on a CMM. This
approach randomizes the contribution of many systematic errors in the respective measurements by
varying the magnitude and coefficient of the error propagation to the measured results. The systematic
error that occurs in CMM measurement is autocorrelated with the position and orientation of the measured
workpiece on the CMM, which means the points nearby have similar systematic errors. This autocorrelation
decreases with the distance from the original position and orientation. The effect of this systematic error is
assumed to follow a normal distribution with an expected value of zero and a standard deviation of u (y).
WO
The effect of the systematic error is then ideally neutralized by averaging the measurement results in
different orientations chosen for the randomization and becomes a randomized systematic error.
NOTE Some systematic errors are possibly not sufficiently randomized, such as those caused by fixturing, see
Annex E.
The contributions of random errors and systematic errors in multi-orientation measurements are evaluated
using two-way repeated measures analysis of variance (referred to as ANOVA in this document). ANOVA
separates the total variance into components attributed to distinct factors, such as random and systematic
sources, without double counting. This method helps identify critical sources of measurement uncertainty
by isolating their respective contributions.
Specifically, random errors correspond to the within-groups variance, while systematic errors are associated
with the between-groups variance. Simple calculations of between-groups variance from raw measurement
data inherently include within-groups variance, leading to double counting in uncertainty assessments. To
address this, ANOVA isolates the between-groups variance, ensuring it represents only the contributions of
systematic errors without overlap from random errors. This distinction is critical for accurate uncertainty
quantification in measurement experiments.
Even with performing multi-orientation measurements, some systematic errors in CMM measurements
are still not randomized. The dominant errors which are not randomized are the scaling error of the CMM
and the probe qualification error. The respective effects of these errors are assessed, and if necessary,
corrected. In addition, their contributions to the measurement uncertainty are evaluated, and included in
the computation of the measurement uncertainty.
7 Procedure
7.1 Measurements
7.1.1 General
Figure 1 shows the flowchart of the operation described in this document. The overall measurement
procedure consists of three steps:
a) multiple measurements of the workpiece;

b) measurements of length standards;
c) measurements of a test sphere.
All measurements are carried out in the same portion of the CMM measuring volume.
The repetitive measurements in one orientation are performed without re-alignment.
The multiple measurements of the workpiece are performed by repetition with several workpiece
orientations with the identical distribution of probing points and the identical measurement strategy. This
procedure is intended to randomize the systematic errors of the CMM including environmental fluctuation
surrounding the CMM.
The measurements of length standards – such as a gauge block – are executed with the standard in three
directions perpendicular to one another, typically along the X, Y and Z axes of the CMM. This procedure
is intended to capture the CMM scale errors, including thermal effects. The length standard should be
measured near or at the position of the workpiece.
The measurements of a test sphere are executed with all probe styli used for the previous steps and applying
the same probing mode(s) as used for the previous steps. This procedure is intended to investigate the
probing errors.
Figure 1 — Flowchart of the operation procedure
7.1.2 Multiple measurements on the workpiece
The workpiece is measured in four orientations as a default. Measurements in more orientations may be
performed to better randomize systematic effect. Figure 2 shows an example of the measurement setup
of a workpiece on the CMM. One orientation is referred to as the "home position". The others are example
orientations to randomize the systematic effects of the CMM.
To avoid a biased result, and to avoid the underestimation of the measurement uncertainty, the variety of
orientations of the workpiece shall be considered carefully. An insufficient variety of workpiece orientations
can fail to randomize the systematic effect of the CMM. This can result in unknown and uncompensated
biases being present in the calibration/test results, leading to an underestimation of measurement
uncertainty.
The workpiece orientation shall be chosen within the rated test conditions of the workpiece measurement.
Other than the home position, three orientations are recommended, obtained by rotating the artefact at
home position 90° in turn about the first CMM axis, obtained by rotating the artefact at home position 90° in
turn about the second CMM axis and obtained by rotating the artefact at home position 90° in turn about the
third CMM axis.
When the orientation of the workpiece against the direction of gravitational force is specified as a part of
test protocol, any orientation for the measurement shall satisfy the specification.
The measurements are carried out with an identical distribution of measured points (the same sampling
pattern) and with an identical measurement strategy, i.e. the number and nominal locations of the measured
points for extraction (see ISO 14406) and as well the probing strategy and the data point analysis (e.g.
filtering) are the same for all orientations. In the case that the method applies to calibration of the workpiece,
the actual distribution of the measured points shall be recorded.
The number of repetitions for each orientation is three by default.
When a CMM is known to have poor repeatability, e.g. the CMM exhibited a large R value in its acceptance/
reverification test or is specified with a large R value according to ISO 10360-2, the number of repetitions
0,MPE
may be increased at the discretion of the CMM user. For example, the CMM user chose the appropriate
number of repetitions against the measurement purpose by PUMA process (see ISO 14253-2).
Ideally the mounting method of the workpiece should be identical for each of the four orientations. But due
to the shape of the workpiece the mounting method of the workpiece, e.g. clamping, may be required to be
different. In order to perform a valid measurement series, the following aspects shall be controlled:
a) The workpiece deformation due to mounting shall be considered and, likewise, controlled.
b) Uncontrolled and exaptational workpiece deformation can be the source of additional measurement
uncertainty contributors, especially if the deformations are strong and different between orientations.
The results of all these measurements are the values y (see Table 2), where j = 1 . n indicates the
ij WO
orientation and i = 1 . n indicates the repeat within the same orientation.
WR
a) Orientation 1 b) Orientation 2
(home position) (Example: 90° rotated from home position about the
first axis of the CMM)
c) Orientation 3 d) Orientation 4
(Example: 90° rotated from home position about the (Example: 90° rotated from home position about the
second axis of the CMM) third axis of the CMM)
Key
X X-axis of the coordinate system on the CMM
Y Y-axis of the coordinate system on the CMM
Z Z-axis of the coordinate system on the CMM
WPO-i (i = 1, 2, 3, 4) workpiece in orientation-i
Figure 2 — Example of measurement setup of the workpiece in four orientations
Table 2 — Summary of measurement results of the workpiece
Orientation 1 Orientation 2 Orientation 3 Orientation 4
(home position)
Repeat 1 y y y y
11 12 13 14
Repeat 2 y y y y
21 22 23 24
Repeat 3 y y y y
31 32 33 34
7.1.3 Measurements of standards of length
Material standards of length (or a single standard featuring multiple test lengths) are measured in the same
portion of the CMM volume where the workpiece is measured. The results of the measurements of the length
standards are used for two purposes:
— for the compensation of the scale error of the CMM in the region of interest when corrected, and
— for the evaluation of the uncertainty derived from that scale error.
The measurements of length standards are performed in at least three orientations to quantify the
three-dimensional spatial scale error of the CMM in the portion of the CMM volume. The orientations are
approximately orthogonal to each other, typically aligned to the CMM axes. Figure 3 shows an example setup.
In each orientation, the length standards are measured at least three times.
NOTE When it is a priori known that the measurement repeatability of the CMM to be used is significantly large,
the number of repetitions may be larger than the default number of three.
Results are the values L in Table 3 and Table 4 with j = 1 . n indicating the orientation and i = 1 . n
Meas.ij LO LR
indicating the repetitions within the same orientation.
In the case the maximum size of the workpiece to be measured is small, or the purpose of the workpiece
measurement is the acceptance test for that workpiece, the measurement using a single length standard
may be sufficient even if the workpiece has multiple size features.
Ideally, the scale error values are detected without the influence of probing errors. Therefore, it is
recommended to measure the length standards in a unidirectional manner (see ISO 10360-2:2009, Annex B)
or E manner (see ISO 10360-13:2021, 3.12).
Vol
a) Orientation 1 b) Orientation 2
(Example: X axis direction) (Example: Y axis direction)

c) Orientation 3
(Example: Z axis direction)
Key
X X-axis of the coordinate system on the CMM
Y Y-axis of the coordinate system on the CMM
Z Z-axis of the coordinate system on the CMM
LS-i (i = X, Y, Z) length standards in direction of i
Figure 3 — Measurement setup of the length standard in three mutually orthogonal directions
Table 3 — Summary of measurement results of the length standard (for ANOVA)
Orientation 1 Orientation 2 Orientation 3
(X axis direction) (Y axis direction) (Z axis direction)
Repeat 1 L L L
Meas.11 Meas.12 Meas.13
Repeat 2 L L L
Meas.21 Meas.22 Meas.23
Repeat 3 L L L
Meas.31 Meas.32 Meas.33
Table 4 — Summary of measurement results of the length standards (for regression analysis)
Orientation 1 Orientation 2 Orientation 3
(X axis direction) (Y axis direction) (Z axis direction)
L Repeat 1 L L L
1 Meas.111 Meas.121 Meas.131
Repeat 2 L L L
Meas.211 Meas.221 Meas.231
Repeat 3 L L L
Meas.311 Meas.321 Meas.331
⋮ ⋮ ⋮ ⋮ ⋮
Repeat 1
L L L L
n Meas.11n Meas.12n Meas.13n
LN LN LN LN
Repeat 2 L L L
Meas.21n Meas.22n Meas.23n
LN LN LN
Repeat 3
L L L
Meas.31n Meas.32n Meas.33n
LN LN LN
7.1.4 Measurements for probe qualification error assessment
A test sphere for probe verification, is measured in the same portion of the CMM where the workpiece is
measured. The results of the measurements of the test sphere are used for two purposes:
— the compensation of the probing size error of the CMM;
— the evaluation of the uncertainty contribution originating from probing.
The test sphere to be used for probe verification shall be different from the reference sphere used for probe
qualification and shall be mounted at a different location. Figure 4 shows an example of the measurement
setup of the reference sphere to be used for probe qualification and the test sphere for verification on the
CMM.
a) Setup of reference sphere and test sphere for probe qualification and verification
b) Probe qualification c) Probe verification
Key
X X-axis of the coordinate system on the CMM
Y Y-axis of the coordinate system on the CMM
Z Z-axis of the coordinate system on the CMM
PS probe styli
RS reference sphere for probe qualification
TS test sphere for probe verification
Figure 4 — Measurement setup of the two different spheres for probe qualification and probe
verification
The test sphere is measured with each probe stylus used for measuring the workpiece and the length
standards, with a minimum of three measurements. The distribution of points, i.e. sampling pattern, shall
be identical for all. By default, 25 points evenly distributed over an accessible hemisphere of the test sphere
should be measured, as described in ISO 10360-5.
When it is a priori known that the measurement repeatability of the CMM to be used is significantly large,
the number of repetitions may be larger than the default number of three.
The least squares diameter and least squares centre coordinates of the test sphere are derived from each
set of individual measured points. Results are the diameters D of the single probes in Table 5 with
Meas.ij
j = 1 . n indicating the probe stylus to be used and i = 1 . n indicating the repetition with the same
PO PR
probe stylus.
Further, the diameter of the minimum circumscribed sphere enclosing the centres of the least square spheres
derived from the measurement points with the respective n probe styli for each repetition i = 1 . n ,
PO PR
results are the values D in Table 5.
MCS.i
Table 5 — Summary of measurement results of the sphere used for probe verification
Diameter as as- Diameter as as- Diameter as Diameter of
sessed with sessed with assessed with minimum
Probe 1 Probe 2 Probe n circumscribed
PO
… sphere around
sphere centres
assessed with
each probe
Repeat 1 D D … D D
Meas.11 Meas.12 Meas.1n MCS.1
PO
Repeat 2 … D
D D D
MCS.2
Meas.21 Meas.22 Meas.2n
PO
Repeat 3 D D … D D
Meas.31 Meas.32 Meas.3n MCS.3
PO
7.2 Evaluation of the measurement value
7.2.1 Calculation of measurement value y without error correction
corr
In case that neither the scale error(s) nor the error of the probe size qualification is corrected, the calibration/
test result value of the feature y is as follows;
result
yy= .
result
7.2.2 Calculation of the bias corrected measurement value y
corr
When corresponding error(s) is/are corrected, the calibration/test result value of the feature y is as
result
follows:
yy= ,
result corr
where y is calculated as shown in Table 6.
corr
Table 6 — The bias corrected measurement value corresponding to measured features
Measurand y
corr
Radius (external feature)
yEE /2
SD
Radius (internal feature)
yEE /2
SD
Linear size (external feature)
yEE
SD
Linear size (internal feature)
yEE
SD
Linear dimensions other than size,
yE−
S
Position
y
Geometrical deviation
Orientation
Angular dimension
NOTE 1 If only scale error(s) or the error of the probe size qualification is corrected the error of the uncorrected
influence (E or E ) must be set to zero.
S D
NOTE 2 Since the influences of the scale error and the probe size error on geometrical deviation, orientation and
angular dimension of the feature are negligible, the corrected value for those measurands y can be approximated
corr
by simply y.
7.3 Evaluation of the measurement uncertainty
The standard uncertainty of measurement of the feature is derived as follows;
2 2
uy uy
22 WR WO 2 22 22 2
uy EE   uy uuuuuu ,
 
result PrbLoc WOdist SD PrbLoc temp UUC
n n
WR WO
where,
2 2
E = (E + E /2) for radius (external feature),
S D
2 2
E = (E – E /2) for radius (internal feature),
S D
2 2
E = (E + E ) for linear size (external feature),
S D
2 2
E = (E – E ) for linear size (internal feature),
S D
2 2
E = E for linear distance,
S
2 2 2
E = E + E for deviations from a CAD element, position and profile related to datums,
S D
E = 0 for other features.
Each uncertainty component is calculated in accordance with Annex A.
E and/or E are only to be considered if the scale and/or probe size errors are not corrected. E = E = 0 if a
S D S D
correction is applied.
u and/or u are to be accounted only for the measurements sensitive to the scale error and/or the stylus tip
S D
radius. u = 0 and u = 0 for the remaining measurements.
s D
E is to be accounted only for measurements sensitive to the stylus tip radius (bidirectional probing). E = 0
D D
for the remaining measurements.
E and u are to be accounted only when multiple probe styli are used in same orientation of the
PrbLoc PrbLoc
workpiece. E = 0 and u = 0 when a single probe stylus is used in same orientation of the workpiece.
PrbLoc PrbLoc
u (y) is only required in the case of measurements of the deviation from CAD or associated (best-fitted)
WO×dist
elements (geometrical deviation of either a profile or a surface).
The examples of the practical uncertainty evaluations for individual workpieces are shown in Annex B. The
application of the uncertainty evaluation for lot inspections is shown in Annex C.
In Table 7, the uncertainty contributions for the measurement are listed.
Table 7 — Uncertainty components and their consideration in the uncertainty assessment
Uncertainty component Taken into account by:
E , E , E , u u (y) u (y), u
S D PrbLoc Pr- WR WO temp
u u bLoc u (y)
S D WO×dist
Point-to-point repeatabil-
ity
Resolution
Dirt on surface and rough-
ness
Geometry errors of the
CMM
Relative probe tip location
Probe tip directional char-
acteristic
TTaabblle 7 e 7 ((ccoonnttiinnueuedd))
Uncertainty component Taken into account by:
E , E , E , u u (y) u (y), u
S D PrbLoc Pr- WR WO temp
u u u (y)
bLoc
S D WO×dist
Probe tip diameter uncer-
tainty
Workpiece alignment
Temperature variation,
drift
Temperature gradient
variation
Clamping, handling
Temperature correction of
CMM
Temperature correction of
workpiece
Dynamic errors when
scanning
Not included in the normative elements of this document
Undetected uncertainty contribution: u
UUC
Finite sampling on surfaces (See Clause 5 and E.2.1).
Influence of the difference of sampling pattern (See Clause 5 and E.2.2).
Systematic errors due to deformation of the workpiece caused by inappropriate clamping (See E.3.1).
Systematic errors due to deformation of the workpiece caused by gravity (See E.3.2).
Systematic errors due to deformation of the workpiece when probing (See E.3.3).
Systematic errors due to the dynamics in scanning mode (See E.4).
Effect of the different functional properties of surface (See E.5).
8 Special considerations
8.1 Geometrical deviation measurement
8.1.1 General
The geometrical deviations are obtained as the range of the tangential distances of the measured points to
the associated feature. The uncertainty component u estimates the uncertainty of these tangential
result,point
distances.
Now, the uncertainty of the geometrical deviation is evaluated as 2u . Here n points are
MP
result,point
extracted on the surface of the feature to compute its geometrical deviation. Th
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