ISO/TR 22514-9:2023

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

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 (process capability index) when geometrical product specifications are used on drawings.

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: Published
• Publication Date: 27-Nov-2023
• 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: 6060 - International Standard published
• Start Date: 28-Nov-2023
• Completion Date: 28-Nov-2023

Overview

ISO/TR 22514-9:2023 is a Technical Report from ISO on statistical methods in process management focused on process capability and performance when product specifications are defined by geometrical product specifications (GPS) rather than simple linear tolerances. The report explains how to calculate process capability indices (PCIs) for features described by geometrical tolerances, modifiers and collective requirements such as Maximum Material Requirement (MMR) and Least Material Requirement (LMR). It reflects modern measurement realities (e.g., point‑cloud data) and supports organizations that must demonstrate process capability for parts with GPS on engineering drawings.

Key topics and technical requirements

• Scope and purpose: Guidance for calculating PCIs when specifications are given as geometric tolerances or linear size with modifiers.
• Statistical foundations: Treatment of location, dispersion, reference limits and reference intervals, and the independency principle used in capability calculations.
• Geometrical product specifications: Definitions and handling of linear sizes with modifiers, ISO tolerance classes with modifiers, and envelope requirements (Taylor principle).
• MMR / LMR / RPR: Definitions and how to combine size and geometrical tolerances into Maximum Material Virtual Size (MMVS) and Least Material Virtual Size (LMVS) to represent collective functional requirements (MMR and LMR). For external vs internal features the virtual size is adjusted by the geometrical tolerance.
• Capability calculations for geometrical tolerances: Methods for form, orientation, location and run‑out tolerances; examples (flatness, roundness) and approaches when inverse distribution functions are known.
• Measurement considerations: Recognition of point‑cloud and other digital measurement outputs; guidance on sample size and distribution identification.
• Supporting annexes: Distribution identification, distributions for geometrical tolerances, recommended number of measurement points, and a process‑improvement case study.

Practical applications and who uses it

• Manufacturing engineers and quality engineers calculating process capability where drawing requirements include GPS, MMR or LMR.
• Metrology teams working from CMMs or point‑cloud scanners to convert geometric measurement results into capability statistics.
• Design and product engineers validating manufacturability (assembly ability, minimum wall thickness) through capability metrics.
• Suppliers and auditors producing capability evidence for acceptance of batches with GPS-based specifications.

Related standards (context)

• ISO 22514 series (other parts on capability and performance)
• GPS standards such as ISO 14405‑1, ISO 8015 and ISO 2692 (terminology and GPS concepts referenced in the report)

Keywords: ISO/TR 22514-9, process capability, geometrical product specifications, MMR, LMR, process capability index, geometrical tolerances, point cloud measurement, capability statistics.

Standards Content (Sample)

TECHNICAL ISO/TR
REPORT 22514-9
First edition
2023-11
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
Reference number
© ISO 2023
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: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland
ii
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
6.2.1 General . 10
6.2.2 Example flatness . 10
6.2.3 Example roundness . 10
6.3 Location tolerances (Figure 5) . 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
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
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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
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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 69, Applications of statistical methods,
Subcommittee SC 4, Applications of statistical methods in products and 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.
iv
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 been 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.
v
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 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 (process capability index) 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 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 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: “may” replaced by “can”, deleted Note 1 to Note 4,
deleted reference to Figure 5 (ISO 17450-1:2011), deleted EXAMPLE 2, added new EXAMPLE 2]
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 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, modified: “and/or” replaced by “and”, Note 2 to entry to Note 4 to
entry deleted.]
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 applied 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
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 linear 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, modified Note 2 to entry deleted.]
3.1.8
least material requirement
LMR
requirement for a feature of linear 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 last material virtual
size, which limits the non-ideal feature on the inside of the material
Note 1 to entry: Least material requirements, LMR is used, for example, to control the minimum wall thickness
between two symmetrical or coaxially located similar features of size.
[SOURCE: ISO 2692:2021, 3.13, modified Note 2 to entry deleted.]
3.1.9
reciprocity requirement
RPR
additional requirement for a feature of linear size indicated in 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 index
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
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 Scale parameter of the Rayleigh distribution
s standard deviation, sample statistic
s
average sample standard deviation
σ standard deviation, population
U upper specification limit
SL
X average from 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.
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 three 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 variation based on
e.g. 50 samples and the standard deviation which measures variation from more than 100 samples.
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 only make sense if the data are 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 formulae 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.
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 (see Figure 1.). 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
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 minimum size
Min
L maximum size (two point)
Max
Figure 3 — Size with envelope modifier
For such tolerances as shown in Figure 2 and Figure 3, values from two different measurements series
can be collected: The two-point size and the envelope size. In principle it is the same in case of internal
diameters. The only differences are that the two-point size have a bigger value than the maximum
inscribed value.
Based on the series of two measurements (the envelope size and the minimum two-point size), two
different minimum indices C , P (envelope size) and C , P (two-point size) can be
pk pk pk pk
U U L L
calculated using the following formulae:
a) for the calculation of index for envelope size, see Formula (1):
UX− UX−
SL 50% SL 50%
C = or P = (1)
pk pk
UU
XX− XX−
99,,865%%50 99 865%%50
b) for the calculation of index for the minimum two-point size, see Formula (2):
XL− XL−
50%SL 50%SL
C = or P = (2)
pk pk
LL
XX− XX−
50%%0,,135 50%%0135
The minimum capability index C , P is the one with the lowest value.
pk pk
The corresponding P or C values can only be used for production monitoring purposes. The method
p p
for the actual calculation of these indices can be found either in ISO 22514-2 in case of time dependent
production models or in ISO 22514-4.
Example from diameter measurements of a shaft diameter (Figure 4) with two different measurement
series (two-point diameter and minimum subscribed diameter).
Key
X value no. U upper specification limit
SL
Y diameter two point measurements
xs+ 3
1 two-point requirement two point measurements
x
2 envelope requirement two point measurements
xs− 3
L lower specification limit
SL
Figure 4 — Example from measurements of a shaft
6 Capability calculation on features defined by geometrical tolerances
6.1 General
Geometrical tolerances as defined in ISO 1101 are very often used in industry to set requirements
for critical and important characteristics. Geometrical tolerances define a tolerance zone where the
toleranced surface or derived element (e.g. centreline or midplane) can be applied. That means that all
measured points on the surface or the derived element are inside the tolerance zone.
Capability indices for geometrical tolerances are usually based on skewed distributions. The skewed
distributions require a minimum of five parts in the subsamples in case of x-bar & R control charts.
In case of logarithmic distribution, the X-bar chart can be calculated based on the logarithm of the
measured values.
Commonly found distribution models when geometrical tolerances are measured:
— Folded normal distribution (FD);
— Logarithmic normal distribution (LD), (This distribution can only be used in special cases because
of the risk on a long “distribution tale”);
— Rayleigh distribution (RD)(often used when the specifications are coaxiality, run-out or position
tolerances) ;
— Weibull distribution (WD).
6.2 Form, orientation, location and run out tolerances
6.2.1 General
Annex A contains guidance on the choice of distribution model when capability indices are calculated
on characteristic defined by geometrical tolerances.
The calculation of the indices will be done by calculating the average of the maximal form failure found
on the workpieces. The distribution model will very often be a folded normal distribution.
6.2.2 Example flatness
The deviation in flatness can be calculated based on the minimum zone plane. From this plane the
maximum deviation in both directions is found and superposed to a maximum
...