Statistical methods in process management -- Capability and performance

ISO 22514-2:2017 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 document 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).

Méthodes statistiques dans la gestion de processus -- Aptitude et performance

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

Ta dokument 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 dokumenta se nanašajo samo na trajne kakovostne karakteristike.
Uporabljajo se za procese v katerem koli industrijskem ali gospodarskem sektorju.
OPOMBA: Ta metoda se običajno uporablja v primeru velikega števila serijskih rezultatov procesov, vendar se lahko uporablja tudi za majhne serije (majhno število rezultatov procesov).

General Information

Status
Published
Publication Date
05-Feb-2017
Current Stage
6060 - International Standard published
Start Date
29-Dec-2016
Completion Date
06-Feb-2017

RELATIONS

Buy Standard

Standard
ISO 22514-2:2017 - Statistical methods in process management -- Capability and performance
English language
21 pages
sale 15% off
Preview
sale 15% off
Preview
Standard
ISO 22514-2:2017 - BARVE na PDF-str 14,15,16,17,18,19,20,21
English language
26 pages
sale 10% off
Preview
sale 10% off
Preview

e-Library read for
1 day

Standards Content (sample)

INTERNATIONAL ISO
STANDARD 22514-2
Second edition
2017-02
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 22514-2:2017(E)
ISO 2017
---------------------- Page: 1 ----------------------
ISO 22514-2:2017(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2017, Published in Switzerland

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
Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. +41 22 749 01 11
Fax +41 22 749 09 47
copyright@iso.org
www.iso.org
ii © ISO 2017 – All rights reserved
---------------------- Page: 2 ----------------------
ISO 22514-2:2017(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 Abbreviated terms ............................................................................................................................................................................... 2

4 Process analysis ..................................................................................................................................................................................................... 3

5 Time-dependent distribution models ............................................................................................................................................ 3

6 Process capability and performance indices .......................................................................................................................14

6.1 Methods for determination of performance and capability indices — Overview .....................14

6.1.1 General...................................................................................................................................................................................14

6.1.2 Calculation of location ........................................................................................................................................... ...15

6.1.3 Calculation of dispersion .......................................................................................................................................16

6.1.4 Calculation of X and X ............................................................................................................

0,135 % 99,865 % 17

6.2 One-sided specification limits.................................................................................................................................................18

6.3 Use of different calculation methods ................................................................................................................................19

7 Reporting process performance/capability indices ....................................................................................................20

Bibliography .............................................................................................................................................................................................................................21

© ISO 2017 – All rights reserved iii
---------------------- Page: 3 ----------------------
ISO 22514-2:2017(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www .iso .org/ patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation on the meaning of ISO specific terms and expressions related to conformity assessment,

as well as information about ISO’s adherence to the World Trade Organization (WTO) principles in the

Technical Barriers to Trade (TBT) see the following URL: www . i so .org/ iso/ foreword .html

The committee responsible for this document is ISO/TC 69, Applications of statistical methods,

Subcommittee SC 4, Applications of statistical methods in process management.

This second edition of ISO 22514-2 cancels and replaces the corrected version of the first edition

(ISO 22514-2:2013), of which it constitutes a minor revision.
The changes compared to the previous edition are as follows:
— the symbols and indices in C , C , P and P have been improved;
pk pk pk pk
L U L U

— in Table 2, row “Location”, column “C”, the letter “s” has been replaced by “s/r”;

— in Table 2, row “Location”, column “D”, the capital letter “S” has been replaced by “s/r”;

— in Table 3, row “Location method label”, rows “3” and “4” – in Formulae (13) and (14) the usage of

indices has been improved and it is more precise now;

— editorial adjustments have been made to comply with the latest edition of the ISO/IEC Directives,

Part 2, 2016.

A list of all parts in the ISO 22514- series, published under the general title Statistical methods in process

management — Capability and performance, can be found on the ISO website.
iv © ISO 2017 – All rights reserved
---------------------- Page: 4 ----------------------
ISO 22514-2:2017(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 document 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 document 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 2017 – All rights reserved v
---------------------- Page: 5 ----------------------
INTERNATIONAL STANDARD ISO 22514-2:2017(E)
Statistical methods in process management — Capability
and performance —
Part 2:
Process capability and performance of time-dependent
process models
1 Scope

This document 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 document 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 are referred to in the text in such a way that some or all of their content

constitutes requirements of this document. For dated references, only the edition cited applies. For

undated references, the latest edition of the referenced document (including any amendments) applies.

ISO 5479, Statistical interpretation of data — Tests for departure from the normal distribution

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 symbols and abbreviated terms given below, apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— IEC Electropedia: available at http:// www .electropedia .org/
— ISO Online browsing platform: available at http:// www .iso .org/ obp
3.1 Symbols
C process capability index
C minimum process capability index
lower process capability index
upper process capability index
c constant based on subgroup size n
© ISO 2017 – All rights reserved 1
---------------------- Page: 6 ----------------------
ISO 22514-2:2017(E)
Δ dispersion of the process
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
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
p total fraction nonconforming
p upper fraction nonconforming
P process performance index
P minimum process performance index
lower process performance index
upper process performance index
R range of the ith subgroup
s standard deviation, realized value
σ standard deviation, population
S standard deviation, sample statistic
S observed sample standard deviation of the ith subgroup
S standard deviation, with the subscript “t” indicating total standard deviation
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 Abbreviated terms
ANOVA analysis of variance
SPC statistical process control
2 © ISO 2017 – All rights reserved
---------------------- Page: 7 ----------------------
ISO 22514-2:2017(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 document 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 2017 – All rights reserved 3
---------------------- Page: 8 ----------------------
ISO 22514-2:2017(E)
4 © ISO 2017 – 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)
Not
Constant
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
---------------------- Page: 9 ----------------------
ISO 22514-2:2017(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
...

SLOVENSKI STANDARD
SIST ISO 22514-2:2017
01-maj-2017
1DGRPHãþD
SIST ISO 22514-2:2014
6WDWLVWLþQHPHWRGH]DREYODGRYDQMHSURFHVRY=PRJOMLYRVWLQGHORYDQMHGHO
3URFHVQH]PRJOMLYRVWLLQGHORYDQMHþDVRYQRRGYLVQLKPRGHOQLKSURFHVRY
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 22514-2:2017
ICS:
03.120.30 8SRUDEDVWDWLVWLþQLKPHWRG Application of statistical
methods
SIST ISO 22514-2:2017 en,fr

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------
SIST ISO 22514-2:2017
---------------------- Page: 2 ----------------------
SIST ISO 22514-2:2017
INTERNATIONAL ISO
STANDARD 22514-2
Second edition
2017-02
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 22514-2:2017(E)
ISO 2017
---------------------- Page: 3 ----------------------
SIST ISO 22514-2:2017
ISO 22514-2:2017(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2017, Published in Switzerland

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
Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. +41 22 749 01 11
Fax +41 22 749 09 47
copyright@iso.org
www.iso.org
ii © ISO 2017 – All rights reserved
---------------------- Page: 4 ----------------------
SIST ISO 22514-2:2017
ISO 22514-2:2017(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 Abbreviated terms ............................................................................................................................................................................... 2

4 Process analysis ..................................................................................................................................................................................................... 3

5 Time-dependent distribution models ............................................................................................................................................ 3

6 Process capability and performance indices .......................................................................................................................14

6.1 Methods for determination of performance and capability indices — Overview .....................14

6.1.1 General...................................................................................................................................................................................14

6.1.2 Calculation of location ........................................................................................................................................... ...15

6.1.3 Calculation of dispersion .......................................................................................................................................16

6.1.4 Calculation of X and X ............................................................................................................

0,135 % 99,865 % 17

6.2 One-sided specification limits.................................................................................................................................................18

6.3 Use of different calculation methods ................................................................................................................................19

7 Reporting process performance/capability indices ....................................................................................................20

Bibliography .............................................................................................................................................................................................................................21

© ISO 2017 – All rights reserved iii
---------------------- Page: 5 ----------------------
SIST ISO 22514-2:2017
ISO 22514-2:2017(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www .iso .org/ patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation on the meaning of ISO specific terms and expressions related to conformity assessment,

as well as information about ISO’s adherence to the World Trade Organization (WTO) principles in the

Technical Barriers to Trade (TBT) see the following URL: www . i so .org/ iso/ foreword .html

The committee responsible for this document is ISO/TC 69, Applications of statistical methods,

Subcommittee SC 4, Applications of statistical methods in process management.

This second edition of ISO 22514-2 cancels and replaces the corrected version of the first edition

(ISO 22514-2:2013), of which it constitutes a minor revision.
The changes compared to the previous edition are as follows:
— the symbols and indices in C , C , P and P have been improved;
pk pk pk pk
L U L U

— in Table 2, row “Location”, column “C”, the letter “s” has been replaced by “s/r”;

— in Table 2, row “Location”, column “D”, the capital letter “S” has been replaced by “s/r”;

— in Table 3, row “Location method label”, rows “3” and “4” – in Formulae (13) and (14) the usage of

indices has been improved and it is more precise now;

— editorial adjustments have been made to comply with the latest edition of the ISO/IEC Directives,

Part 2, 2016.

A list of all parts in the ISO 22514- series, published under the general title Statistical methods in process

management — Capability and performance, can be found on the ISO website.
iv © ISO 2017 – All rights reserved
---------------------- Page: 6 ----------------------
SIST ISO 22514-2:2017
ISO 22514-2:2017(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 document 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 document 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 2017 – All rights reserved v
---------------------- Page: 7 ----------------------
SIST ISO 22514-2:2017
---------------------- Page: 8 ----------------------
SIST ISO 22514-2:2017
INTERNATIONAL STANDARD ISO 22514-2:2017(E)
Statistical methods in process management — Capability
and performance —
Part 2:
Process capability and performance of time-dependent
process models
1 Scope

This document 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 document 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 are referred to in the text in such a way that some or all of their content

constitutes requirements of this document. For dated references, only the edition cited applies. For

undated references, the latest edition of the referenced document (including any amendments) applies.

ISO 5479, Statistical interpretation of data — Tests for departure from the normal distribution

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 symbols and abbreviated terms given below, apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— IEC Electropedia: available at http:// www .electropedia .org/
— ISO Online browsing platform: available at http:// www .iso .org/ obp
3.1 Symbols
C process capability index
C minimum process capability index
lower process capability index
upper process capability index
c constant based on subgroup size n
© ISO 2017 – All rights reserved 1
---------------------- Page: 9 ----------------------
SIST ISO 22514-2:2017
ISO 22514-2:2017(E)
Δ dispersion of the process
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
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
p total fraction nonconforming
p upper fraction nonconforming
P process performance index
P minimum process performance index
lower process performance index
upper process performance index
R range of the ith subgroup
s standard deviation, realized value
σ standard deviation, population
S standard deviation, sample statistic
S observed sample standard deviation of the ith subgroup
S standard deviation, with the subscript “t” indicating total standard deviation
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 Abbreviated terms
ANOVA analysis of variance
SPC statistical process control
2 © ISO 2017 – All rights reserved
---------------------- Page: 10 ----------------------
SIST ISO 22514-2:2017
ISO 22514-2:2017(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 document 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 2017 – All rights reserved 3
---------------------- Page: 11 ----------------------
SIST ISO 22514-2:2017
ISO 22514-2:2017(E)
4 © ISO 2017 – 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)
Not
Constant
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
...

Questions, Comments and Discussion

Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.