SIST ISO 22514-2:2014

Statistical methods in process management - Capability and performance - Part 2: Process capability and performance of time-dependent process models

This part of ISO 22514 describes a procedure for the determination of statistics for estimating the quality capability or performance of product and process characteristics. The process results of these quality characteristics are categorized into eight possible distribution types. Calculation formulae for the statistical measures are placed with every distribution. The statistical methods described in this part of ISO 22514 only relate to continuous quality characteristics. They are applicable to processes in any industrial or economical sector.

Méthodes statistiques dans la gestion de processus - Aptitude et performance - Partie 2: Aptitude de processus et performance des modèles de processus dépendants du temps

Statistične metode za obvladovanje procesov - Sposobnost in delovanje - 2. del: Procesne sposobnosti in delovanje časovno odvisnih modelnih procesov

Ta del standarda ISO 22514 opisuje postopek za ugotavljanje statističnih podatkov za oceno kakovostne sposobnosti ali delovanja proizvodnih in procesnih karakteristik. Procesni rezultati teh kakovostnih karakteristik so razvrščeni v osem možnih vrst porazdelitve. Formule za izračun za statistična merjenja so zabeležene z vsako porazdelitvijo. Statistične metode iz tega dela standarda ISO 22514 se nanašajo samo na trajne kakovostne karakteristike. Uporabljajo se za procese v katerem koli industrijskem ali gospodarskem sektorju.

General Information

• Status: Withdrawn
• Publication Date: 28-Nov-2013
• Withdrawal Date: 16-Mar-2017
• ICS: 03.120.30 - Application of statistical methods
• Technical Committee: ISTM - Statistical methods
• Current Stage: 9900 - Withdrawal (Adopted Project)
• Start Date: 17-Mar-2017
• Due Date: 09-Apr-2017
• Completion Date: 17-Mar-2017
• Ref Project: ISO 22514-2:2013 - Statistical methods in process management — Capability and performance — Part 2: Process capability and performance of time-dependent process models

Relations

• Replaces: SIST ISO 21747:2006 - Statistical methods -- Process performance and capability statistics for measured quality characteristics
• Effective Date: 01-Jan-2014
• Replaced By: SIST ISO 22514-2:2017 - Statistical methods in process management - Capability and performance - Part 2: Process capability and performance of time-dependent process models
• Effective Date: 01-May-2017

Standards Content (Sample)

SLOVENSKI STANDARD
SIST ISO 22514-2:2014
01-januar-2014
1DGRPHãþD
SIST ISO 21747:2006
6WDWLVWLþQHPHWRGH]DREYODGRYDQMHSURFHVRY6SRVREQRVWLQGHORYDQMHGHO
3URFHVQHVSRVREQRVWLLQGHORYDQMHþDVRYQRRGYLVQLKPRGHOQLKSURFHVRY
Statistical methods in process management - Capability and performance - Part 2:
Process capability and performance of time-dependent process models
Méthodes statistiques dans la gestion de processus - Aptitude et performance - Partie 2:
Aptitude de processus et performance des modèles de processus dépendants du temps
Ta slovenski standard je istoveten z: ISO 22514-2:2013
ICS:
03.120.30 8SRUDEDVWDWLVWLþQLKPHWRG Application of statistical
methods
SIST ISO 22514-2:2014 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST ISO 22514-2:2014

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SIST ISO 22514-2:2014
INTERNATIONAL ISO
STANDARD 22514-2
First edition
2013-09-01
Statistical methods in process
management — Capability and
performance —
Part 2:
Process capability and performance of
time-dependent process models
Méthodes statistiques dans la gestion de processus — Aptitude et
performance —
Partie 2: Aptitude de processus et performance des modèles de
processus dépendants du temps
Reference number
ISO 22514-2:2013(E)
©
ISO 2013

---------------------- Page: 3 ----------------------

SIST ISO 22514-2:2014
ISO 22514-2:2013(E)

COPYRIGHT PROTECTED DOCUMENT
© 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 [e-mail]
Web www.iso.org
Published in Switzerland
ii © ISO 2013 – All rights reserved

---------------------- Page: 4 ----------------------

SIST ISO 22514-2:2014
ISO 22514-2:2013(E)

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms, definitions, symbols and abbreviated terms . 1
3.1 Symbols . 1
3.2 Abbreviations . 2
4 Process analysis . 3
5 Time-dependent distribution models . 3
6 Process capability and performance indices .15
6.1 Methods for determination of performance and capability indices — Overview .15
6.2 One-sided specification limits.18
6.3 Use of different calculation methods .20
7 Reporting process performance/capability indices .21
Bibliography .22
© ISO 2013 – All rights reserved iii

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SIST ISO 22514-2:2014
ISO 22514-2:2013(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. 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. 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.
The committee responsible for this document is ISO/TC 96, Applications of statistical methods,
Subcommittee SC 4, Applications of statistical methods in process management.
This first edition of ISO 22514-2 cancels and replaces ISO 21747:2006, of which it constitutes a
technical revision.
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
— 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

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SIST ISO 22514-2:2014
ISO 22514-2:2013(E)

Introduction
Many standards have been created concerning the quality capability/performance of processes by
international, regional and national standardization bodies and also by industry. All of them assume
that the process is in a state of statistical control, with stationary, normally distributed processes.
However, a comprehensive analysis of production processes shows that, over time, it is very rare for
processes to remain in such a state.
In recognition of this fact, this part of ISO 22514 provides a framework for estimating the quality
capability/performance of industrial processes for an array of standard circumstances. These
circumstances are categorized based on the stability of the mean and variance, as to whether they are
constant, changing systematically, or changing randomly. As such, the quality capability/performance
can be assessed for very differently shaped distributions with respect to time.
In other parts of ISO 22514 more detailed information about calculations of indices can be found. It
should be noted that where the capability indices given in this part of ISO 22514 are computed they
only form point estimates of their true values. It is therefore recommended that wherever possible the
indices’ confidence intervals are computed and reported.
© ISO 2013 – All rights reserved v

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SIST ISO 22514-2:2014

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SIST ISO 22514-2:2014
INTERNATIONAL STANDARD ISO 22514-2:2013(E)
Statistical methods in process management — Capability
and performance —
Part 2:
Process capability and performance of time-dependent
process models
1 Scope
This part of ISO 22514 describes a procedure for the determination of statistics for estimating the
quality capability or performance of product and process characteristics. The process results of these
quality characteristics are categorized into eight possible distribution types. Calculation formulae for
the statistical measures are placed with every distribution.
The statistical methods described in this part of ISO 22514 only relate to continuous quality
characteristics. They are applicable to processes in any industrial or economical sector.
NOTE This method is usually applied in case of a great number of serial process results, but it can also be
used for small series (a small number of process results).
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 3534-2, Statistics — Vocabulary and symbols — Part 2: Applied statistics
ISO 5479, Statistical interpretation of data — Tests for departure from the normal distribution
ISO 22514-1, Statistical methods in process management — Capability and performance — Part 1: General
principles and concepts
3 Terms, definitions, symbols and abbreviated terms
For the purposes of this document, the terms and definitions given in ISO 3534-2 and ISO 22514-1, and
the following symbols and abbreviated terms, apply.
3.1 Symbols
C process capability index
p
C minimum process capability index
pk
C lower process capability index
pkL
C upper process capability index
pkU
c constant based on subgroup size n
4
Δ dispersion of the process
© ISO 2013 – All rights reserved 1

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SIST ISO 22514-2:2014
ISO 22514-2:2013(E)

Δ difference between X and X of the distribution of the product characteristic
L mid 0,135 %
Δ difference between X and X of the distribution of the product characteristic
U 99,865 % mid
d constant based on subgroup size n
2
k number of subgroups of the same size n
μ average location of the process
L lower specification limit
M Calculation methods with location method label l and dispersion method label d
l,d
N sample size
p lower fraction nonconforming
L
p total fraction nonconforming
t
p upper fraction nonconforming
U
P process performance index
p
P minimum process performance index
pk
P lower process performance index
pkL
P upper process performance index
pkU
R range of the ith subgroup
i
s standard deviation, realized value
σ standard deviation, population
S standard deviation, sample statistic
S observed sample standard deviation of the ith subgroup
i
S standard deviation, with the subscript “t” indicating total standard deviation
t
U upper specification limit
X 0,135 % distribution quantile
0,135 %
X 99,865 % distribution quantile
99,865 %
X 50 % distribution quantile
50 %
X distribution midpoint
mid
3.2 Abbreviations
ANOVA analysis of variance
SPC statistical process control
2 © ISO 2013 – All rights reserved

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SIST ISO 22514-2:2014
ISO 22514-2:2013(E)

4 Process analysis
The purpose of process analysis is to obtain knowledge of a process. This knowledge is necessary for
controlling the process efficiently and effectively so that the products realized by the process fulfil the
quality requirement. It is a general assumption of this part of ISO 22514 that a process analysis has been
carried out and subsequent process improvements have been implemented.
The behaviour of a characteristic under consideration can be described by the distribution, the location,
the dispersion and the shape, parameters of which are time-dependent functions, in general. Different
models of such resulting distributions the parameters of which are time-dependent functions are
discussed in Clauses 6 and 7. To indicate whether a time-dependent distribution model fits, statistical
methods [e.g. estimating parameters, analysis of variance (ANOVA)] including graphical tools (e.g.
probability plots, control charts) are used.
The values of the characteristics under consideration are typically determined on the basis of samples
taken from the process flow. The sample size and frequency should be chosen depending on the type
of process and the type of product so that all important changes are detected in time. The samples
should be representative for the characteristic under consideration. To asses the stability of the process
a control chart should be used. Information on the use of control charts can be found in ISO 7870-2.
5 Time-dependent distribution models
The instantaneous distribution characterizes the behaviour of the characteristic under investigation
during a short interval. Usually, it is the time interval during which the sample (e.g. the subgroup) can be
taken from the process. Observing the process continuously in time for a longer time interval the output
from the process is called the resulting process distribution and it is described by a corresponding time-
dependent distribution model that reflects
— the instantaneous distribution of the characteristic under consideration, and
— the changes of its location, dispersion and shape parameters during the time interval of process
observation.
In practice, the resulting distribution can be represented by the whole data set, e.g. when SPC is applied,
by all subgroups gained during the interval of the process observation.
Time-dependent distribution models can be classified into four groups according to whether the location
and dispersion moments are constant or changing (see Table 1).
a) A process whose location and dispersion are constant is in time-dependent distribution model A.
In this case only, all the means and variances of the instantaneous distributions are equal to each
other and they are equal to the resulting distribution.
b) If the dispersion of a process is changing with time, but the location stays constant, the process is
said to be in time-dependent distribution model B.
c) If the dispersion is constant, but the location is changing, we have time-dependent distribution model C.
d) Otherwise, we have time-dependent distribution model D.
© ISO 2013 – All rights reserved 3

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SIST ISO 22514-2:2014
ISO 22514-2:2013(E)

4 © ISO 2013 – All rights reserved
Table 1 — Classification of time-dependent distribution models
Process average µ(t)
Process-standard
deviation s(t)
Constant Not constant
A C

A1 A2 C1 C2 C3 C4
Systematic and
Systematic
random
Location Random Random
(e.g. trend)
(e.g. lot to lot)
Constant Not
Short
Short time distribu- Normal Normal Normal Normal
Normal normal
time
tion distributed distributed distributed distributed
distributed distributed
distribution
– unimodal
Not
Normal normal distrib- Any shape
Resulting distribution Any shape
distributed uted (e.g. multimodal)
– unimodal
B D
Not Resulting
Resulting distribution
constant distribution
Any shape – unimodal Any shape

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SIST ISO 22514-2:2014
ISO 22514-2:2013(E)

For changing moments, the models can be classified according to whether the changes are random,
systematic or both.
NOTE Model A2 is known as stationary in time-series analysis literature and model A1 is known as second
order stationary.
Table 2 summarizes the basic features of individual time-dependent distribution models; their graphical
representations are given in Figures 1 to 8. Ther
...

INTERNATIONAL ISO
STANDARD 22514-2
First edition
2013-09-01
Corrected version
2013-10-15
Statistical methods in process
management — Capability and
performance —
Part 2:
Process capability and performance of
time-dependent process models
Méthodes statistiques dans la gestion de processus — Aptitude et
performance —
Partie 2: Aptitude de processus et performance des modèles de
processus dépendants du temps
Reference number
ISO 22514-2:2013(E)
©
ISO 2013

---------------------- Page: 1 ----------------------
ISO 22514-2:2013(E)

COPYRIGHT PROTECTED DOCUMENT
© 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 [e-mail]
Web www.iso.org
Published in Switzerland
ii © ISO 2013 – All rights reserved

---------------------- Page: 2 ----------------------
ISO 22514-2:2013(E)

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms, definitions, symbols and abbreviated terms . 1
3.1 Symbols . 1
3.2 Abbreviations . 2
4 Process analysis . 3
5 Time-dependent distribution models . 3
6 Process capability and performance indices .15
6.1 Methods for determination of performance and capability indices — Overview .15
6.2 One-sided specification limits.18
6.3 Use of different calculation methods .20
7 Reporting process performance/capability indices .21
Bibliography .22
© ISO 2013 – All rights reserved iii

---------------------- Page: 3 ----------------------
ISO 22514-2:2013(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. 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. 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.
The committee responsible for this document is ISO/TC 96, Applications of statistical methods,
Subcommittee SC 4, Applications of statistical methods in process management.
This first edition of ISO 22514-2 cancels and replaces ISO 21747:2006, of which it constitutes a
technical revision.
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
— 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
This corrected version of ISO 22514-2:2013 incorporates the following corrections: in Table 3, rows 3
.
and 4, the formulae have been corrected by replacing “k n” with”k” in the denominators.
iv © ISO 2013 – All rights reserved

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ISO 22514-2:2013(E)

Introduction
Many standards have been created concerning the quality capability/performance of processes by
international, regional and national standardization bodies and also by industry. All of them assume
that the process is in a state of statistical control, with stationary, normally distributed processes.
However, a comprehensive analysis of production processes shows that, over time, it is very rare for
processes to remain in such a state.
In recognition of this fact, this part of ISO 22514 provides a framework for estimating the quality
capability/performance of industrial processes for an array of standard circumstances. These
circumstances are categorized based on the stability of the mean and variance, as to whether they are
constant, changing systematically, or changing randomly. As such, the quality capability/performance
can be assessed for very differently shaped distributions with respect to time.
In other parts of ISO 22514 more detailed information about calculations of indices can be found. It
should be noted that where the capability indices given in this part of ISO 22514 are computed they
only form point estimates of their true values. It is therefore recommended that wherever possible the
indices’ confidence intervals are computed and reported.
© ISO 2013 – All rights reserved v

---------------------- Page: 5 ----------------------
INTERNATIONAL STANDARD ISO 22514-2:2013(E)
Statistical methods in process management — Capability
and performance —
Part 2:
Process capability and performance of time-dependent
process models
1 Scope
This part of ISO 22514 describes a procedure for the determination of statistics for estimating the
quality capability or performance of product and process characteristics. The process results of these
quality characteristics are categorized into eight possible distribution types. Calculation formulae for
the statistical measures are placed with every distribution.
The statistical methods described in this part of ISO 22514 only relate to continuous quality
characteristics. They are applicable to processes in any industrial or economical sector.
NOTE This method is usually applied in case of a great number of serial process results, but it can also be
used for small series (a small number of process results).
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 3534-2, Statistics — Vocabulary and symbols — Part 2: Applied statistics
ISO 5479, Statistical interpretation of data — Tests for departure from the normal distribution
ISO 22514-1, Statistical methods in process management — Capability and performance — Part 1: General
principles and concepts
3 Terms, definitions, symbols and abbreviated terms
For the purposes of this document, the terms and definitions given in ISO 3534-2 and ISO 22514-1, and
the following symbols and abbreviated terms, apply.
3.1 Symbols
C process capability index
p
C minimum process capability index
pk
C lower process capability index
pkL
C upper process capability index
pkU
c constant based on subgroup size n
4
Δ dispersion of the process
© ISO 2013 – All rights reserved 1

---------------------- Page: 6 ----------------------
ISO 22514-2:2013(E)

Δ difference between X and X of the distribution of the product characteristic
L mid 0,135 %
Δ difference between X and X of the distribution of the product characteristic
U 99,865 % mid
d constant based on subgroup size n
2
k number of subgroups of the same size n
μ average location of the process
L lower specification limit
M Calculation methods with location method label l and dispersion method label d
l,d
N sample size
p lower fraction nonconforming
L
p total fraction nonconforming
t
p upper fraction nonconforming
U
P process performance index
p
P minimum process performance index
pk
P lower process performance index
pkL
P upper process performance index
pkU
R range of the ith subgroup
i
s standard deviation, realized value
σ standard deviation, population
S standard deviation, sample statistic
S observed sample standard deviation of the ith subgroup
i
S standard deviation, with the subscript “t” indicating total standard deviation
t
U upper specification limit
X 0,135 % distribution quantile
0,135 %
X 99,865 % distribution quantile
99,865 %
X 50 % distribution quantile
50 %
X distribution midpoint
mid
3.2 Abbreviations
ANOVA analysis of variance
SPC statistical process control
2 © ISO 2013 – All rights reserved

---------------------- Page: 7 ----------------------
ISO 22514-2:2013(E)

4 Process analysis
The purpose of process analysis is to obtain knowledge of a process. This knowledge is necessary for
controlling the process efficiently and effectively so that the products realized by the process fulfil the
quality requirement. It is a general assumption of this part of ISO 22514 that a process analysis has been
carried out and subsequent process improvements have been implemented.
The behaviour of a characteristic under consideration can be described by the distribution, the location,
the dispersion and the shape, parameters of which are time-dependent functions, in general. Different
models of such resulting distributions the parameters of which are time-dependent functions are
discussed in Clauses 6 and 7. To indicate whether a time-dependent distribution model fits, statistical
methods [e.g. estimating parameters, analysis of variance (ANOVA)] including graphical tools (e.g.
probability plots, control charts) are used.
The values of the characteristics under consideration are typically determined on the basis of samples
taken from the process flow. The sample size and frequency should be chosen depending on the type
of process and the type of product so that all important changes are detected in time. The samples
should be representative for the characteristic under consideration. To asses the stability of the process
a control chart should be used. Information on the use of control charts can be found in ISO 7870-2.
5 Time-dependent distribution models
The instantaneous distribution characterizes the behaviour of the characteristic under investigation
during a short interval. Usually, it is the time interval during which the sample (e.g. the subgroup) can be
taken from the process. Observing the process continuously in time for a longer time interval the output
from the process is called the resulting process distribution and it is described by a corresponding time-
dependent distribution model that reflects
— the instantaneous distribution of the characteristic under consideration, and
— the changes of its location, dispersion and shape parameters during the time interval of process
observation.
In practice, the resulting distribution can be represented by the whole data set, e.g. when SPC is applied,
by all subgroups gained during the interval of the process observation.
Time-dependent distribution models can be classified into four groups according to whether the location
and dispersion moments are constant or changing (see Table 1).
a) A process whose location and dispersion are constant is in time-dependent distribution model A.
In this case only, all the means and variances of the instantaneous distributions are equal to each
other and they are equal to the resulting distribution.
b) If the dispersion of a process is changing with time, but the location stays constant, the process is
said to be in time-dependent distribution model B.
c) If the dispersion is constant, but the location is changing, we have time-dependent distribution model C.
d) Otherwise, we have time-dependent distribution model D.
© ISO 2013 – All rights reserved 3

---------------------- Page: 8 ----------------------
ISO 22514-2:2013(E)

4 © ISO 2013 – All rights reserved
Table 1 — Classification of time-dependent distribution models
Process average µ(t)
Process-standard
deviation s(t)
Constant Not constant
A C

A1 A2 C1 C2 C3 C4
Systematic and
Systematic
random
Location Random Random
(e.g. trend)
(e.g. lot to lot)
Constant Not
Short
Short time distribu- Normal Normal Normal Normal
Normal normal
time
tion distributed distributed distributed distributed
distributed distributed
distribution
– unimodal
Not
Normal normal distrib- Any shape
Resulting distribution Any shape
distributed uted (e.g. multimodal)
– unimodal
B D
Not Resulting
Resulting distribution
constant distribution
Any shape – unimodal Any shape

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ISO 22514-2:2013(E)

For changing moments, the models can be classified according to whether the changes are random,
systematic or both.
NOTE Model A2 is known as stationary in time-series analysis literature and model A1 is known as second
order stationary.
Table 2 summarizes the basic features of individual time-dependent distribution models; their graphical
representations are given in Figures 1 to 8. There are subclasses of time-dependent distribution models
A and C which are introduced due to their practical importance. They differ in the shape of the resulting
distribution and in the cause of the process being in an out-of-control state.
Table 2 — Basic features of time-dependent distribution models
a
Time-dependent distribution models
Characteristic
A1 A2 B C1 C2 C3 C4 D
Location c c c
...