ISO/DTR 22514-9.2

Statistical methods in process management — Capability and performance — Part 9: Process capability statistics for characteristics defined by geometrical specifications

Méthodes statistiques dans la gestion de processus — Aptitude et performance — Partie 9: Méthodes statistiques pour l'aptitude des processus dont les caractéristiques sont définies par des spécifications géométriques

General Information

• Status: Not Published
• ICS: 03.120.30 - Application of statistical methods
• Technical Committee: ISO/TC 69/SC 4 - Applications of statistical methods in product and process management
• Drafting Committee: ISO/TC 69/SC 4/WG 11 - Process capability and performance
• Current Stage: 5020 - FDIS ballot initiated: 2 months. Proof sent to secretariat
• Start Date: 04-Sep-2023
• Completion Date: 04-Sep-2023

Standards Content (Sample)

FINAL
TECHNICAL ISO/DTR
DRAFT
REPORT 22514-9
ISO/TC 69/SC 4
Statistical methods in process
Secretariat: DIN
management — Capability and
Voting begins on:
2023-04-18 performance —
Voting terminates on:
Part 9:
2023-06-13
Process capability statistics for
characteristics defined by geometrical
specifications
Méthodes statistiques dans la gestion de processus — Aptitude et
performance —
Partie 9: Méthodes statistiques pour l'aptitude des processus dont les
caractéristiques sont définies par des spécifications géométriques
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
Reference number
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO-
ISO/DTR 22514-9:2023(E)
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. © ISO 2023

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FINAL
TECHNICAL ISO/DTR
DRAFT
REPORT 22514-9
ISO/TC 69/SC 4
Statistical methods in process
Secretariat: DIN
management — Capability and
Voting begins on:
performance —
Voting terminates on:
Part 9:
Process capability statistics for
characteristics defined by geometrical
specifications
Méthodes statistiques dans la gestion de processus — Aptitude et
performance —
Partie 9: Méthodes statistiques pour l'aptitude des processus dont les
caractéristiques sont définies par des spécifications géométriques
COPYRIGHT PROTECTED DOCUMENT
© ISO 2023
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
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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.
RECIPIENTS OF THIS DRAFT ARE INVITED TO
ISO copyright office
SUBMIT, WITH THEIR COMMENTS, NOTIFICATION
OF ANY RELEVANT PATENT RIGHTS OF WHICH
CP 401 • Ch. de Blandonnet 8
THEY ARE AWARE AND TO PROVIDE SUPPOR TING
CH-1214 Vernier, Geneva
DOCUMENTATION.
Phone: [phone]
IN ADDITION TO THEIR EVALUATION AS
Reference number
Email: [e-mail]
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO-
ISO/DTR 22514-9:2023(E)
Website: www.iso.org
LOGICAL, COMMERCIAL AND USER PURPOSES,
DRAFT INTERNATIONAL STANDARDS MAY ON
Published in Switzerland
OCCASION HAVE TO BE CONSIDERED IN THE
LIGHT OF THEIR POTENTIAL TO BECOME STAN-
DARDS TO WHICH REFERENCE MAY BE MADE IN
ii
  © ISO 2023 – All rights reserved
NATIONAL REGULATIONS. © ISO 2023

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ISO/DTR 22514-9:2023(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
3.1 Terms. 1
3.2 Abbreviated terms . 4
3.3 Symbols . 4
4 Statistical measures used in the calculation of process capability or performance .5
4.1 General . 5
4.2 Independency principle . 5
4.2.1 General . 5
4.2.2 Maximum Material ISO versus ASME . 6
4.2.3 Measurement procedure . 6
4.3 Location . 6
4.4 Dispersion . 6
4.5 Reference limits . 6
4.6 Reference interval . 6
5 Geometrical product specifications .6
5.1 General . 6
5.2 Linear size with modifiers . 7
5.3 ISO tolerance classes with modifier . 8
6 Capability calculation on features defined by geometrical tolerances .9
6.1 General . 9
6.2 Form, orientation, location and run out tolerances . 10
6.3 Location tolerances . 10
6.4 Example on capability calculation in case of known inverse distribution function .12
7 Maximum material requirement .14
7.1 Information about maximum material requirement . 14
7.2 Calculation of results .15
7.3 Least material requirement LMR . 20
7.4 Methodology . 21
Annex A (informative) Distribution identification .23
Annex B (informative) Distributions used in case of geometrical tolerances .26
Annex C (informative) Number of points to be collected .28
Annex D (informative) Process analysis for improvement .31
Bibliography .33
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ISO/DTR 22514-9:2023(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.
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 documents 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).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. 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 on 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 the following
URL: www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 4, Applications of statistical methods in process management.
This document is a second draft for approval and only editorial changes will be made before publication.
A list of all parts in the ISO 22514 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.
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ISO/DTR 22514-9:2023(E)
Introduction
Many organizations will need to evaluate the capability and performance of their key processes when
the specifications are defined by requirements other than linear size. The methods described in this
document are intended to assist the organization in this respect.
During the last couple of years, it has more common in the design and development departments in
companies to not only use linear tolerances alone, but also including modifiers as well as geometrical
tolerances with or without use of the maximum material requirements.
This situation has been supported by new measurement methods used in production, where it is
common to use measurement equipment, where the results are given in form of point clouds instead of
one single value.
It is a challenge in such cases to calculate capability and performance, but organizations and customers
still require the capability indices in acceptance of produced or delivered batches of parts.
This document describes how to calculate capability or performance where functional requirements on
parts are given.
As an example, the “maximum material requirement”, MMR, covers “assemble ability” and the “least
material requirement”, LMR, covers, for example, “minimum wall thickness” of a part. Each requirement
(MMR and LMR) combines two independent requirements into one collective requirement, which
simulates the intended function of the workpiece. In some cases of both MMR and LMR, the “reciprocity
requirement”, RPR, can be added.
In Annex D, a case study of process analysis, where the characteristic to be improved is perpendicularity,
is introduced.
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TECHNICAL REPORT ISO/DTR 22514-9:2023(E)
Statistical methods in process management — Capability
and performance —
Part 9:
Process capability statistics for characteristics defined by
geometrical specifications
1 Scope
This document describes process capability and performance measures when the specifications are
given by geometrical product specifications e.g. maximum material requirements or linear size with a
modifier.
The purpose of this document of the international series of standards on capability calculation is to
assist the organizations to calculate the PCIs when geometrical product specifications are used on
drawings.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological 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 Terms
3.1.1
feature of size
feature of linear size
geometrical feature, having one or more intrinsic characteristics, only one of which can be considered as
variable parameter, that additionally is a member of a “one parameter family”, and obeys the monotonic
containment property for that parameter
EXAMPLE 1 A single cylindrical hole or shaft is a feature of linear size. Its linear size is its diameter.
EXAMPLE 2 Two opposite parallel plane surfaces are a feature of linear size. Its linear size is the distance
between the two parallel planes.
[SOURCE: ISO 17450-1:2011, 3.3.1.5.1., modified: deleted Note 1 to Note 4, deleted reference to Figure 5
(ISO 17450-1:2011), deleted EXAMPLE 2, added new EXAMPLE 2]
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ISO/DTR 22514-9:2023(E)
3.1.2
local size
local linear size
local size characteristic
local linear size characteristic
size characteristic having by definition a non-unique result of evaluation along and/or around the
feature of size
Note 1 to entry: For a given feature, an infinity of local sizes exists.
[SOURCE: ISO 14405-1:2016, 3.6]
3.1.3
two-point size
distance between two opposite points on an extracted integral linear feature of size
Note 1 to entry: A two-point size taken on a cylinder can be called a “two-point diameter”. In ISO 17450-3, this is
defined as a local diameter of an extracted cylinder.
Note 2 to entry: A two-point size taken on two opposite planes can be called “two-point distance”. In ISO 17450-3,
this is defined as a local size of two parallel extracted surfaces.
[SOURCE: ISO 14405-1:2016, 3.6.1, modified: deleted Note 1 to entry to Note 3 to entry, added two new
notes]
3.1.4
envelope requirement
combination of the two-point size applied for the least material limit of the size and either the minimum
circumscribed size or the maximum inscribed size for the maximum material limit of the size
Note 1 to entry: The “envelope requirement” was previously referred to as the “Taylor principle”.
Note 2 to entry: According to ISO 8015, the surface of a single feature of size (e.g. cylindrical surface or a feature
based on two parallel plane surfaces) cannot violate the envelope of a geometrical ideal form at a maximum
material limit of size
[SOURCE: ISO 14405-1:2016, 3.8, modified: Note 2 to entry added]
3.1.5
maximum material virtual size
MMVS
size generated by the collective effect of the maximum material size, MMS, of a feature of size and the
geometrical tolerance (form, orientation or location) given for the derived feature of the same feature
of size
Note 1 to entry: Maximum material virtual size, MMVS, is a parameter for size used as a numerical value
connected to maximum material virtual condition, MMVC.
Note 2 to entry: For external features, MMVS is the sum of MMS and the geometrical tolerance, whereas for
internal features, it is the difference between MMS and the geometrical tolerance.
Note 3 to entry: The MMVS for external features of size, l , is given by the following formula:
MMVS,e
l = l + δ
MMVS,e MMS
and the MMVS for internal features of size, l , is given by the following one:
MMVS,i
l = l − δ
MMVS,i MMS
where
2
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ISO/DTR 22514-9:2023(E)
l is the maximum material size;
MMS
δ is the geometrical tolerance.
3.1.6
least material virtual size
LMVS
size generated by the collective effect of the least material size, LMS, of a feature of size and the
geometrical tolerance (form, orientation or location) given for the derived feature of the same feature
of size
Note 1 to entry: Least material virtual size, LMVS, is a parameter for size used as a numerical value connected to
least material virtual condition, LMVC.
Note 2 to entry: For external features, LMVS is the difference between LMS and the geometrical tolerance,
whereas for internal features, it is the sum of LMS and the geometrical tolerance.
Note 3 to entry: The LMVS for external features of size, l , is given by the following formula:
LMVS,e
l = l − δ
LMVS,e LMS
and the LMVS for internal features of size, l , is given by the following one:
LMVS,i
l = l + δ
LMVS,i LMS
where
l is the least material size;
LMS
δ is the geometrical tolerance.
3.1.7
maximum material requirement
MMR
requirement for a feature of size, defining a geometrical feature of the same type and of perfect form,
with a given value for the intrinsic characteristic (dimension) equal to the maximum material virtual
size, which limits the non-ideal feature on the outside of the material
Note 1 to entry: Maximum material requirement, MMR, is used to control the assembly ability of a workpiece.
[SOURCE: ISO 2692:2021, 3.12]
3.1.8
least material requirement
LMR
requirement for a feature of size, defining a geometrical feature of the same type and of perfect form,
with a given value for the intrinsic characteristic (dimension) equal to LMVS, which limits the non-ideal
feature on the inside of the material
Note 1 to entry: Least material requirements, LMR, are used in pairs, e.g. to control the minimum wall thickness
between two symmetrical or coaxially located similar features of size.
[SOURCE: ISO 2692:2021, 3.13]
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ISO/DTR 22514-9:2023(E)
3.1.9
reciprocity requirement
RPR
additional requirement for a feature of size used as an addition to the maximum material requirement,
MMR, or the least material requirement, LMR to indicate that the size tolerance is increased by the
difference between the geometrical tolerance and the actual geometrical deviation
[SOURCE: ISO 2692:2021, 3.14]
3.2 Abbreviated terms
ASME American Society of Mechanical Engineers
LMC least material conditions
LMS least material size
LMR least material requirement
LMVC least material virtual condition
LMVS least material virtual size
MMC maximum material condition
MMR maximum material requirement
MMS maximum material size
MMVS maximum material virtual size
PCI process capability indices
RPR reciprocity requirement
3.3 Symbols
In addition to the symbols listed below, some symbols are defined where they are used within the text.
C process capability index
p
C minimum process capability index
pk
C lower process capability index
pk
L
C
upper process capability index
pk
U
D Diameter
Δ geometrical tolerance
δ measured geometrical tolerance
A
l least material size
LMS
l LMVS for external features of size
LMVS,e
l LMVS for internal features of size
LMVS,i
l maximum material size
MMS
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ISO/DTR 22514-9:2023(E)
l maximum material virtual size
MMVS
l MMVS for external features of size
MMVS,e
l MMVS for internal features of size
MMVS,i
L lower specification limit
SL
N total sample size
n subgroup sample size
μ location of the process; population mean value
P  P process performance index
p po
P  P minimum process performance index
pk pok
P
lower process performance index
pk
L
P upper process performance index
pk
U
θ parameter required for the Rayleigh distribution
s standard deviation, sample statistic
s
average sample standard deviation
σ standard deviation, population
U upper specification limit
SL
X arithmetic mean value, sample
X upper 99,865 % quantile
99,865 %
X lower 0,135 % quantile
0,135 %
4 Statistical measures used in the calculation of process capability or
performance
4.1 General
The statistical analysis described in this document is designed to determine capability or performance
indices when the characteristic of interest is a feature of linear size, and this size has a geometrical
modifier added to the specification or a geometrical tolerance with or without maximum material
condition.
4.2 Independency principle
4.2.1 General
A GPS specification for a feature or relation between features can be fulfilled independent of other
specifications except when it is stated by special indication e.g. modifiers according to ISO 2692,
CZ according to ISO 1101 or modifiers according to ISO 14405-1 as part of the specification. Each
requirement ( , MMR and LMR) combines two independent requirements into one collective
requirement, which more accurately simulates the intended function of the workpiece. In some cases of
both MMR and LMR, the “reciprocity requirement”, RPR, can be added.
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ISO/DTR 22514-9:2023(E)
If those special indications are used as requirements, they need to be considered as a collective
requirement and the capability indices can be calculated as one common value.
4.2.2 Maximum Material ISO versus ASME
In this standard the ISO definitions as defined in ISO 8015 are used. Geometrical product specifications
in ASME are defined in Y 14.5 that often differs from the definitions in ISO. Tolerancing in ISO
geometrical features are individual and independent of each other. In ASME tolerancing of the mating
behaviour of the part in the assembly group used.
4.2.3 Measurement procedure
The measurement procedure is especially important when measuring properties with modifiers or
geometric tolerances. The tolerance applies to the entire surface of the workpiece in 3 dimensions
with an infinite number of points, therefore a sufficient number of measuring points defined in the
procedure can be measured on every workpiece. You also have to consider the distribution of these
points. More information can be found in Annex C.
4.3 Location
It is a precondition, that the size of the characteristic of interest can have only one value assigned and
a characterisations of process location can be the mean, μ, or the median, X . If the variation of the
50 %
characteristic can be described by a symmetric distribution the mean is the most natural selection,
with non-symmetric distributions the median is the preferred selection.
4.4 Dispersion
It is important to differentiate between a standard deviation that measures only short-term variation
and the standard deviation which measures longer-term variation. Methods for calculating standard
deviations representing these two cases are given in Annex A. Very often, when data are gathered over
a long period of time, the standard deviation is larger due to the effects of fluctuations in the process. It
is important that the use and calculation of the standard deviation in the formulae’s only make sense if
the data is normally distributed.
In case of a characteristics with modifiers added or characteristics defined with geometrical tolerances
the actual distribution in most cases cannot be described by a normal distribution therefore, the
capability calculation formula based on reference limits can be used instead. The formulas for the
distribution models can be found in Annex B.
4.5 Reference limits
The lower and upper reference limits are respectively defined as the 0,135 % and the 99,865 % quantiles
of the distribution that describes the output of the process characteristic. They are described as X
0,135 %
and X .
99,865 %
4.6 Reference interval
The reference interval is the interval between the upper and the lower reference limits. The reference
interval includes 99,73 % of the individual values in the population from a process.
5 Geometrical product specifications
5.1 General
Produced workpieces exhibit deviations from the ideal geometric form shown on a drawing. The real
value of the dimension of a feature of size is dependent on the form deviations and on the specific type
of size applied.
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ISO/DTR 22514-9:2023(E)
The definition of an indication of a size tolerance by direct indication (plus and minus tolerancing), or
indication by the limit values of the upper and the lower deviation limits, e.g. 25,65 ± 0,05 has not been
defined before the first version of ISO 14405-1 was published, and therefore resulted in an ambiguous
requirement when used on features of size of imperfect form.
The type of size to be applied to a feature of size depends on the function of the workpiece in the
product. The type of size can be indicated on the drawing by a specification modifier for controlling the
feature definition and evaluation method to be used. If no modifier has been added to the tolerance, the
two-point size is the default requirement. In this case, there can be a lot of different values because a
number of measurements has to be taken on the workpiece.
Key
1 set of values of local sizes 5 average size (= 10,011 69)
2 positions along the axis 6 median size (= 9,969 86)
3 maximum size (= 10,497 88) 7 mid-range size (= 10,020 345)
4 minimum size (= 9,542 81) 8 size range (= 0,955 07)
d , d , d different values of local size
i 1 n
Figure 1 — Different results for two-point requirement (adapted from ISO 14405-1:2016,
Figure 8)
The calculation of capability in case of two-point size can be based on the average and the reference
interval of the minimum two-point value found on the workpieces and the average and the reference
interval of the maximum measured values on the workpieces. The two distribution models will very
often be extreme value distributions.
5.2 Linear size with modifiers
Geometrical product specifications with different modifiers such as or are very often used
in modern drawings to specify the function of the workpiece. The combination of such requirement
when the calculation of capability indices is required will often be a subject to discussions between the
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ISO/DTR 22514-9:2023(E)
customers and the production because of the interpretation of the specification cannot result in only
one value. ISO 14405-1 defines the different modifiers.
5.3 ISO tolerance classes with modifier
If a fit has been toleranced, the ISO tolerance class code system (in accordance with ISO 286-1) can
be indicated on the drawing. An ISO tolerance class code without a modifier is a standard linear size
defined as a two-point size. In case of a fit, a modifier or can be added to the tolerance. There
will then be two different requirements to the characteristic: The two-point size and the envelope size.
Dimensions in millimetres
a
Minimum requirement value (two point).
b
Envelope requirement – maximum value.
Figure 2 — ISO tolerance on a shaft with a modifier
Key
L mini
...

ISO/TR 22514-9:2023(E) Style Definition: Heading 1: Indent: Left: 0 pt, First
line: 0 pt, Tab stops: Not at 21.6 pt
ISO TC 69/SC 4
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at 18 pt
Date: 2023-xx
Style Definition: Heading 3: Font: Bold
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Statistical methods in process management — Capability and performance —
Style Definition: Heading 5: Font: Bold
Part 9: Process capability statistics for characteristics defined by geometrical
specifications
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Méthodes statistiques dans la gestion de processus — Aptitude et performance — Partie 9:
Style Definition: AMEND Terms Heading: Font: Bold
Méthodes statistiques pour l'aptitude des processus dont les caractéristiques sont définies
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par des spécifications géométriques
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ISO/TR 22514-9:2023(E)
© ISO 2023
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standard which has been replaced

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ISO/TR 22514-9:2023(E)
Contents
Foreword . v
Introduction . vi
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
3.1 Terms . 2
3.2 Abbreviated terms . 4
3.3 Symbols . 4
4 Statistical measures used in the calculation of process capability or performance . 5
4.1 General . 5
4.2 Independency principle . 6
4.2.1 General . 6
4.2.2 Maximum Material ISO versus ASME . 6
4.2.3 Measurement procedure . 6
4.3 Location . 6
4.4 Dispersion . 6
4.5 Reference limits . 6
4.6 Reference interval . 6
5 Geometrical product specifications . 7
5.1 General . 7
5.2 Linear size with modifiers . 8
5.3 ISO tolerance classes with modifier . 8
6 Capability calculation on features defined by geometrical tolerances . 9
6.1 General . 9
6.2 Form, orientation, location and run out tolerances . 10
6.3 Location tolerances . 10
6.4 Example on capability calculation in case of known inverse distribution function . 12
7 Maximum material requirement . 13
7.1 Information about maximum material requirement. 13
7.2 Calculation of results . 14
7.3 Least material requirement LMR . 19
7.4 Methodology . 20
Annex A (informative) Distribution identification . 22
A.1 General . 22
A.2 Calculation of dispersion . 23
Annex B (informative) Distributions used in case of Geometrical tolerances . 25
B.1 General . 25
B.2 Normal distribution . 25
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ISO/TR 22514-9:2023(E)
B.3 Rayleigh distribution . 25
B.4 Folded normal distribution . 25
B.5 Log-normal distribution . 26
Annex C (informative) Number of points to be collected. 27
C.1 General . 27
C.2 Example . 27
Annex D (informative) Process analysis for improvement . 29
D.1 General . 29
D.2 Case study . 29
Bibliography . 31
Foreword . v
Introduction . vi
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
3.1 Terms . 2
3.2 Abbreviated terms . 4
3.3 Symbols . 4
4 Statistical measures used in the calculation of process capability or performance . 5
4.1 General . 5
4.2 Independency principle . 6
4.2.1 General . 6
4.2.2 Maximum Material ISO versus ASME . 6
4.2.3 Measurement procedure . 6
4.3 Location . 6
4.4 Dispersion . 6
4.5 Reference limits . 6
4.6 Reference interval . 6
5 Geometrical product specifications . 7
5.1 General . 7
5.2 Linear size with modifiers . 8
5.3 ISO tolerance classes with modifier . 8
6 Capability calculation on features defined by geometrical tolerances . 9
6.1 General . 9
6.2 Form, orientation, location and run out tolerances . 10
6.3 Location tolerances . 10
6.4 Example on capability calculation in case of known inverse distribution function . 12
7 Maximum material requirement . 13
7.1 Information about maximum material requirement . 13
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ISO/TR 22514-9:2023(E)
7.2 Calculation of results . 14
7.3 Least material requirement LMR . 19
7.4 Methodology . 20
Annex A (informative) Distribution identification . 22
Annex B (informative) Distributions used in case of Geometrical tolerances . 25
Annex C (informative) Number of points to be collected . 27
Annex D (informative) Process analysis for improvement . 29
Bibliography . 31
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ISO/TR 22514-9:2023(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.
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 documents 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 drawn to the possibility that some of the elements of this document may be the subject of
patent rights. 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/patentswww.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 on 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 the following URL:
www.iso.org/iso/foreword.htmlwww.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 4, Applications of statistical methods in process management.
This document is a second draft for approval and only editorial changes will be made before publication.
A list of all parts in the ISO 22514 series can be found on the ISO website.
Commented [eXtyles2]: Invalid reference: "ISO 22514
series"
Any feedback or questions on this document should be directed to the user’s national standards body. A
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complete listing of these bodies can be found at
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www.iso.org/members.htmlwww.iso.org/members.html.
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ISO/TR 22514-9:2023(E)
Introduction
Many organizations will need to evaluate the capability and performance of their key processes when the
specifications are defined by requirements other than linear size. The methods described in this part of
ISO 22514document are intended to assist the organization in this respect.
During the last couple of years, it has more common in the design and development departments in
companies to not only use linear tolerances alone, but also including modifiers as well as geometrical
tolerances with or without use of the maximum material requirements.
This situation has been supported by new measurement methods used in production, where it is common
to use measurement equipment, where the results are given in form of point clouds instead of one single
value.
It is a challenge in such cases to calculate capability and performance, but organizations and customers
still require the capability indices in acceptance of produced or delivered batches of parts.
This part of ISO 22514document describes how to calculate capability or performance where functional
requirements on parts are given.
As an example, the “maximum material requirement”, MMR, covers “assemble ability” and the “least
material requirement”, LMR, covers, for example, “minimum wall thickness” of a part. Each requirement
(MMR and LMR) combines two independent requirements into one collective requirement, which
simulates the intended function of the workpiece. In some cases of both MMR and LMR, the “reciprocity
requirement”, RPR, can be added.
In Annex D, a case study of process analysis, where the characteristic to be improved is perpendicularity,
is introduced.
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TECHNICAL REPORT ISO/TR 22514-9:2023(E)

Statistical methods in process management — Capability and
performance — Part 9: Process capability statistics for
characteristics defined by geometrical specification
1 Scope
This part of ISO 22514document describes process capability and performance measures when the
specifications are given by geometrical product specifications e.g.,. maximum material requirements or
linear size with a modifier.
The purpose of this partdocument of the international series of standards on capability calculation is to
assist the organizations to calculate the PCIs when geometrical product specifications are used on
drawings.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https://www.iso.org/obphttps://www.iso.org/obp
— IEC Electropedia: available at https://www.electropedia.org/https://www.electropedia.org/
3.1 Terms
3.1.1
feature of size
feature of linear size
geometrical feature, having one or more intrinsic characteristics, only one of which maycan be considered
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as variable parameter, that additionally is a member of a “one parameter family”, and obeys the
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monotonic containment property for that parameter
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EXAMPLE 1 A single cylindrical hole or shaft is a feature of linear size. Its linear size is its diameter.
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EXAMPLE 2 Two opposite parallel plane surfaces are a feature of linear size. Its linear size is the distance between
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the two parallel planes.
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[SOURCE: ISO 17450-1:2011, 3.3.1.5.1., modified: deleted Note 1 to Note 4, deleted reference to Figure 5
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(ISO 17450-1:2011), deleted EXAMPLE 2, added new EXAMPLE 2]
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3.1.2
local size
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ISO/TR 22514-9:2023(E)
local linear size
Commented [eXtyles3]: The term "local linear size" has
not been used anywhere in this document
local size characteristic
local linear size characteristic
Commented [eXtyles4]: The term "local size
size characteristic having by definition a non-unique result of evaluation along and/or around the feature characteristic" has not been used anywhere in this document
of size
Commented [eXtyles5]: The term "local linear size
characteristic" has not been used anywhere in this document
Note 1 to entry: For a given feature, an infinity of local sizes exists.
[SOURCE: ISO 14405-1:2016, 3.6]
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3.1.3
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two-point size
distance between two opposite points on an extracted integral linear feature of size
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Note 1 to entry: A two-point size taken on a cylinder can be called a “two-point diameter”. In ISO 17450-3, this is
defined as a local diameter of an extracted cylinder.
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Note 2 to entry: A two-point size taken on two opposite planes can be called “two-point distance”. In
ISO 17450-3, this is defined as a local size of two parallel extracted surfaces.
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[SOURCE: ISO 14405-1:2016, 3.6.1, modified: deleted Note 1 to entry to Note 3 to entry, added two new
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notes]
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3.1.4
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envelope requirement
combination of the two-point size applied for the least material limit of the size and either the minimum
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circumscribed size or the maximum inscribed size for the maximum material limit of the size
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Note 1 to entry: The “envelope requirement” was previously referred to as the “Taylor principle”.
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Note 2 to entry: According to ISO 8015:2011, the surface of a single feature of size (e.g.,. cylindrical surface or a
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feature based on two parallel plane surfaces) may notcannot violate the envelope of a geometrical ideal form at a
maximum material limit of size
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[SOURCE: ISO 14405-1:2016, 3.8, modified: Note 2 to entry added]
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3.1.5
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maximum material virtual size
MMVS
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size generated by the collective effect of the maximum material size, MMS, of a feature of size and the
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geometrical tolerance (form, orientation or location) given for the derived feature of the same feature of
size Commented [eXtyles6]: The term "maximum material
virtual size" is used only in terms and definitions section
Note 1 to entry: Maximum material virtual size, MMVS, is a parameter for size used as a numerical value
connected to maximum material virtual condition, MMVC.
Note 2 to entry: For external features, MMVS is the sum of MMS and the geometrical tolerance, whereas for
internal features, it is the difference between MMS and the geometrical tolerance.
Note 3 to entry: The MMVS for external features of size, l , is given by Formulathe following formula:
MMVS,e
l = l + δ
MMVS,e MMS
and the MMVS for internal features of size, l , is given by Formulathe following one:
MMVS,i
lMMVS,i = lMMS − δ
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ISO/TR 22514-9:2023(E)
where
 lMMS is the maximum material size;
Formatted: Table body (-), Justified, Adjust space
 δ is the geometrical tolerance. between Latin and Asian text, Adjust space between
Asian text and numbers
3.1.6
least material virtual size Formatted: Table body (-), Justified, Adjust space
between Latin and Asian text, Adjust space between
LMVS
Asian text and numbers
size generated by the collective effect of the least material size, LMS, of a feature of size and the
geometrical tolerance (form, orientation or location) given for the derived feature of the same feature of
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size
Commented [eXtyles7]: The term "least material virtual
size" is used only in terms and definitions section
Note 1 to entry: Least material virtual size, LMVS, is a parameter for size used as a numerical value connected to
least material virtual condition, LMVC.
Note 2 to entry: For external features, LMVS is the difference between LMS and the geometrical tolerance,
whereas for internal features, it is the sum of LMS and the geometrical tolerance.
Note 3 to entry: The LMVS for external features of size, lLMVS,e, is given by Formulathe following formula:
l = l − δ
LMVS,e LMS
and the LMVS for internal features of size, lLMVS,i, is given by Formulathe following one:
l = l + δ
LMVS,i LMS
where
 l is the least material size;
LMS
 δ is the geometrical tolerance.
3.1.7
maximum material requirement
MMR
requirement for a feature of size, defining a geometrical feature of the same type and of perfect form, with
a given value for the intrinsic characteristic (dimension) equal to the maximum material virtual size,
which limits the non-ideal feature on the outside of the material
Commented [eXtyles8]: The reference is to a withdrawn
standard which has been replaced
Note 1 to entry: Maximum material requirement, MMR, is used to control the assembly ability of a workpiece.
ISO 2692:2021, Geometrical product specifications (GPS)
— Geometrical tolerancing — Maximum material
[SOURCE: ISO 2692:20142021, 3.12]
requirement (MMR), least material requirement (LMR) and
reciprocity requirement (RPR)
3.1.8
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least material requirement
LMR
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requirement for a feature of size, defining a geometrical feature of the same type and of perfect form, with
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a given value for the intrinsic characteristic (dimension) equal to LMVS, which limits the non-ideal feature
Commented [eXtyles9]: The reference is to a withdrawn
on the inside of the material
standard which has been replaced

Note 1 to entry: Least material requirements, LMR, are used in pairs, e.g.,. to control the minimum wall thickness
ISO 2692:2021, Geometrical product specifications (GPS)
between two symmetrical or coaxially located similar features of size.
— Geometrical tolerancing — Maximum material
requirement (MMR), least material requirement (LMR) and
reciprocity requirement (RPR)
[SOURCE: ISO 2692:20142021, 3.13]
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3.1.9
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reciprocity requirement
RPR
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ISO/TR 22514-9:2023(E)
additional requirement for a feature of size used as an addition to the maximum material requirement,
MMR, or the least material requirement, LMR to indicate that the size tolerance is increased by the
difference between the geometrical tolerance and the actual geometrical deviation
[SOURCE: ISO 2692:20142021, 3.14]
Commented [eXtyles10]: The reference is to a withdrawn
standard which has been replaced

3.2 Abbreviated terms
ISO 2692:2021, Geometrical product specifications (GPS)
— Geometrical tolerancing — Maximum material
ASME American Society of Mechanical Engineers
requirement (MMR), least material requirement (LMR) and
reciprocity requirement (RPR)
LMC least material conditions
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LMS least material size
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LMR least material requirement
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LMVC least material virtual condition
LMVS least material virtual size
MMC maximum material condition
MMR maximum material requirement
MMS maximum material size
MMVS maximum material virtual size
PCI process capability indices
RPR reciprocity requirement
3.3 Symbols
In addition to the symbols listed below, some symbols are defined where they are used within the text.
C process capability index
p
Cpk minimum process capability index
C
pk lower process capability index
L
C
pk upper process capability index
U
D Diameter
Δ geometrical tolerance
δ measured geometrical tolerance
A
lLMS least material size
l LMVS for external features of size
LMVS,e
l LMVS for internal features of size
LMVS,i
l maximum material size
MMS
l maximum material virtual size
MMVS
lMMVS,e MMVS for external features of size
l MMVS for internal features of size
MMVS,i
L lower specification limit
SL
N total
...