ISO/DTS 15530-2

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

This document describes a procedure for the evaluation of the uncertainty of measurements with coordinate measuring machines (CMMs). The method described in this document uses multiple measurement strategies (multiple artefact orientations and repetitions), the measurement of standards of length and the measurement of standards for probe qualification error assessment. The task-specific measurement uncertainty is evaluated based on analysis of variance (ANOVA). This document is applicable to the conformity verification of products against their geometrical specifications in accordance with ISO 14253-1 or ISO/TR 14253-6. It is also applicable to the calibration of the geometrical properties of workpieces with the special consideration described in Clause 8.3. This document is also applicable to the task which needs the estimation or upper bounding of the task-specific measurement uncertainty, e.g. PUMA method in ISO 14253-2. Although this document has been prepared for measurements using CMMs equipped with tactile probing systems, it could be as well applicable to other coordinate measuring systems (CMSs). Note When applying this document to other types of CMSs, the testers should carefully consider the difference of the kinematic model and measurement error propagation between those of Cartesian CMMs and those of the systems to be used.

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

General Information

• Status: Not Published
• ICS: 17.040.30 - Measuring instruments
• ICS: 17.040.40 - Geometrical Product Specification (GPS)
• Technical Committee: ISO/TC 213 - Dimensional and geometrical product specifications and verification
• Drafting Committee: ISO/TC 213 - Dimensional and geometrical product specifications and verification
• Current Stage: 5020 - FDIS ballot initiated: 2 months. Proof sent to secretariat
• Start Date: 02-Oct-2025
• Completion Date: 02-Oct-2025

Standards Content (Sample)

FINAL DRAFT
Technical
Specification
ISO/TC 213
Geometrical product specifications
Secretariat: BSI
(GPS) — Coordinate measuring
Voting begins on:
machines (CMM): Technique for
2025-10-02
determining the uncertainty of
Voting terminates on:
measurement —
2025-11-27
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: Evaluation de l'incertitude de mesure spécifique à une
tâche par des stratégies de mesurage multiple utilisant une pièce
non-étalonnée
RECIPIENTS OF THIS DRAFT ARE INVITED TO SUBMIT,
WITH THEIR COMMENTS, NOTIFICATION OF ANY
RELEVANT PATENT RIGHTS OF WHICH THEY ARE AWARE
AND TO PROVIDE SUPPOR TING DOCUMENTATION.
IN ADDITION TO THEIR EVALUATION AS
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO-
LOGICAL, COMMERCIAL AND USER PURPOSES, DRAFT
INTERNATIONAL STANDARDS MAY ON OCCASION HAVE
TO BE CONSIDERED IN THE LIGHT OF THEIR POTENTIAL
TO BECOME STAN DARDS TO WHICH REFERENCE MAY BE
MADE IN NATIONAL REGULATIONS.
Reference number
FINAL DRAFT
Technical
Specification
ISO/TC 213
Geometrical product specifications
Secretariat: BSI
(GPS) — Coordinate measuring
Voting begins on:
machines (CMM): Technique for
determining the uncertainty of
Voting terminates on:
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: Evaluation de l'incertitude de mesure spécifique à une
tâche par des stratégies de mesurage multiple utilisant une pièce
non-étalonnée
RECIPIENTS OF THIS DRAFT ARE INVITED TO SUBMIT,
WITH THEIR COMMENTS, NOTIFICATION OF ANY
RELEVANT PATENT RIGHTS OF WHICH THEY ARE AWARE
AND TO PROVIDE SUPPOR TING DOCUMENTATION.
© ISO 2025
IN ADDITION TO THEIR EVALUATION AS
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO-
LOGICAL, COMMERCIAL AND USER PURPOSES, DRAFT
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
INTERNATIONAL STANDARDS MAY ON OCCASION HAVE
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
TO BE CONSIDERED IN THE LIGHT OF THEIR POTENTIAL
or ISO’s member body in the country of the requester.
TO BECOME STAN DARDS TO WHICH REFERENCE MAY BE
MADE IN NATIONAL REGULATIONS.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland Reference number
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 . 5
7.1 Measurements . .5
7.1.1 General .5
7.1.2 Multiple measurements on the workpiece .6
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 test . 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
ISO technical committees. Each member body interested in a subject for which a technical committee
has been established has the right to be represented on that committee. International organizations,
governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely
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)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent
rights in respect thereof. As of the date of publication of this document, ISO had not received notice of (a)
patent(s) which may be required to implement this document. However, implementers are cautioned that
this may not represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions
related to conformity assessment, as well as information about ISO's adherence to the World Trade
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 geometric 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 inve
...

ISO/TS DTS 15530-2:2025(E)
ISO /TC 213/WG 10
Secretariat: BSI
Date:
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
Spécification géométrique des produits (GPS) — Machines à mesurer tridimensionnelles (MMT): Technique
pour la détermination de l'incertitude de mesure —
Partie 2: Evaluation de l'incertitude de mesure spécifique à une tâche par des stratégies de mesurage multiple
utilisant une pièce non-étalonnée

ISO/TS DTS 15530-2:2025(E:(en)
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication
may be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying,
or posting on the internet or an intranet, without prior written permission. Permission can be requested from either ISO
at the address below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: + 41 22 749 01 11
EmailE-mail: [e-mail]
Website: www.iso.orgwww.iso.org
Published in Switzerland
© ISO 2025 – All rights reserved

ii
ISO/TS DTS 15530-2:2025(E:(en)
Contents
Foreword . iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols . 2
5 Requirements for uncertainty assessment . 4
6 Principle of measurement and uncertainty assessment . 4
7 Procedure . 5
7.1 Measurements . 5
7.2 Evaluation of the measurement value . 15
7.3 Evaluation of the measurement uncertainty . 16
8 Special considerations . 19
8.1 Geometrical deviation measurement . 19
8.2 Tolerances . 20
8.3 Calibration . 20
Annex A (normative) Formulae . 22
Annex B (informative) Examples for calibration/test use . 32
Annex C (informative) Application for lot inspection in conformance test . 51
Annex D (normative) Calculation of the coverage factor k using the effective degrees of freedom53
Annex E (informative) Guidance of the undetected uncertainty contributors . 55
Annex F (informative) Relation to the GPS matrix model . 58
Bibliography . 60

© ISO 2025 – All rights reserved

iii
ISO/TS DTS 15530-2:2025(E:(en)
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
ISO technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely 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 documentsdocument should be noted. This document was drafted in accordance with the editorial rules
of the ISO/IEC Directives, Part 2 (see www.iso.org/directiveswww.iso.org/directives). ).
Attention is drawnISO draws attention to the possibility that some of the elementsimplementation of this
document may beinvolve the subjectuse of (a) patent(s). ISO takes no position concerning the evidence,
validity or applicability of any claimed patent rights in respect thereof. As of the date of publication of this
document, ISO had not received notice of (a) patent(s) which may be required to implement this document.
However, implementers are cautioned that this may not represent the latest information, which may be
obtained from the patent database available at www.iso.org/patents. ISO shall not be held responsible for
identifying any or all such patent rights. Details of any patent rights identified during the development of the
document will be in the Introduction and/or on the ISO list of patent declarations received (see
www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions
related to conformity assessment, as well as information about ISO's adherence to the World Trade
Organization (WTO) principles in the Technical Barriers to Trade (TBT), see
www.iso.org/iso/foreword.htmlwww.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.htmlwww.iso.org/members.html.
© ISO 2025 – All rights reserved

iv
ISO/TS DTS 15530-2:2025(E:(en)
Introduction
This document is a geometrical product specification (GPS) Technical Specification.). 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 standarddocument to the GPS matrix model, see Annex F.
.
Coordinate measuring systems (CMS) have become essential for verifying geometric 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 mightcan 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 desiredsought regarding its usage and
performance within its scope (i.e., on contact Cartesian Coordinate Measuring MachineCMM). 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.

© ISO 2025 – All rights reserved

v
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 of the instrument when verifying
measurements 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 specificationsProduct 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, Guide to the expression of uncertainty inUncertainty 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, VIM and GUMISO/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
© ISO 2025 – All rights reserved

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 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 EAnnex E. .
4 Symbols
For the purpose of this document, the symbols given in Table 1 apply.
Table 1 — Symbols
Symbol InterpretationDefinition
u(y ) standard uncertainty of the final corrected result of the measurement
result
U(yresult) expanded uncertainty of th
...

PROJET FINAL
Spécification
technique
ISO/TC 213
Spécification géométrique des
Secrétariat: BSI
produits (GPS) — Machines à
Début de vote:
mesurer tridimensionnelles (MMT)
2025-10-02
: Technique pour la détermination
Vote clos le:
de l'incertitude de mesure —
2025-11-27
Partie 2:
Utilisation de plusieurs orientations
de la pièce et d'étalons simples
étalonnés
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
LES DESTINATAIRES DU PRÉSENT PROJET SONT
INVITÉS À PRÉSENTER, AVEC LEURS OBSERVATIONS,
NOTIFICATION DES DROITS DE PROPRIÉTÉ DONT ILS
AURAIENT ÉVENTUELLEMENT CONNAISSANCE ET À
FOURNIR UNE DOCUMENTATION EXPLICATIVE.
OUTRE LE FAIT D’ÊTRE EXAMINÉS POUR
ÉTABLIR S’ILS SONT ACCEPTABLES À DES FINS
INDUSTRIELLES, TECHNOLOGIQUES ET COM-MERCIALES,
AINSI QUE DU POINT DE VUE DES UTILISATEURS, LES
PROJETS DE NORMES
INTERNATIONALES DOIVENT PARFOIS ÊTRE CONSIDÉRÉS
DU POINT DE VUE DE LEUR POSSI BILITÉ DE DEVENIR DES
NORMES POUVANT
SERVIR DE RÉFÉRENCE DANS LA RÉGLEMENTATION
NATIONALE.
Numéro de référence
PROJET FINAL
Spécification
technique
ISO/TC 213
Spécification géométrique des
Secrétariat: BSI
produits (GPS) — Machines à
Début de vote:
mesurer tridimensionnelles (MMT)
2025-10-02
: Technique pour la détermination
Vote clos le:
de l'incertitude de mesure —
2025-11-27
Partie 2:
Utilisation de plusieurs orientations
de la pièce et d'étalons simples
étalonnés
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
LES DESTINATAIRES DU PRÉSENT PROJET SONT
INVITÉS À PRÉSENTER, AVEC LEURS OBSERVATIONS,
NOTIFICATION DES DROITS DE PROPRIÉTÉ DONT ILS
AURAIENT ÉVENTUELLEMENT CONNAISSANCE ET À
FOURNIR UNE DOCUMENTATION EXPLICATIVE.
DOCUMENT PROTÉGÉ PAR COPYRIGHT
OUTRE LE FAIT D’ÊTRE EXAMINÉS POUR
ÉTABLIR S’ILS SONT ACCEPTABLES À DES FINS
© ISO 2025 INDUSTRIELLES, TECHNOLOGIQUES ET COM-MERCIALES,
AINSI QUE DU POINT DE VUE DES UTILISATEURS, LES
Tous droits réservés. Sauf prescription différente ou nécessité dans le contexte de sa mise en œuvre, aucune partie de cette
PROJETS DE NORMES
INTERNATIONALES DOIVENT PARFOIS ÊTRE CONSIDÉRÉS
publication ne peut être reproduite ni utilisée sous quelque forme que ce soit et par aucun procédé, électronique ou mécanique,
DU POINT DE VUE DE LEUR POSSI BILITÉ DE DEVENIR DES
y compris la photocopie, ou la diffusion sur l’internet ou sur un intranet, sans autorisation écrite préalable. Une autorisation peut
NORMES POUVANT
être demandée à l’ISO à l’adresse ci-après ou au comité membre de l’ISO dans le pays du demandeur.
SERVIR DE RÉFÉRENCE DANS LA RÉGLEMENTATION
NATIONALE.
ISO copyright office
Case postale 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Genève
Tél.: [phone]
E-mail: [e-mail]
Web: www.iso.org
Publié en Suisse Numéro de référence
ii
Sommaire Page
Avant-propos .iv
Introduction .v
1 Domaine d'application . 1
2 Références normatives . 1
3 Termes et définitions . 1
4 Symboles . 2
5 Exigences relatives à l'évaluation de l'incertitude . 3
6 Principe de mesurage et d'évaluation de l'incertitude .4
7 Procédure . 5
7.1 Mesurages .5
7.1.1 Généralités .5
7.1.2 Mesurages multiples sur la pièce .6
7.1.3 Mesurages des étalons de longueur .8
7.1.4 Mesurages pour l'évaluation de l'erreur de qualification du palpeur .10
7.2 Évaluation de la valeur de mesure . 12
7.2.1 Calcul de la valeur de mesure y sans correction d'erreur . 12
corr
7.2.2 Calcul de la valeur de mesure corrigée de l'erreur de justesse y . 12
corr
7.3 Évaluation de l'incertitude de mesure. 13
8 Considérations spéciales . 14
8.1 Mesurage d'écart géométrique.14
8.1.1 Généralités .14
8.1.2 Cas d'informations complètes . 15
8.1.3 Cas où les informations sont moindres .16
8.2 Tolérances .16
8.3 Étalonnage .16
8.3.1 Exigences relatives à la traçabilité .16
8.3.2 Éviter les erreurs de justesse inconnues et les autres sous-estimations de
l'incertitude .16
8.3.3 Calcul de l'incertitude de mesure étendue .16
Annexe A (normative) Formules .18
Annexe B (informative) Exemples d'utilisation pour l'étalonnage/l'essai .27
Annexe C (informative) Application pour le contrôle du lot durant un essai de conformité .42
Annexe D (normative) Calcul du facteur d'élargissement k en utilisant le nombre effectif de
degrés de liberté .44
Annexe E (informative) Recommandations relatives aux contributeurs à l'incertitude non
détectés .46
Annexe F (informative) Relation avec le modèle de matrice GPS .49
Bibliographie .50

iii
Avant-propos
L'ISO (Organisation internationale de normalisation) est une fédération mondiale d'organismes nationaux
de normalisation (comités membres de l'ISO). L'élaboration des Normes internationales est en général
confiée aux comités techniques de l'ISO. Chaque comité membre intéressé par une étude a le droit de faire
partie du comité technique créé à cet effet. Les organisations internationales, gouvernementales et non
gouvernementales, en liaison avec l'ISO participent également aux travaux. L'ISO collabore étroitement avec
la Commission électrotechnique internationale (IEC) en ce qui concerne la normalisation électrotechnique.
Les procédures utilisées pour élaborer le présent document et celles destinées à sa mise à jour sont
décrites dans les Directives ISO/IEC, Partie 1. Il convient, en particulier, de prendre note des différents
critères d'approbation requis pour les différents types de documents ISO. Le présent document
a été rédigé conformément aux règles de rédaction données dans les Directives ISO/IEC, Partie 2
(voir www.iso.org/directives).
L’ISO attire l’attention sur le fait que la mise en application du présent document peut entraîner l’utilisation
d’un ou de plusieurs brevets. L’ISO ne prend pas position quant à la preuve, à la validité et à l’applicabilité de
tout droit de propriété revendiqué à cet égard. À la date de publication du présent document, l’ISO n'avait pas
reçu notification qu’un ou plusieurs brevets pouvaient être nécessaires à sa mise en application. Toutefois,
il y a lieu d’avertir les responsables de la mise en application du présent document que des informations
plus récentes sont susceptibles de figurer dans la base de données de brevets, disponible à l'adresse
www.iso.org/brevets. L’ISO ne saurait être tenue pour responsable de ne pas avoir identifié tout ou partie de
tels droits de propriété.
Les appellations commerciales éventuellement mentionnées dans le présent document sont données pour
information, par souci de commodité, à l’intention des utilisateurs et ne sauraient constituer un engagement.
Pour une explication de la nature volontaire des normes, la signification des termes et expressions
spécifiques de l'ISO liés à l'évaluation de la conformité, ou pour toute information au sujet de l'adhésion de
l'ISO aux principes de l’Organisation mondiale du commerce (OMC) concernant les obstacles techniques au
commerce (OTC), voir www.iso.org/avant-propos.
Le présent document a été élaboré par le comité technique ISO/TC 213, Spécifications et vérification
dimensionnelles et géométriques des produits.
Une liste de toutes les parties de la série ISO 15530 se trouve sur le site web de l'ISO.
Il convient que l'utilisateur adresse tout retour d'information ou toute question concernant le présent
document à l'organisme national de normalisation de son pays. Une liste exhaustive desdits organismes se
trouve à l'adresse www.iso.org/fr/members.html.

iv
Introduction
Le présent document est une spécification géométrique des produits (GPS). Elle influence le maillon G des
chaînes de normes sur la taille, la distance, la forme, l'orientation, la position et le battement dans la matrice
GPS générale (voir l’Annexe F).
Le modèle de matrice ISO GPS de l'ISO 14638 donne une vue d'ensemble du système ISO GPS, dont le présent
document fait partie. Les principes fondamentaux du système ISO GPS, donnés dans l'ISO 8015, s'appliquent
au présent document et les règles de décision par défaut, données dans l'ISO 14253-1, s'appliquent aux
spécifications faites conformément au présent document, sauf indication contraire.
Pour de plus amples informations sur la relation du présent document avec le modèle de matrice GPS, voir
l’Annexe F.
Les systèmes de mesure tridimensionnels (SMT) sont devenus essentiels pour la vérification des données
géométriques dans l'industrie. Selon la série de normes ISO 9000, dans un système de management de la
qualité, il est requis d'étalonner l’équipement de mesure approprié par rapport à un équipement certifié
ayant une relation connue et valable avec les étalons reconnus au niveau national ou international afin
d'établir la traçabilité. Conformément le Guide ISO/IEC 99, Vocabulaire international des termes fondamentaux
et gé
...