ENV ISO 14253-2:2001

SLOVENSKI STANDARD
01-januar-2002
Geometrical Product Specifications (GPS) - Inspection by measurement of
workpieces and measuring equipments - Guide to the estimation of uncertainty in
GPS measurement, in calibration of measuring equipment and in product
verification (ISO/TS 14253-2:1999)
Geometrical Product Specifications (GPS) - Inspection by measurement of workpieces
and measuring equipments - Part 2: Guide to the estimation of uncertainty in GPS
measurement, in calibration of measuring equipment and in product verification (ISO/TS
14253-2:1999)
Geometrische Produktspezifikationen (GPS) - Prüfung von Werkstücken und
Messgeräten durch Messungen - Teil 2: Leitfaden zur Schätzung der Unsicherheit von
GPS-Messungen bei der Kalibrierung von Messgeräten und bei der Produktprüfung
(ISO/TS 14253-2:1999)
Spécification géométrique des produits (GPS) - Vérification par la mesure des pieces et
des équipements de mesure - Guide pour l'estimation de l'incertitude de mesure dans
l'étalonnage des équipements de mesure et dans la vérification des produits (ISO/TS
14253-2:1999)
Ta slovenski standard je istoveten z: ENV ISO 14253-2:2001
ICS:
17.040.01 Linearne in kotne meritve na Linear and angular
splošno measurements in general
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

CORRECTED  2002-03-27
Foreword
The text of the Technical Specification from Technical Committee ISO/TC 213 "Dimensional and
geometrical product specifications and verification" of the International Organization for
Standardization (ISO) has been taken over as a European Prestandard by Technical Committee
CEN/TC 290 "Dimensional and geometrical product specification and verification", the
secretariat of which is held by AFNOR.
According to the CEN/CENELEC Internal Regulations, the national standards organizations of
the following countries are bound to announce this European Prestandard: Austria, Belgium,
Czech Republic, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy,
Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and the United
Kingdom.
Endorsement notice
The text of the International Technical Specification ISO/TS 14253-2:1999 has been approved
by CEN as a European Prestandard without any modifications.
NOTE Normative references to International Standards are listed in annex ZA (normative).
In other circumstances, particularly when there is an urgent market requirement for such
documents, a technical committee may decide to publish other types of normative document:
- an ISO Publicly Available Specification (ISO/PAS) represents an agreement
between technical experts in an ISO working group and is accepted for publication if
it is approved by more than 50 % of the members of the parent committee casting a
vote;
- an ISO Technical Specification (ISO/TS) represents an agreement between the
members of a technical committee and is accepted for publication if it is approved
by 2/3 of the members of the committee casting a vote.
An ISO/PAS or ISO/TS is reviewed every three years with a view to deciding whether it can be
transformed into an International Standard.
Attention is drawn to the possibility that some of the elements of this Technical Specification may
be the subject of patent rights. ISO shall not be held responsible for identifying any or all such
patent rights.
ISO/TS 14253-2 was prepared by Technical Committee ISO/TC 213, Dimensional and
geometrical product specifications and verification.
ISO 14253 consists of the following parts, under the general title, Geometrical product
specifications (GPS) – Inspection by measurement of workpieces and measuring equipment:
- Part 1: Decision rules for proving conformance or non-conformance with
specification
- Part 2: Guide to the estimation of uncertainty in GPS measurement, in calibration of
measuring equipment and in product verification [Technical Specification]
- Part 3: Procedures for evaluating the integrity of uncertainty in measurement values
Annexes A to D of this Technical Specification are for information only.
Annex ZA
(normative)
Normative references to international publications
with their relevant European publications
This European Standard incorporates by dated or undated reference, provisions from other
publications. These normative references are cited at the appropriate places in the text and the
publications are listed hereafter. For dated references, subsequent amendments to or revisions of
any of these publications apply to this European Standard only when incorporated in it by
amendment or revision. For undated references the latest edition of the publication referred to
applies (including amendments).
NOTE Where an International Publication has been modified by common modifications, indicated
by (mod.), the relevant EN/HD applies.
Publication Year Title EN Year
ISO 4288 1996 Geometrical product specifications EN ISO 4288 1997
(GPS) - Surface texture: Profile
method - Rules and procedures for
the assessment of surface texture
ISO 9001 2000 Quality management systems - EN ISO 9001 2000
Requirements
ISO 9004 2000 Quality management systems - EN ISO 9004 2000
Guidelines for performance
improvements
ISO 14253-1 1998 Geometrical Product Specifications EN ISO 14253-1 1998
(GPS) - Inspection by
measurement of workpieces and
measuring equipment - Part 1:
Decision rules for proving
conformance or non-conformance
with specifications
TECHNICAL ISO/TS
SPECIFICATION 14253-2
First edition
1999-12-01
Geometrical Product Specifications
(GPS) — Inspection by measurement of
workpieces and measuring equipment —
Part 2:
Guide to the estimation of uncertainty
in GPS measurement, in calibration
of measuring equipment and in product
verification
Spécification géométrique des produits (GPS) — Vérification par la mesure
des pièces et des équipements de mesure —
Partie 2: Guide pour l'estimation de l'incertitude dans les mesures GPS,
dans l'étalonnage des équipements de mesure et dans la vérification
des produits
Reference number
ISO/TS 14253-2:1999(E)
©
ISO 1999
ISO/TS 14253-2:1999(E)
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ii © ISO 1999 – All rights reserved

ISO/TS 14253-2:1999(E)
Contents Page
Foreword.iv
Introduction.v
1 Scope .1
2 Normative references .2
3 Terms and definitions .2
4 Symbols .6
5 Concept of the iterative GUM-method for estimation of uncertainty of measurement .7
6 Procedure for Uncertainty MAnagement — PUMA .8
7 Sources of errors and uncertainty of measurement.13
8 Tools for the estimation of uncertainty components, standard uncertainty and expanded
uncertainty.17
9 Practical estimation of uncertainty — Uncertainty budgeting with PUMA.26
10 Applications .30
Annex A (informative) Example of uncertainty budgets — Calibration of a setting ring.34
Annex B (informative) Example of uncertainty budgets — Design of a calibration hierarchy.41
Annex C (informative) Example of uncertainty budgets — Measurement of roundness .65
Annex D (informative) Relation to the GPS matrix model.71
Bibliography.73
© ISO 1999 – All rights reserved iii

ISO/TS 14253-2:1999(E)
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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 3.
The main task of technical committees is to prepare International Standards. Draft International Standards adopted
by the technical committees are circulated to the member bodies for voting. Publication as an International
Standard requires approval by at least 75 % of the member bodies casting a vote.
In other circumstances, particularly when there is an urgent market requirement for such documents, a technical
committee may decide to publish other types of normative document:
— an ISO Publicly Available Specification (ISO/PAS) represents an agreement between technical experts in an
ISO working group and is accepted for publication if it is approved by more than 50 % of the members of the
parent committee casting a vote;
— an ISO Technical Specification (ISO/TS) represents an agreement between the members of a technical
committee and is accepted for publication if it is approved by 2/3 of the members of the committee casting a
vote.
An ISO/PAS or ISO/TS is reviewed every three years with a view to deciding whether it can be transformed into an
International Standard.
Attention is drawn to the possibility that some of the elements of this Technical Specification may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO/TS 14253-2 was prepared by Technical Committee ISO/TC 213, Dimensional and geometrical product
specifications and verification.
ISO 14253 consists of the following parts, under the general title Geometrical product specifications (GPS) —
Inspection by measurement of workpieces and measuring equipment:
� Part 1: Decision rules for proving conformance or non-conformance with specification
� Part 2: Guide to the estimation of uncertainty in GPS measurement, in calibration of measuring equipment and
in product verification [Technical Specification]
� Part 3: Procedures for evaluating the integrity of uncertainty in measurement values
Annexes A to D of this Technical Specification are for information only.
iv © ISO 1999 – All rights reserved

ISO/TS 14253-2:1999(E)
Introduction
This Technical Specification is a global GPS technical report (see ISO/TR 14638:1995). This global GPS Technical
Report influences chain link 4, 5 and 6 in all chains of standards.
For more detailed information of the relation of this report to other standards and the GPS matrix model, see
annex D.
This Technical Specification is developed to support ISO 14253-1. This Technical Specification establishes a
simplified, iterative procedure of the concept and the way to evaluate and determine uncertainty (standard
uncertainty and expanded uncertainty) of measurement, and the recommendations of the format to document and
report the uncertainty of measurement information as given in "Guide to the expression of uncertainty in
measurement" (GUM). In most cases only very limited resources are necessary to estimate uncertainty of
measurement by this simplified, iterative procedure, but the procedure may lead to a slight overestimation of the
uncertainty of measurement. If a more accurate estimation of the uncertainty of measurement is needed, the more
elaborated procedures of the GUM must be applied.
This simplified, iterative procedure of the GUM methods is intended for GPS measurements, but may be used in
other areas of industrial (applied) metrology.
Uncertainty of measurement and the concept of handling uncertainty of measurement being of importance to all the
technical functions in a company, this Technical Specification relates to e.g. management function, design and
development function, manufacture function, quality assurance function, metrology function, etc.
This Technical Specification is of special importance in relation to ISO 9000 quality assurance systems, where
it is a requirement that the uncertainty of measurement is known [e.g. 4.11.1, 4.11.2 a) and 4.11.2 b) of
ISO 9001:1994].
In this Technical Specification the uncertainty of the result of a process of calibration and a process of
measurement is handled in the same way:
� calibration is treated as "measurement of metrological characteristics of a measuring equipment or a
measurement standard";
� measurement is treated as "measurement of geometrical characteristics of a workpiece".
Therefore, in most cases no distinction is made in the text between measurement and calibration. The term
"measurement" is used as a synonym for both.
© ISO 1999 – All rights reserved v

TECHNICAL SPECIFICATION ISO/TS 14253-2:1999(E)
Geometrical product specifications (GPS) — Inspection by
measurement of workpieces and measuring equipment —
Part 2:
Guide to the estimation of uncertainty in GPS measurement, in
calibration of measuring equipment and in product verification
1 Scope
This Technical Specification gives guidance on the implementation of the concept of "Guide to the estimation of
uncertainty in measurement" (in short GUM) to be applied in industry for the calibration of (measurement)
standards and measuring equipment in the field of GPS and the measurement of workpiece GPS-characteristics.
The aim is to promote full information on how to achieve uncertainty statements and provide the basis for
international comparison of results of measurements and their uncertainties (relationship between purchaser and
supplier).
This Technical Specification is intended to support ISO 14253-1. This Technical Specification and ISO 14253-1 are
beneficial to all technical functions in a company in the interpretation of GPS specifications (i.e. tolerances of
workpiece characteristics and values of maximum permissible errors (MPE) for metrological characteristics of
measuring equipment).
This Technical Specification introduces the Procedure for Uncertainty MAnagement (PUMA), which is a practical,
iterative procedure based on the GUM for estimating uncertainty of measurement without changing the basic
concepts of the GUM and is intended to be used generally for estimating uncertainty of measurement and giving
statements of uncertainty for:
� single results of measurement;
� comparison of two or more results of measurement;
� comparison of results of measurement — from one or more workpieces or pieces of measurement equipment
— with given specifications [i.e. maximum permissible errors (MPE) for a metrological characteristic of a
measurement instrument or measurement standard, and tolerance limits for a workpiece characteristic, etc.],
for proving conformance or non-conformance with the specification.
The iterative method is based basically on an upper bound strategy, i.e. overestimation of the uncertainty at all
levels, but the iterations control the amount of overestimation. Intentional overestimation — and not under-
estimation — is necessary to prevent wrong decisions based on measurement results. The amount of
overestimation shall be controlled by economical evaluation of the situation.
The iterative method is a tool to maximize profit and minimize cost in the metrological activities of a company. The
iterative method/procedure is economically self-adjusting and is also a tool to change/reduce existing uncertainty in
measurement with the aim of reducing cost in metrology (manufacture). The iterative method makes it possible to
compromise between risk, effort and cost in uncertainty estimation and budgeting.
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ISO/TS 14253-2:1999(E)
2 Normative references
The following normative documents contain provisions which, through reference in this text, constitute provisions of
this Technical Specification. For dated references, subsequent amendments to, or revisions of, any of these
publications do not apply. However, parties to agreements based on this Technical Specification are encouraged to
investigate the possibility of applying the most recent editions of the normative documents indicated below. For
undated references, the latest edition of the normative document referred to applies. Members of ISO and IEC
maintain registers of currently valid International Standards.
ISO 1:1975, Standard reference temperature for industrial length measurements.
ISO 4288:1996, Geometrical Product Specifications (GPS) — Surface texture: Profile method — Rules and
procedures for the assessment of surface texture.
ISO 9001:1994, Quality systems — Model for quality systems in design, development, production, installation and
servicing.
ISO 9004-1:1994, Quality management and quality system elements — Part 1: Guidelines.
ISO 14253-1:1998, Geometrical Product Specification (GPS) — Inspection by measurement of workpieces and
measuring instruments — Part 1: Decision rules for proving conformance or non-conformance with specifications.
1)
ISO 14253-3:— , Geometrical Product Specification (GPS) — Inspection by measurement of workpieces and
measuring instruments — Part 3: Procedures for evaluating the integrity of uncertainty of measurement values.
ISO 14660-1:1999, Geometrical Product Specification (GPS) — Geometric features — Part 1: General terms and
definitions.
Guide to the expression of uncertainty in measurement (GUM).BIPM, IEC, IFCC,ISO,IUPAC,IUPAP,OIML,
1st edition, 1995.
International Vocabulary of Basic and General Terms in Metrology (VIM). BIPM, IEC, IFCC, ISO, IUPAC, IUPAP,
OIML, 2nd edition, 1993.
3 Terms and definitions
For the purposes of this Technical Specification, the terms and definitions given in ISO 14253-1, ISO 14660-1, VIM,
GUM and the following apply.
3.1
black box model for uncertainty estimation
method of/model for uncertainty estimation in which the output value of a measurement is obtained in the same unit
as the input (stimuli), rather than by measurement of other quantities functionally related to the measurand
NOTE 1 In the black box model — in this Technical Specification — the uncertainty components are assumed additive, the
influence quantities is transformed to the unit of the measurand and the sensitivity coefficients are equal to 1.
NOTE 2 In many cases a complex method of measurement may be looked upon as one simple black box with stimulus in
and result out from the black box. When a black box is opened, it may turn out to contain several "smaller" black boxes and/or
several transparent boxes.
NOTE 3 The method of uncertainty estimation remains a black box method even if it is necessary to make supplementary
measurements to determine the values of influence quantities in order to make corresponding corrections.
1) To be published.
2 © ISO 1999 – All rights reserved

ISO/TS 14253-2:1999(E)
3.2
transparent box model for uncertainty estimation
method of/model for uncertainty estimation in which the value of a measurand is obtained by measurement of other
quantities functionally related to the measurand
3.3
measuring task
quantification of a measurand according to its definition
3.4
basic measurement task (basic measurement)
measurement task(s) which form the basis for evaluation of more complicated characteristics of a workpiece or a
measuring equipment
NOTE Examples of a basic measurement are:
a) one of several individual measurements of the deviation from straightness of a feature of a workpiece;
b) one of the individual measurements of error of indication of a micrometer when measuring the range of error of indication.
3.5
overall measurement task
complicated measuring task, which is evaluated on the basis of several and maybe different basic measurements
NOTE Examples of an overall measuring task are:
a) the measurement of straightness of a feature of a workpiece;
b) the range of error of indication of a micrometer.
3.6
expanded uncertainty (of a measurement)
U
[3.16 of ISO 14253-1:1998 and 2.3.5 of GUM:1995]
NOTE U (capital) always indicates expanded uncertainty of measurement.
3.7
true uncertainty
U
A
uncertainty of measurement that would be obtained by a perfect uncertainty estimation
NOTE 1 True uncertainties are by nature indeterminate.
NOTE 2 See also 8.8.
3.8
conventional true uncertainty — GUM uncertainty
U
c
uncertainty of measurement estimated completely according to the more elaborate procedures of GUM
NOTE 1 The conventional true uncertainty of measurement may differ from an uncertainty of measurement estimated
according to this Technical Specification.
NOTE 2 See also 8.8.
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ISO/TS 14253-2:1999(E)
3.9
approximated uncertainty
U
EN
uncertainty of measurement estimated by the simplified, iterative method
NOTE 1 The index N indicates that U is assessed by iteration number N. The designation U may be used without indication
EN E
of the iteration number, when it is without importance to know the number of iterations.
NOTE 2 See also 8.8.
3.10
target uncertainty (for a measurement or calibration)
U
T
uncertainty determined as the optimum for the measuring task
NOTE 1 Target uncertainty is the result of a management decision involving e.g. design, manufacturing, quality assurance,
service, marketing, sales and distribution.
NOTE 2 Target uncertainty is determined (optimized) taking into account the specification [tolerance or maximum
permissible error (MPE)], the process capability, cost, criticality and the requirements of 4.11.1, 4.11.2 of ISO 9001:1994, 13.1
of ISO 9004-1:1994 and ISO 14253-1.
NOTE 3 See also 8.8.
3.11
required uncertainty of measurement
U
R
uncertainty required for a given measurement process and task
NOTE See also 6.2. The required uncertainty may be specified by, for example, a customer.
3.12
uncertainty management
process of deriving an adequate measurement procedure from the measuring task and the target uncertainty by
using uncertainty budgeting techniques
3.13
uncertainty budget (for a measurement or calibration)
statement summarizing the estimation of the uncertainty components that contributes to the uncertainty of a result
of a measurement
NOTE 1 The uncertainty of the result of the measurement is unambiguous only when the measurement procedure (including
the measurement object, measurand, measurement method and conditions) is defined.
NOTE 2 The term "budget" is used for the assignment of numerical values to the uncertainty components, their combination
and expansion, based on the measurement procedure, measurement conditions and assumptions.
3.14
uncertainty contributor
xx
source of uncertainty of measurement for a measuring process
3.15
limit value (variation limit) for an uncertainty contributor
a
xx
absolute value of the extreme value(s) of the uncertainty contributor, xx
4 © ISO 1999 – All rights reserved

ISO/TS 14253-2:1999(E)
3.16
uncertainty component
u
xx
standard uncertainty of the uncertainty contributor, xx
NOTE The iteration method uses the designation u for all uncertainty components. This is not consistent with the present
xx
version of GUM which sometimes uses the designation s for uncertainty components evaluated by A evaluation and the
xx
designation u for uncertainty components evaluated by B evaluation.
xx
3.17
influence quantity of a measurement instrument
characteristic of a measuring instrument that affects the result of a measurement performed by the instrument
3.18
influence quantity of a workpiece
characteristic of a workpiece that affects the result of a measurement performed on that workpiece
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ISO/TS 14253-2:1999(E)
4 Symbols
For the purposes of this Technical Specification, the generic symbols given in Table 1 apply.
Table 1 — Generic symbols
Symbol Description
a
limit value for a distribution
a
limit value for an error or uncertainty contributor (in the unit of the result of measurement, of the measurand)
xx
a* limit value for an error or uncertainty contributor (in the unit of the influence quantity)
xx
linear coefficient of thermal expansion
�
b
coefficient for transformation of a to u
xx xx
C correction (value)
d
resolution of a measurement equipment
E
Young's modulus
ER error (value of a measurement)
G function of several measurement values [G( X , X , . X , .)]
1 2 i
h hysteresis value
k
coverage factor
m number of standard deviations in the half of a confidence interval
MR measurement result (value)
n number of .
N number of iterations
Poisson's number
�
p number of total uncorrelated uncertainty contributors
r number of total correlated uncertainty contributors
correlation coefficient
�
TV true value of a measurement
u, u standard uncertainty (standard deviation)
i
s
standard deviation of a sample
x
s
x standard deviation of a mean value of a sample
u combined standard uncertainty
c
u standard deviation of uncertainty contributor xx — uncertainty component
xx
U expanded uncertainty of measurement
U true uncertainty of measurement
A
U conventional true uncertainty of measurement
C
U approximated uncertainty of measurement (number of iteration not stated)
E
U approximated uncertainty of measurement of iteration number N
EN
U required uncertainty
R
U target uncertainty
T
U uncertainty value (not estimated according to GUM or this Technical Specification)
V
X measurement result (uncorrected)
X measurement result (in the transparent box model of uncertainty estimation)
i
Y measurement result (corrected)
6 © ISO 1999 – All rights reserved

ISO/TS 14253-2:1999(E)
5 Concept of the iterative GUM-method for estimation of uncertainty of measurement
Applying the GUM method completely one will find a conventional true uncertainty of measurement, U .
C
The simplified, iterative method/procedure of this Technical Specification is to achieve estimated uncertainties of
measurements, U by overestimating the influencing uncertainty components/contributors (U W U ). The process
E E C
of overestimating provides "worst-case-contributions" at the upper bound from each known or predictable
uncertainty contributor, thus ensuring results of estimations "on the safe side", i.e. not underestimating the
uncertainty of measurement. The simplified, iterative method of this Technical Specification is based on the
following:
� all uncertainty contributors are identified;
� it is decided which of the possible corrections shall be made (see 8.4.6);
� the influence on the uncertainty of the result of measurement from each contributor is evaluated as a standard
uncertainty u , called the uncertainty component;
xx
NOTE As a convention in the iterative method the influence of each contributor must be converted into the unit of the
measurand — using relevant physical equations/formulae and sensibility coefficients.
� an iteration process, PUMA (see clause 6);
� the evaluation of each of the uncertainty components (standard uncertainties) u can take place either by type
xx
A-evaluation or by type B-evaluation;
� type B-evaluation is preferred — if possible — in the first iteration in order to get a rough uncertainty estimate
to establish an overview and to save cost;
� the total effect of all contributors (called the combined standard uncertainty) is calculated by the formula:
22 2 2
uu��u�u� .�u (1)
c1xx2 x3 xn
� the formula (1) is only valid for a black box model of the uncertainty estimation and when the components u
xx
are all uncorrelated (for more details and other formulas see 8.6 and 8.7);
� for simplification the only correlation coefficients between contributors considered are
� =1, –1, 0 (2)
if the uncertainty components are not known to be uncorrelated, full correlation is assumed, either � =1 or� 1.
Correlated components are added arithmetically before put into the formula above (see 8.5 and 8.6);
� the expanded uncertainty U is calculated by the formula:
Uk��u (3)
c
where k =2; k is the coverage factor (see also 8.8);
The simplified, iterative method normally will consist of at least two iterations of estimating the components of
uncertainty.
a) The first very rough, quick and cheap iteration has the purpose of identifying the largest components of
uncertainty (see Figure 1);
b) The following iterations — if any — only deal with making more accurate "upper bound" estimates of the largest
components to lower the estimate of the uncertainty (u and U) to a possible acceptable magnitude.
c
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ISO/TS 14253-2:1999(E)
The simplified and iterative method may be used for two purposes:
a) Management of the uncertainty of measurement for a result of a given measurement process (can be used for
the results from a known measuring process or for comparison of two or more of such results) — see 6.2.
b) Uncertainty management for a measuring process. Development of an adequate measuring process i.e.
U u U — see 6.3.
E T
6 Procedure for Uncertainty MAnagement — PUMA
6.1 General
The prerequisite for uncertainty budgeting and management is a clearly identified and defined measuring task; i.e.
the measurand to be quantified (a GPS characteristic of a workpiece or a metrological characteristic of a GPS
measuring equipment). The uncertainty of measurement is a measure of the quality of the measured value
according to the definitions of a GPS characteristic of the workpiece or a metrological characteristic of the GPS
measuring equipment given in GPS standards.
GPS standards define the "conventional true values" (see 1.20 of VIM:1993) of the characteristics to be measured
by chains of standards and global standards (see ISO/TR 14638). GPS standards in many cases also define the
ideal — or conventional true — principle of measurement (see 2.3 of VIM:1993), method of measurement (see 2.4
of VIM:1993), measurement procedure (see 2.5 of VIM:1003) and Standard "reference conditions" (see 5.7 of
VIM:1993).
Deviations from the standardized conventional true values of the characteristics, etc. (the ideal operator) are
contributing to the uncertainty of measurement.
6.2 Uncertainty management for a given measurement process
Management of the uncertainty of measurement for a given measuring task (box 1 of Figure 1) and for an existing
measurement process is illustrated in Figure 1. The principle of measurement (box 3), measurement method
(box 4), measurement procedure (box 5) and measurement conditions (box 6) are fixed and given or decided in this
case, and cannot be changed. The only task is to evaluate the consequence on the uncertainty of measurement. A
required U may be given or decided.
R
Using the iterative GUM method the first iteration is only for orientation, and to look for the dominant uncertainty
contributors. The only thing to do — in the management process in this case — is to refine the estimation of the
dominant contributors to come closer to a true estimate of the uncertainty components thus avoiding a too big
overestimate — if necessary.
Figure 1 — Uncertainty management for a result of measurement from a given measurement process
8 © ISO 1999 – All rights reserved

ISO/TS 14253-2:1999(E)
The procedure is as follows:
a) make a first iteration based preferably on a black box model of the uncertainty estimation process and set up a
preliminary uncertainty budget (boxes 7 to 9) leading to the first rough estimate of the expanded uncertainty,
U (box 10). For details about uncertainty estimation see 9. All estimates of uncertainties U are performed
E1 EN
as upper bound estimates;
b) compare the first estimated uncertainty, U , with the required uncertainty U (box A) for the actual measuring
E1 R
task
1) If U is acceptable (i.e. if U u U ), then the uncertainty budget of the first iteration has proven that the
E1 E1 R
given measurement procedure is adequate for the measuring task (box 11);
2) If U is not acceptable (i.e. if U > U ) or if there is no required uncertainty, but a lower and more true
E1 E1 R
value is desired, the iteration process continues;
c) before the new iteration, analyze the relative magnitude of the uncertainty contributors. In many cases a few
uncertainty components dominate the combined standard uncertainty and expanded uncertainty;
d) change the assumptions or improve the knowledge about the uncertainty components to make a more
accurate (see 3.5 of VIM:1993) upper bound estimation of the largest (dominant) uncertainty components (box
12).
Change to a more detailed model of the uncertainty estimation process or a higher resolution of the measuring
process (box 12);
e) make the second iteration of the uncertainty budget (boxes 7 to 9) leading to the second, lower and more
accurate (see 3.5 of VIM:1993) upper bound estimate of the uncertainty of measurement, U (box 10);
E2
f) compare the second estimated uncertainty U (box A) with uncertainty required U for the actual measuring
E2 R
task
1) if U is acceptable (i.e. if U u U ), then the uncertainty budget of the second iteration has proven that
E2 E2 R
the given measurement procedure is adequate to the measuring task (box 11);
2) if U is not acceptable (i.e. if U > U ), or if there is no required uncertainty, but a lower and more true
E2 E2 R
value is desired, then a third (and possibly more) iteration(s) is (are) needed. Repeat the analysis of the
uncertainty contributors [additional changes of assumptions, improve in knowledge, changes in modelling,
etc. (box 12)] and concentrate on the currently largest uncertainty contributors;
g) when all possibilities have been used for making more accurate (lower) upper bound estimates of the
measuring uncertainties without coming to an acceptable measuring uncertainty U u U , then it is proven,
EN R
that it is not possible to fulfil the given requirement U .
R
6.3 Uncertainty management for design and development of a measurement process/procedure
Uncertainty management in this case is performed to develop an adequate measurement procedure [measurement
of the geometrical characteristics of a workpiece or the metrological characteristics of a measuring equipment
(calibration)]. Uncertainty management is performed on the basis of a defined measuring task (box 1 in Figure 2)
and a given target uncertainty, U (box 2 in Figure 2). Definition of the measuring task and target uncertainty are
T
company policy decisions to be made at a sufficiently high management level. An adequate measurement
procedure is a procedure which results in an estimated uncertainty of measurement less than or equal to the target
uncertainty. If the estimated uncertainty of measurement is much less than the target uncertainty, the measurement
procedure may not be (economically) optimal for performing the measuring task (i.e. the measurement process is
too costly).
© ISO 1999 – All rights reserved 9

ISO/TS 14253-2:1999(E)
The PUMA, based on a given measuring task (box 1) and a given target uncertainty U (box 2), includes the
T
following (see Figure 2):
a) choose the principle of measurement (box 3) on the basis of experience and possible measurement
instruments present in the company;
b) set up and document a preliminary method of measurement (box 4), measurement procedure (box 5) and
measurement conditions (box 6) on the basis of experience and known possibilities in the company;
c) make a first iteration based preferably on a black box model of the uncertainty estimation process and set up a
preliminary uncertainty budget (boxes 7 to 9) leading to the first rough estimate of the expanded uncertainty,
U (box 10). For details about uncertainty estimation see clause 9. All estimates of uncertainties U are
E1 EN
performed as upper bound estimates;
d) compare the first estimated uncertainty, U , with the given target uncertainty, U (box A);
E1 T
1) if U is acceptable (i.e. if U u U ), then the uncertainty budget of the first iteration has proven that the
E1 E1 T
measurement procedure is adequate for the measuring task (box 11);
2) if U << U , then the measurement procedure is technically acceptable, but a possibility may exist to
E1 T
change the method and/or the procedure (box 13) in order to make the measuring process more cost
effective while increasing the uncertainty. A new iteration is then needed to estimate the resulting
measurement uncertainty, U (box 10);
E2
3) if U is not acceptable (i.e. if U > U ), the iteration process continues, or it is concluded that no
E1 E1 T
adequate measurement procedure is possible;
e) before the new iteration, analyze the relative magnitude of the uncertainty contributors. In many cases a few
uncertainty components pre-dominate the combined standard uncertainty and expanded uncertainty;
f) if U > U , then change the assumptions, the modelling or increase the knowledge about the uncertainty
E1 T
components (box 12) to make a more accurate (see 3.5 of VIM:1993) upper bound estimation of the largest
(dominant) uncertainty components;
g) make the second iteration of the uncertainty budget (boxes 7 to 9) leading to the second, lower and more
accurate (see 3.5 of VIM:1993) upper bound estimate of the uncertainty of measurement, U (box 10);
E2
h) compare the second estimated uncertainty U with the given target uncertainty, U (box A);
E2 T
1) if U is acceptable (i.e. if U u U ), then the uncertainty budget of the second iteration has proven that
E2 E2 T
the measurement procedure is adequate for the measuring task (box 11);
2) if U is not acceptable (i.e. if U > U ) then a third (and possibly more) iteration(s) is (are) needed.
E2 E2 T
Repeat the analysis of the uncertainty contributors (additional changes of assumptions, modelling and
increase in knowledge (box 12)) and concentrate on the currently largest uncertainty contributors;
i) when all possibilities has been used for making more accurate (lower) upper bound estimates of the measuring
uncertainties without coming to an acceptable measuring uncertainty U u U , then a change of the
EN T
measurement method or the measurement procedure or the conditions of measurement (box 13) is needed to
(possibly) bring down the magnitude of the estimated uncertainty, U . The iteration procedure starts again
EN
with a first iteration;
j) if changes in the measurement method or the measurement procedure or conditions (box 13) do not lead to an
acceptable uncertainty of measurement, the final possibility is to change the principle of measurement (box 14)
and start the above mentioned procedure again;
10 © ISO 1999 – All rights reserved

ISO/TS 14253-2:1999(E)
k) if change of the measuring principle and the related iterations described above do not lead to an acceptable
uncertainty of measurement the ultimate possibility is to change the measuring task and/or target uncertainty
(box 15) and start the above mentioned procedure again;
l) if change of measuring task or target uncertainty is not possible, it is demonstrated, that no adequate
measurement procedure exists (box 16).
© ISO 1999 – All rights reserved 11

ISO/TS 14253-2:1999(E)
Figure 2 — Procedure for Uncertainty of Measurement MAnagement (PUMA) for a measurement
process/procedure
12 © ISO 1999 – All rights reserved

ISO/TS 14253-2:1999(E)
7 Sources of errors and uncertainty of measurement
7.1 Types of errors
Different types of errors regularly shows up in measurement results.
� systematic errors;
� random errors;
� drift;
� outliers.
All errors are by nature systematic. When we see errors as non-systematic it is because the reason for the error is
not looked for or because the level of resolution is not sufficient. Systematic errors may be characterised by size
and sign (+ or�).
ER = MR� TV
where
ER is the error,
MR is the measurement result;
TV is thetruevalue.
Random errors are systematic errors caused by non-controlled random influence quantities. Random errors may be
characterized by the standard deviation and the type of distribution. The mean value of the random errors is often
considered as a basis for the evaluation of the systematic error (see Figure 3).
Key
1 Outlier
2 Dispersion 1
3 Dispersion 2
4 Systematic error 1
5 Systematic error 2
6 True value
Figure 3 — Types of errors in results of measurements
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ISO/TS 14253-2:1999(E)
Drift is caused by a systematic influence of non-controlled influence quantities. Drift is often a time effect or a wear
effect. Drift may be characterized by change per unit time or per amount of u
...