SIST ISO 22514-6:2014
Statistical methods in process management - Capability and performance - Part 6: Process capability statistics for characteristics following a multivariate normal distribution
Statistical methods in process management - Capability and performance - Part 6: Process capability statistics for characteristics following a multivariate normal distribution
ISO 22514-6:2013 provides methods for calculating performance and capability statistics for process or product quantities where it is necessary or beneficial to consider a family of singular quantities in relation to each other. The methods provided here mostly are designed to describe quantities that follow a bivariate normal distribution. In principle, this part of ISO 22514 can be used for multivariate cases.
ISO 22514-6:2013 does not offer an evaluation of the different provided methods with respect to different situations of possible application of each method. For the current state, the selection of one preferable method might be done following the users preferences.
The purpose is to give definitions for different approaches of index calculation for performance and capability in the case of a multiple process or product quantity description.
Méthodes statistiques dans la gestion de processus - Aptitude et performance - Partie 6: Statistiques de capacité opérationnelle d'un processus pour les caractéristiques qui suivent une distribution normale à plusieurs variables
Statistične metode za obvladovanje procesov - Sposobnost in delovanje - 6. del: Statistike procesne sposobnosti karakteristik, porazdeljenih po multivariatni normalni porazdelitvi
Ta del standarda ISO 22514 zagotavlja metode za izračunavanje statistik glede delovanja in sposobnosti za procesne ali proizvodne količine, kadar je potrebno ali koristno obravnavati družino posameznih količin v medsebojni povezavi. Tu navedene metode so namenjene predvsem opisu količin, porazdeljenih po bivariatni normalni porazdelitvi. Ta del standarda ISO 22514 ne omogoča ocene različnih zagotovljenih metod ob upoštevanju različnih razmer možne uporabe vsake metode. Za trenutno stanje se lahko izvede izbira ene prednostne metode v skladu z izbirami uporabnikov. Namen je navesti definicije za različne pristope izračuna indeksa za delovanje in sposobnosti v primeru opisa več procesnih ali proizvodnih količin.
General Information
Standards Content (Sample)
SLOVENSKI STANDARD
01-januar-2014
6WDWLVWLþQHPHWRGH]DREYODGRYDQMHSURFHVRY6SRVREQRVWLQGHORYDQMHGHO
6WDWLVWLNHSURFHVQHVSRVREQRVWLNDUDNWHULVWLNSRUD]GHOMHQLKSRPXOWLYDULDWQL
QRUPDOQLSRUD]GHOLWYL
Statistical methods in process management - Capability and performance - Part 6:
Process capability statistics for characteristics following a multivariate normal distribution
Méthodes statistiques dans la gestion de processus - Aptitude et performance - Partie 6:
Statistiques de capacité opérationnelle d'un processus pour les caractéristiques qui
suivent une distribution normale à plusieurs variables
Ta slovenski standard je istoveten z: ISO 22514-6:2013
ICS:
03.120.30 8SRUDEDVWDWLVWLþQLKPHWRG Application of statistical
methods
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
INTERNATIONAL ISO
STANDARD 22514-6
First edition
2013-02-15
Statistical methods in process
management — Capability and
performance —
Part 6:
Process capability statistics
for characteristics following a
multivariate normal distribution
Méthodes statistiques dans la gestion des processus — Capabilité et
performance —
Partie 6: Statistiques de capabilité pour un processus caractérisé par
une distribution normale multivariée
Reference number
©
ISO 2013
© ISO 2013
All rights reserved. Unless otherwise specified, 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
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2013 – All rights reserved
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Abbreviated terms . 3
5 Process analysis . 4
6 Use of multivariate process capability and performance assessment .4
7 Calculation of process capability and process performance . 4
7.1 Description of Types I and II . 4
7.2 Designation and symbols of the indices . 5
7.3 Types Ιc and ΙΙc process capability index . 8
7.4 Types ΙΙa and Type ΙΙb process capability index .10
8 Examples .11
8.1 Two-dimensional position tolerances .11
8.2 Position and dimension of a slot .16
Annex A (informative) Derivation of formulae .20
Annex B (informative) Shaft imbalance example .25
Annex C (informative) Hole position example .29
Annex D (informative) Construction of the quality function .33
Bibliography .34
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 2.
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.
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.
ISO 22514-6 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 4, Applications of statistical methods in process management.
ISO 22514 consists of the following parts, under the general title Statistical methods in process
management — Capability and performance:
— Part 1: General principles and concepts
— Part 2: Process capability and performance of time-dependent process models
— Part 3: Machine performance studies for measured data on discrete parts
— Part 4: Process capability estimates and performance measures [Technical Report]
— Part 5: Process capability statistics for attribute characteristics
— Part 6: Process capability statistics for characteristics following a multivariate normal distribution
— Part 7: Capability of measurement processes
— Part 8: Machine performance of a multi-state production process
iv © ISO 2013 – All rights reserved
Introduction
Due to the increased complexity of the production methods and the increasing quality requirements for
products and processes, a process analysis based on univariate quantities is in many cases not sufficient.
Instead, it may be necessary to analyse the process on the basis of multivariate product quantities. This
can, for instance, be in such cases where geometric tolerances, dynamic magnitudes such as imbalance,
correlated quantities of materials or other procedural products are observed.
By analogy with ISO 22514-2, ISO 22514-6 provides calculation formulae for process performance and
process capability indices, which take into consideration process dispersion as well as process location
as an extension to the corresponding indices for univariate quantities. The indices proposed are indeed
based on the classical C and C indices for the one-dimensional case. The motivation for the extension
p pk
to the multivariate case is explained in Annex A.
Examples of possible applications are two-dimensional or three-dimensional positions, imbalance or
several correlated quantities of chemical products.
The dispersion of the measuring results comprises the dispersion of the product realization process and
the precision of the measuring process. It is assumed that the capability of the used measuring system
was demonstrated prior to the determination of the capability of the product realization process.
The calculation method described here should be used to support an unambiguous decision, especially if
— limiting values for process capability indices for multivariate, continuous product quantities are
specified as part of a contract between customers and suppliers, or
— the capabilities of different constructions, production methods or suppliers are to be compared, or
— production processes are to be approved, or
— problems are to be analysed and decisions made in complaint cases or damage events.
NOTE Product realization processes include e.g. manufacturing processes, service processes, product
assembly processes.
INTERNATIONAL STANDARD ISO 22514-6:2013(E)
Statistical methods in process management — Capability
and performance —
Part 6:
Process capability statistics for characteristics following a
multivariate normal distribution
1 Scope
This part of ISO 22514 provides methods for calculating performance and capability statistics for process
or product quantities where it is necessary or beneficial to consider a family of singular quantities in
relation to each other. The methods provided here mostly are designed to describe quantities that follow
a bivariate normal distribution.
NOTE In principle, this part of ISO 22514 can be used for multivariate cases.
This part of ISO 22514 does not offer an evaluation of the different provided methods with respect to
different situations of possible application of each method. For the current state, the selection of one
preferable method might be done following the users preferences.
The purpose is to give definitions for different approaches of index calculation for performance and
capability in the case of a multiple process or product quantity description.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
ISO 22514-1, Statistical methods in process management — Capability and performance — Part 1: General
principles and concepts
ISO 22514-2, Statistical methods in process management — Capability and performance — Part 2: Process
capability and performance of time-dependent process models
3 Terms and definitions
For the purpose of this document, the terms and definitions given in ISO 22514-1 and ISO 22514-2 and
the following apply.
3.1
quantity
property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed
as a number and a reference
[ISO/IEC Guide 99:2007, 1.1]
3.2
multivariate quantity
set of distinguishing features
Note 1 to entry: The set can be expressed by a d-tuple, i.e. an ordered set consisting of d elements.
Note 2 to entry: If the single quantities in the set are denoted by x where i = 1, 2…d, the multivariate quantity is
i
T
expressed as the vector x = (x , x , … x ) . Thus, a multivariate quantity can be considered as a feature vector of
1 2 d
a product. The value of the multivariate quantity is represented by a point in the d-dimensional feature space.
Note 3 to entry: The selection of the quantities in a vector is made for specific technical reason.
Note 4 to entry: All single quantities combined in the vector of a multivariate must be measurable in the same
product or object.
Note 5 to entry: If the multivariate quantity is to be described by means of statistics, the vector is to be considered
as a random vector following a d-dimensional multivariate distribution.
EXAMPLE 1 A number of d = 3 quantities like x = colour, x = mass and x = number of defects are combined in
1 2 3
order to use only one statistic for process assessment. The dimension of vector x is d = 3.
EXAMPLE 2 In order to evaluate a boring process, the position of the borehole axis is measured in an
x-coordinate and y-coordinate. The coordinates are combined to the two-dimensional multivariate quantity x
where the component x is the x-coordinate and x is the y-coordinate.
1 2
EXAMPLE 3 Imbalance of a wheel.
3.3
tolerance region
region in the feature space that contains all permitted values of the multivariate quantity (3.2)
Note 1 to entry: The region is limited by lines, surfaces or hyper-surfaces in the d-di
...
INTERNATIONAL ISO
STANDARD 22514-6
First edition
2013-02-15
Statistical methods in process
management — Capability and
performance —
Part 6:
Process capability statistics
for characteristics following a
multivariate normal distribution
Méthodes statistiques dans la gestion des processus — Capabilité et
performance —
Partie 6: Statistiques de capabilité pour un processus caractérisé par
une distribution normale multivariée
Reference number
©
ISO 2013
© ISO 2013
All rights reserved. Unless otherwise specified, 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
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2013 – All rights reserved
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Abbreviated terms . 3
5 Process analysis . 4
6 Use of multivariate process capability and performance assessment .4
7 Calculation of process capability and process performance . 4
7.1 Description of Types I and II . 4
7.2 Designation and symbols of the indices . 5
7.3 Types Ιc and ΙΙc process capability index . 8
7.4 Types ΙΙa and Type ΙΙb process capability index .10
8 Examples .11
8.1 Two-dimensional position tolerances .11
8.2 Position and dimension of a slot .16
Annex A (informative) Derivation of formulae .20
Annex B (informative) Shaft imbalance example .25
Annex C (informative) Hole position example .29
Annex D (informative) Construction of the quality function .33
Bibliography .34
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 2.
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.
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.
ISO 22514-6 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 4, Applications of statistical methods in process management.
ISO 22514 consists of the following parts, under the general title Statistical methods in process
management — Capability and performance:
— Part 1: General principles and concepts
— Part 2: Process capability and performance of time-dependent process models
— Part 3: Machine performance studies for measured data on discrete parts
— Part 4: Process capability estimates and performance measures [Technical Report]
— Part 5: Process capability statistics for attribute characteristics
— Part 6: Process capability statistics for characteristics following a multivariate normal distribution
— Part 7: Capability of measurement processes
— Part 8: Machine performance of a multi-state production process
iv © ISO 2013 – All rights reserved
Introduction
Due to the increased complexity of the production methods and the increasing quality requirements for
products and processes, a process analysis based on univariate quantities is in many cases not sufficient.
Instead, it may be necessary to analyse the process on the basis of multivariate product quantities. This
can, for instance, be in such cases where geometric tolerances, dynamic magnitudes such as imbalance,
correlated quantities of materials or other procedural products are observed.
By analogy with ISO 22514-2, ISO 22514-6 provides calculation formulae for process performance and
process capability indices, which take into consideration process dispersion as well as process location
as an extension to the corresponding indices for univariate quantities. The indices proposed are indeed
based on the classical C and C indices for the one-dimensional case. The motivation for the extension
p pk
to the multivariate case is explained in Annex A.
Examples of possible applications are two-dimensional or three-dimensional positions, imbalance or
several correlated quantities of chemical products.
The dispersion of the measuring results comprises the dispersion of the product realization process and
the precision of the measuring process. It is assumed that the capability of the used measuring system
was demonstrated prior to the determination of the capability of the product realization process.
The calculation method described here should be used to support an unambiguous decision, especially if
— limiting values for process capability indices for multivariate, continuous product quantities are
specified as part of a contract between customers and suppliers, or
— the capabilities of different constructions, production methods or suppliers are to be compared, or
— production processes are to be approved, or
— problems are to be analysed and decisions made in complaint cases or damage events.
NOTE Product realization processes include e.g. manufacturing processes, service processes, product
assembly processes.
INTERNATIONAL STANDARD ISO 22514-6:2013(E)
Statistical methods in process management — Capability
and performance —
Part 6:
Process capability statistics for characteristics following a
multivariate normal distribution
1 Scope
This part of ISO 22514 provides methods for calculating performance and capability statistics for process
or product quantities where it is necessary or beneficial to consider a family of singular quantities in
relation to each other. The methods provided here mostly are designed to describe quantities that follow
a bivariate normal distribution.
NOTE In principle, this part of ISO 22514 can be used for multivariate cases.
This part of ISO 22514 does not offer an evaluation of the different provided methods with respect to
different situations of possible application of each method. For the current state, the selection of one
preferable method might be done following the users preferences.
The purpose is to give definitions for different approaches of index calculation for performance and
capability in the case of a multiple process or product quantity description.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
ISO 22514-1, Statistical methods in process management — Capability and performance — Part 1: General
principles and concepts
ISO 22514-2, Statistical methods in process management — Capability and performance — Part 2: Process
capability and performance of time-dependent process models
3 Terms and definitions
For the purpose of this document, the terms and definitions given in ISO 22514-1 and ISO 22514-2 and
the following apply.
3.1
quantity
property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed
as a number and a reference
[ISO/IEC Guide 99:2007, 1.1]
3.2
multivariate quantity
set of distinguishing features
Note 1 to entry: The set can be expressed by a d-tuple, i.e. an ordered set consisting of d elements.
Note 2 to entry: If the single quantities in the set are denoted by x where i = 1, 2…d, the multivariate quantity is
i
T
expressed as the vector x = (x , x , … x ) . Thus, a multivariate quantity can be considered as a feature vector of
1 2 d
a product. The value of the multivariate quantity is represented by a point in the d-dimensional feature space.
Note 3 to entry: The selection of the quantities in a vector is made for specific technical reason.
Note 4 to entry: All single quantities combined in the vector of a multivariate must be measurable in the same
product or object.
Note 5 to entry: If the multivariate quantity is to be described by means of statistics, the vector is to be considered
as a random vector following a d-dimensional multivariate distribution.
EXAMPLE 1 A number of d = 3 quantities like x = colour, x = mass and x = number of defects are combined in
1 2 3
order to use only one statistic for process assessment. The dimension of vector x is d = 3.
EXAMPLE 2 In order to evaluate a boring process, the position of the borehole axis is measured in an
x-coordinate and y-coordinate. The coordinates are combined to the two-dimensional multivariate quantity x
where the component x is the x-coordinate and x is the y-coordinate.
1 2
EXAMPLE 3 Imbalance of a wheel.
3.3
tolerance region
region in the feature space that contains all permitted values of the multivariate quantity (3.2)
Note 1 to entry: The region is limited by lines, surfaces or hyper-surfaces in the d-dimensional space and not
necessarily closed. The form and extension of the region are specified by one or more parameters.
Note 2 to entry: Typical shapes of tolerance regions are rectangles, ellipses (or circles) in the two-dimensional
case, cuboids or hyper-cuboids, ellipsoids or hyper-ellipsoids or composite prismatic shapes. Figure 1 shows
examples of tolerance regions in the two-dimensional space.
Note 3 to entry: The tolerance region is specified based on the required function of the product. Products showing
values outside the region are assumed to not fulfil functional requirements. Those products are considered to be
nonconforming parts.
Note 4 to entry: In order to assess a product with respect to the limits of the tolerance region, the order of the
single quantity in the multivariate quantity and the number d of dimension must be equal to that of the tolerance
region description.
EXAMPLE A tolerance zone as it is defined in ISO 1101 for geometrical product features can be considered as
a tolerance region. In that case, limiting geometrically perfect lines or surfaces correspond to the boundary and
the tolerance correspond to the parameter of the tolerance region.
2 © ISO 2013 – All rights reserved
ISO 2
...
INTERNATIONAL ISO
STANDARD 22514-6
First edition
2013-02-15
Statistical methods in process
management — Capability and
performance —
Part 6:
Process capability statistics
for characteristics following a
multivariate normal distribution
Méthodes statistiques dans la gestion des processus — Capabilité et
performance —
Partie 6: Statistiques de capabilité pour un processus caractérisé par
une distribution normale multivariée
Reference number
©
ISO 2013
© ISO 2013
All rights reserved. Unless otherwise specified, 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
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2013 – All rights reserved
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Abbreviated terms . 3
5 Process analysis . 4
6 Use of multivariate process capability and performance assessment .4
7 Calculation of process capability and process performance . 4
7.1 Description of Types I and II . 4
7.2 Designation and symbols of the indices . 5
7.3 Types Ιc and ΙΙc process capability index . 8
7.4 Types ΙΙa and Type ΙΙb process capability index .10
8 Examples .11
8.1 Two-dimensional position tolerances .11
8.2 Position and dimension of a slot .16
Annex A (informative) Derivation of formulae .20
Annex B (informative) Shaft imbalance example .25
Annex C (informative) Hole position example .29
Annex D (informative) Construction of the quality function .33
Bibliography .34
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 2.
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.
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.
ISO 22514-6 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 4, Applications of statistical methods in process management.
ISO 22514 consists of the following parts, under the general title Statistical methods in process
management — Capability and performance:
— Part 1: General principles and concepts
— Part 2: Process capability and performance of time-dependent process models
— Part 3: Machine performance studies for measured data on discrete parts
— Part 4: Process capability estimates and performance measures [Technical Report]
— Part 5: Process capability statistics for attribute characteristics
— Part 6: Process capability statistics for characteristics following a multivariate normal distribution
— Part 7: Capability of measurement processes
— Part 8: Machine performance of a multi-state production process
iv © ISO 2013 – All rights reserved
Introduction
Due to the increased complexity of the production methods and the increasing quality requirements for
products and processes, a process analysis based on univariate quantities is in many cases not sufficient.
Instead, it may be necessary to analyse the process on the basis of multivariate product quantities. This
can, for instance, be in such cases where geometric tolerances, dynamic magnitudes such as imbalance,
correlated quantities of materials or other procedural products are observed.
By analogy with ISO 22514-2, ISO 22514-6 provides calculation formulae for process performance and
process capability indices, which take into consideration process dispersion as well as process location
as an extension to the corresponding indices for univariate quantities. The indices proposed are indeed
based on the classical C and C indices for the one-dimensional case. The motivation for the extension
p pk
to the multivariate case is explained in Annex A.
Examples of possible applications are two-dimensional or three-dimensional positions, imbalance or
several correlated quantities of chemical products.
The dispersion of the measuring results comprises the dispersion of the product realization process and
the precision of the measuring process. It is assumed that the capability of the used measuring system
was demonstrated prior to the determination of the capability of the product realization process.
The calculation method described here should be used to support an unambiguous decision, especially if
— limiting values for process capability indices for multivariate, continuous product quantities are
specified as part of a contract between customers and suppliers, or
— the capabilities of different constructions, production methods or suppliers are to be compared, or
— production processes are to be approved, or
— problems are to be analysed and decisions made in complaint cases or damage events.
NOTE Product realization processes include e.g. manufacturing processes, service processes, product
assembly processes.
INTERNATIONAL STANDARD ISO 22514-6:2013(E)
Statistical methods in process management — Capability
and performance —
Part 6:
Process capability statistics for characteristics following a
multivariate normal distribution
1 Scope
This part of ISO 22514 provides methods for calculating performance and capability statistics for process
or product quantities where it is necessary or beneficial to consider a family of singular quantities in
relation to each other. The methods provided here mostly are designed to describe quantities that follow
a bivariate normal distribution.
NOTE In principle, this part of ISO 22514 can be used for multivariate cases.
This part of ISO 22514 does not offer an evaluation of the different provided methods with respect to
different situations of possible application of each method. For the current state, the selection of one
preferable method might be done following the users preferences.
The purpose is to give definitions for different approaches of index calculation for performance and
capability in the case of a multiple process or product quantity description.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
ISO 22514-1, Statistical methods in process management — Capability and performance — Part 1: General
principles and concepts
ISO 22514-2, Statistical methods in process management — Capability and performance — Part 2: Process
capability and performance of time-dependent process models
3 Terms and definitions
For the purpose of this document, the terms and definitions given in ISO 22514-1 and ISO 22514-2 and
the following apply.
3.1
quantity
property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed
as a number and a reference
[ISO/IEC Guide 99:2007, 1.1]
3.2
multivariate quantity
set of distinguishing features
Note 1 to entry: The set can be expressed by a d-tuple, i.e. an ordered set consisting of d elements.
Note 2 to entry: If the single quantities in the set are denoted by x where i = 1, 2…d, the multivariate quantity is
i
T
expressed as the vector x = (x , x , … x ) . Thus, a multivariate quantity can be considered as a feature vector of
1 2 d
a product. The value of the multivariate quantity is represented by a point in the d-dimensional feature space.
Note 3 to entry: The selection of the quantities in a vector is made for specific technical reason.
Note 4 to entry: All single quantities combined in the vector of a multivariate must be measurable in the same
product or object.
Note 5 to entry: If the multivariate quantity is to be described by means of statistics, the vector is to be considered
as a random vector following a d-dimensional multivariate distribution.
EXAMPLE 1 A number of d = 3 quantities like x = colour, x = mass and x = number of defects are combined in
1 2 3
order to use only one statistic for process assessment. The dimension of vector x is d = 3.
EXAMPLE 2 In order to evaluate a boring process, the position of the borehole axis is measured in an
x-coordinate and y-coordinate. The coordinates are combined to the two-dimensional multivariate quantity x
where the component x is the x-coordinate and x is the y-coordinate.
1 2
EXAMPLE 3 Imbalance of a wheel.
3.3
tolerance region
region in the feature space that contains all permitted values of the multivariate quantity (3.2)
Note 1 to entry: The region is limited by lines, surfaces or hyper-surfaces in the d-dimensional space and not
necessarily closed. The form and extension of the region are specified by one or more parameters.
Note 2 to entry: Typical shapes of tolerance regions are rectangles, ellipses (or circles) in the two-dimensional
case, cuboids or hyper-cuboids, ellipsoids or hyper-ellipsoids or composite prismatic shapes. Figure 1 shows
examples of tolerance regions in the two-dimensional space.
Note 3 to entry: The tolerance region is specified based on the required function of the product. Products showing
values outside the region are assumed to not fulfil functional requirements. Those products are considered to be
nonconforming parts.
Note 4 to entry: In order to assess a product with respect to the limits of the tolerance region, the order of the
single quantity in the multivariate quantity and the number d of dimension must be equal to that of the tolerance
region description.
EXAMPLE A tolerance zone as it is defined in ISO 1101 for geometrical product features can be considered as
a tolerance region. In that case, limiting geometrically perfect lines or surfaces correspond to the boundary and
the tolerance correspond to the parameter of the tolerance region.
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ISO 2
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