# ISO 22514-4:2016

(Main)## Statistical methods in process management — Capability and performance — Part 4: Process capability estimates and performance measures

## Statistical methods in process management — Capability and performance — Part 4: Process capability estimates and performance measures

ISO 22514-4:2016 describes process capability and performance measures that are commonly used.

## Méthodes statistiques dans la gestion de processus — Aptitude et performance — Partie 4: Estimations de l'aptitude de processus et mesures de performance

## Statistične metode za obvladovanje procesov - Zmogljivost in delovanje - 4. del: Ocene zmogljivosti procesov in merila za delovanje

Ta del standarda ISO 22514 opisuje zmogljivost procesov in merila učinkovitosti, ki se običajno uporabljajo.

### General Information

### Relations

### Standards Content (Sample)

INTERNATIONAL ISO

STANDARD 22514-4

First edition

2016-08-01

Statistical methods in process

management — Capability and

performance —

Part 4:

Process capability estimates and

performance measures

Méthodes statistiques dans la gestion de processus — Aptitude et

performance —

Partie 4: Estimations de l’aptitude de processus et mesures de

performance

Reference number

ISO 22514-4:2016(E)

©

ISO 2016

---------------------- Page: 1 ----------------------

ISO 22514-4:2016(E)

COPYRIGHT PROTECTED DOCUMENT

© ISO 2016, 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 2016 – All rights reserved

---------------------- Page: 2 ----------------------

ISO 22514-4:2016(E)

Contents Page

Foreword .v

Introduction .vi

1 Scope . 1

2 Symbols and abbreviated terms . 1

2.1 Symbols . 1

2.2 Abbreviated terms . 3

3 Basic concepts used for process capability and performance . 3

3.1 General . 3

3.2 Location . 3

3.3 Dispersion . 3

3.3.1 Inherent dispersion . 3

3.3.2 Total dispersion . 3

3.3.3 Short-term dispersion . 3

3.4 Mean square error (MSE) . 4

3.5 Reference limits . 4

3.6 Reference interval (also known as process spread) . 4

4 Capability . 4

4.1 General . 4

4.2 Process capability . 6

4.2.1 Normal distribution . 6

4.2.2 Non-normal distribution. 7

4.3 Process location . 7

4.4 Process capability indices for measured data . 8

4.4.1 General. 8

4.4.2 C index (for the normal distribution) . 9

p

4.4.3 C index (for the normal distribution) .10

pk

4.4.4 C index for unilateral tolerances .10

pk

4.5 Process capability indices for measured data (non-normal) .10

4.5.1 General.10

4.5.2 Probability paper method .11

4.5.3 Pearson curves method .11

4.5.4 Distribution identification method .12

4.6 Alternative method for describing and calculating process capability estimates .12

4.7 Other capability measures for continuous data .13

4.7.1 Process capability fraction (PCF) .13

4.7.2 Indices when the specification limit is one-sided or no specification limit

is given .13

4.8 Assessment of proportion out-of-specification (normal distribution) .15

5 Performance .16

5.1 General .16

5.2 Process performance indices for measured data (normal distribution) .16

5.2.1 P index .16

p

5.2.2 P index .17

pk

5.3 Process performance indices for measured data (non-normal distribution) .17

5.3.1 General.17

5.3.2 Probability paper method .17

5.3.3 Pearson curves method .18

5.3.4 Distribution identification method .18

5.4 Other performance indices for measured data .18

5.5 Assessment of proportion out-of-specification for a normal distribution of the

total distribution .18

6 Reporting process capability and performance indices .19

© ISO 2016 – All rights reserved iii

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ISO 22514-4:2016(E)

Annex A (informative) Estimating standard deviations .21

Annex B (informative) Estimating capability and performance measures using Pearson

curves — Procedure and example .23

Annex C (informative) Distribution identification .37

Annex D (informative) Confidence intervals .42

Bibliography .44

iv © ISO 2016 – All rights reserved

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

ISO 22514-4:2016(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 WTO principles in the Technical

Barriers to Trade (TBT) see the following URL: Foreword - Supplementary information.

The committee responsible for this document is Technical Committee ISO/TC 69, Applications of

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

This first edition of ISO 22514-4 cancels and replaces ISO/TR 22514-4:2007, which has been technically

revised.

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 estimates and performance for attributive 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

© ISO 2016 – All rights reserved v

---------------------- Page: 5 ----------------------

ISO 22514-4:2016(E)

Introduction

Many organizations have embarked upon a continuous improvement strategy. To comply with such a

strategy, any organization will need to evaluate the capability and performance of its key processes.

The methods described in this part of ISO 22514 are intended to assist any management in this respect.

These evaluations need to be constantly reviewed by the management so that actions compatible with

continuous improvement can be taken when required.

The content of this part of ISO 22514 has been subject to large shifts of opinion during recent times. The

most fundamental shift has been to philosophically separate what is named in this part of ISO 22514 as

capability conditions from performance conditions, the primary difference being whether statistical

stability has been obtained (capability) or not (performance). This naturally leads onto the two sets of

indices that are to be found in their relevant clauses. It has become necessary to draw a firm distinction

between these since it has been observed in the industry that companies have been deceived about

their true capability position due to inappropriate indices being calculated and published.

The progression of this part of ISO 22514 is from the general condition to the specific and this approach

leads to general formulae being presented before their more usual, but specific manifestations.

There exist numerous references that describe the importance of understanding the processes at

work within any organization, be it a manufacturing process or an information handling process. As

organizations compete for sales with each other, it has become increasingly apparent that it is not only

the price paid for a product or service that matters so much, but also what costs will be incurred by the

purchaser from using such a product or service. The objective for any supplier is to continually reduce

variability and not to just satisfy specification.

Continual improvement leads to reductions in the costs of failure and assists in the drive for survival in

an increasingly more competitive world. There will also be savings in appraisal costs for as variation is

reduced, the need to inspect product might disappear or the frequency of sampling might be reduced.

Process capability and performance evaluations are necessary to enable organizations to assess the

capability and performance of their suppliers. Those organizations will find the indices contained

within this part of ISO 22514 useful in this endeavour.

Quantifying the variation present within a process enables judgement of its suitability and ability

to meet some given requirement. The following paragraphs and clauses provide an outline of the

philosophy required to be understood to determine the capability or performance of any process.

All processes will be subject to certain inherent variability. This part of ISO 22514 does not attempt

to explain what is meant by inherent variation, why it exists, where it comes from nor how it affects a

process. This part of ISO 22514 starts from the premise that it exists and is stable.

Process owners should endeavour to understand the sources of variation in their processes. Methods

such as flowcharting the process and identifying the inputs and outputs from a process assist in

identification of these variations together with the appropriate use of cause and effect (fishbone)

diagrams.

It is important for the user of this part of ISO 22514 to appreciate that variations exist that will be of a

short-term nature, as well as those that will be of a long-term nature and that capability determinations

using only the short-term variation might be greatly different to those which have used the long-term

variability.

When considering short-term variation, a study that uses only the shortest-term variation, sometimes

known as a machine study and described in ISO 22514-3, might be carried out. The method required to

carry out such a study will be outside the scope of this part of ISO 22514; however, it should be noted

that such studies are important and useful.

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

vi © ISO 2016 – All rights reserved

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ISO 22514-4:2016(E)

indices’ confidence intervals are computed and reported. This part of ISO 22514 describes methods by

which these can be computed.

© ISO 2016 – All rights reserved vii

---------------------- Page: 7 ----------------------

INTERNATIONAL STANDARD ISO 22514-4:2016(E)

Statistical methods in process management — Capability

and performance —

Part 4:

Process capability estimates and performance measures

1 Scope

This part of ISO 22514 describes process capability and performance measures that are commonly used.

2 Symbols and abbreviated terms

2.1 Symbols

In addition to the symbols listed below, some symbols are defined where they are used within the text.

α fraction or proportion

β shape parameter in a Weibull distribution

β coefficient of kurtosis

2

c constant based on subgroup size, n (see ISO 7870-2)

4

C process capability index

p

C minimum process capability index

pk

lower process capability index

C

pk

L

upper process capability index

C

pk

U

C alternative process capability index

pm

C process capability fraction (PCF)

R

d constant based on subgroup size, n (see ISO 7870-2)

2

e Eulers’s number (approximately 2,718), mathematical constant

Φ distribution function of the standard normal distribution

γ location parameter in a Weibull distribution

γ coefficient of skewness

1

m number of subgroups

K , K multipliers for estimating the confidence limits for a process capability index

l u

L lower specification limit

© ISO 2016 – All rights reserved 1

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ISO 22514-4:2016(E)

P lower 0,135 % percentile

0,135 %

μ location of the process; population mean value

N total sample size

n number of values or subgroup size (for a control chart)

P α percentile

α %

p lower fraction nonconforming

L

P process performance index

p

P minimum process performance index

pk

lower process performance index

P

pk

L

upper process performance index

P

pk

U

p total fraction nonconforming

t

p upper fraction nonconforming

U

P upper 99,865 % percentile

99,865 %

π geometric constant

Q process variation index

k

θ parameter required for the Rayleigh distribution

average subgroup range

R

S standard deviation, sample statistic

S standard deviation, with the subscript ‘t’ indicating total

t

average sample standard deviation

S

th

S observed sample standard deviation of the j subgroup

j

σ standard deviation, population

estimated standard deviation, total

ˆ

σ

t

T target value

U upper specification limit

X α % percentile

α %

th

X i value in a sample

i

arithmetic mean value, sample

X

arithmetic mean, of a number of sample arithmetic means

X

2 © ISO 2016 – All rights reserved

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ISO 22514-4:2016(E)

ξ scale parameter in a Weibull distribution

Y , Y values read from a graph

1 2

z quantile of the standardized normal distribution from −∞ to α

α

2.2 Abbreviated terms

MSE mean square error

PCF process capability fraction

PCI process capability index

3 Basic concepts used for process capability and performance

3.1 General

The measures referred to in 4.2 to 4.6 refer only to measured data. They are unsuitable for count or

attributes data and information concerning the expression of measures for such data will be found in

ISO 22514-5.

3.2 Location

The characterization of location is the mean, μ, or the median, X . Although for symmetric

50 %

distributions the mean is the most natural selection, with non-symmetric distributions the median is

the preferred selection.

3.3 Dispersion

3.3.1 Inherent dispersion

The preferred selection to quantify inherent dispersion is the standard deviation σ. This is often

estimated from the mean range value, R , taken from a range (R) chart or S from a standard deviation

(S) chart when the process is stable and in a state of statistical control as indicated in 4.1. Methods used

to estimate the process standard deviation are given in Annex A.

3.3.2 Total dispersion

It is necessary to differentiate between a standard deviation that measures only short-term variation

and that which measures longer-term variation. The total dispersion is the dispersion that is inherent in

the long-term variation. Methods of calculating the standard deviations representing these variations

are given in Annex A. Very often, when data are gathered over a long period of time, the standard

deviation is made larger by the effects of fluctuations in the process, σ .

t

3.3.3 Short-term dispersion

A process may have a short-term dispersion effect that is a part of the total dispersion. Figure 1

illustrates this. The short-term dispersion includes the inherent dispersion and can also include some

short-term instability effect.

© ISO 2016 – All rights reserved 3

---------------------- Page: 10 ----------------------

ISO 22514-4:2016(E)

Key

1 short-term dispersion

2 overall dispersion

Figure 1 — Short-term dispersion and its relationship to the total dispersion

The total dispersion can be any shape and not necessarily normal as illustrated here.

3.4 Mean square error (MSE)

When minimizing variation, some practitioners use the mean square error as the preferred measure. It

is compatible with the methods used in off-line quality techniques.

3.5 Reference limits

The lower and upper reference limits are respectively defined as the 0,135 % and the 99,865 %

percentiles of the distribution that describe the output of the process characteristic. They are written

as X and X .

0,135 5 % 99,865 %

3.6 Reference interval (also known as process spread)

The reference interval is the interval between the upper and the lower reference limits. The reference

interval includes 99,73 % of the individuals in the population from a process that is in a state of

statistical control.

4 Capability

4.1 General

Process capability is a measure of inherent process variability. The variability that is inherent in a

process when operating in a state of statistical control is known as the inherent process variability. It

represents the variation that remains after all known removable assignable causes have been eliminated.

If the process is monitored using a control chart, the control chart will show an in control state.

Capability is often regarded as being related to the proportion of output that will occur within the

product specification tolerances. Since a process in statistical control should be described by a

predictable distribution, the proportion of out-of-specification outputs can be estimated. As long

as the process remains in statistical control, it will continue to produce the same proportion out-of-

specification.

Management actions to reduce the variation from random causes are required to improve the process’

ability to consistently meet the specification requirements.

4 © ISO 2016 – All rights reserved

---------------------- Page: 11 ----------------------

ISO 22514-4:2016(E)

In short, the following will be necessary:

— define the process and its operating conditions. If there is a change to those conditions, it will

necessitate a new process study;

— assess the short-term and long-term measurement variabilities as percentages of the total variability

and minimize them;

— preserve the process stability and maintain its statistical control;

— estimate the remaining inherent variation;

— select an appropriate measure of capability.

The following are the conditions that will apply for capability:

— all technical conditions, e.g. temperature and humidity, shall be clearly stated;

— the uncertainty of the measurement system shall be estimated and judged appropriate (see

ISO 22514-7);

— multi-factor, multi-level aspects of the process should be allowed;

— the duration over which the data has been gathered shall be recorded;

— the frequency of sampling and sample size shall be specified and the start and finish dates of data

collection;

— the process shall be controlled with a control chart;

— the process shall be in a state of statistical control.

It is necessary to check the control chart from which the data have been taken for statistical control

and to examine a histogram of the data with any specification limits superimposed upon it. A valid

[15]

test for normality should be used in assessing the data such as the Anderson-Darling test or any

other suitable method. This test is powerful in detecting departures from normality in the tails of

the distribution and is suggested here as this is the region of interest for capability and performance

indices. Additionally, a normal probability plot can be used to look for the following:

a) verification of normality;

b) outliers;

c) data beyond any specification limit;

d) whether the data are well inside the specification limit(s);

e) evidence of asymmetry (i.e. skewness);

f) evidence of “long tails” in the data (i.e. kurtosis);

g) off-centre distribution;

h) any unusual patterns.

Explanations of anomalies should be sought in relation to these mentioned features and appropriate

action taken on the data prior to the calculation of any measure. It would be inappropriate to just discard

data that do not appear to fit any preconceived pattern. Such departures might be very revealing about

the process’ behaviour and should be thoroughly investigated.

© ISO 2016 – All rights reserved 5

---------------------- Page: 12 ----------------------

ISO 22514-4:2016(E)

4.2 Process capability

4.2.1 Normal distribution

Process capability is defined as a statistical measure of inherent process variability for a given

characteristic. The conventional method is to take the reference interval that describes 99,73 % of the

individual values from a process that is in a state of statistical control with the 0,135 % remaining on

each side. This applies even if the population of individual values is not normally distributed. For a

normal distribution, this process interval is represented by six standard deviations (see Figure 2).

Y₂

Y₁

a

0,135 %

0,135 %

Key

a

Reference interval 99,73 %.

Figure 2 — Normal distribution

On occasions, process capability is taken to account for extra sources of variation such as a multiple

stream process, for example, output from a multi-cavity injection moulding press. Under these

circumstances, the distribution of all values from all cavities could still be approximately normal,

but with extra variability so that the standard deviation shall represent the total variation, σ . It is

t

important to state how the standard deviation has been calculated, as well as the sampling strategy

used, sample size and the quantity and variability of output produced between samples as these will, in

practice, affect the validity of the capability assessment (see ISO 22514-2 for further information).

Data will usually be taken from a control chart. If the control chart had relaxed control lines or modified

control lines, the real process standard deviation will be lar

**...**

SLOVENSKI STANDARD

SIST ISO 22514-4:2017

01-maj-2017

1DGRPHãþD

SIST-TP ISO/TR 22514-4:2010

6WDWLVWLþQHPHWRGH]DREYODGRYDQMHSURFHVRY=PRJOMLYRVWLQGHORYDQMHGHO

2FHQH]PRJOMLYRVWLSURFHVRYLQPHULOD]DGHORYDQMH

Statistical methods in process management - Capability and performance - Part 4:

Process capability estimates and performance measures

Méthodes statistiques dans la gestion de processus - Aptitude et performance - Partie 4:

Estimations de l'aptitude de processus et mesures de performance

Ta slovenski standard je istoveten z: ISO 22514-4:2016

ICS:

03.120.30 8SRUDEDVWDWLVWLþQLKPHWRG Application of statistical

methods

SIST ISO 22514-4:2017 en,fr

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

---------------------- Page: 1 ----------------------

SIST ISO 22514-4:2017

---------------------- Page: 2 ----------------------

SIST ISO 22514-4:2017

INTERNATIONAL ISO

STANDARD 22514-4

First edition

2016-08-01

Statistical methods in process

management — Capability and

performance —

Part 4:

Process capability estimates and

performance measures

Méthodes statistiques dans la gestion de processus — Aptitude et

performance —

Partie 4: Estimations de l’aptitude de processus et mesures de

performance

Reference number

ISO 22514-4:2016(E)

©

ISO 2016

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

SIST ISO 22514-4:2017

ISO 22514-4:2016(E)

COPYRIGHT PROTECTED DOCUMENT

© ISO 2016, 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 2016 – All rights reserved

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

SIST ISO 22514-4:2017

ISO 22514-4:2016(E)

Contents Page

Foreword .v

Introduction .vi

1 Scope . 1

2 Symbols and abbreviated terms . 1

2.1 Symbols . 1

2.2 Abbreviated terms . 3

3 Basic concepts used for process capability and performance . 3

3.1 General . 3

3.2 Location . 3

3.3 Dispersion . 3

3.3.1 Inherent dispersion . 3

3.3.2 Total dispersion . 3

3.3.3 Short-term dispersion . 3

3.4 Mean square error (MSE) . 4

3.5 Reference limits . 4

3.6 Reference interval (also known as process spread) . 4

4 Capability . 4

4.1 General . 4

4.2 Process capability . 6

4.2.1 Normal distribution . 6

4.2.2 Non-normal distribution. 7

4.3 Process location . 7

4.4 Process capability indices for measured data . 8

4.4.1 General. 8

4.4.2 C index (for the normal distribution) . 9

p

4.4.3 C index (for the normal distribution) .10

pk

4.4.4 C index for unilateral tolerances .10

pk

4.5 Process capability indices for measured data (non-normal) .10

4.5.1 General.10

4.5.2 Probability paper method .11

4.5.3 Pearson curves method .11

4.5.4 Distribution identification method .12

4.6 Alternative method for describing and calculating process capability estimates .12

4.7 Other capability measures for continuous data .13

4.7.1 Process capability fraction (PCF) .13

4.7.2 Indices when the specification limit is one-sided or no specification limit

is given .13

4.8 Assessment of proportion out-of-specification (normal distribution) .15

5 Performance .16

5.1 General .16

5.2 Process performance indices for measured data (normal distribution) .16

5.2.1 P index .16

p

5.2.2 P index .17

pk

5.3 Process performance indices for measured data (non-normal distribution) .17

5.3.1 General.17

5.3.2 Probability paper method .17

5.3.3 Pearson curves method .18

5.3.4 Distribution identification method .18

5.4 Other performance indices for measured data .18

5.5 Assessment of proportion out-of-specification for a normal distribution of the

total distribution .18

6 Reporting process capability and performance indices .19

© ISO 2016 – All rights reserved iii

---------------------- Page: 5 ----------------------

SIST ISO 22514-4:2017

ISO 22514-4:2016(E)

Annex A (informative) Estimating standard deviations .21

Annex B (informative) Estimating capability and performance measures using Pearson

curves — Procedure and example .23

Annex C (informative) Distribution identification .37

Annex D (informative) Confidence intervals .42

Bibliography .44

iv © ISO 2016 – All rights reserved

---------------------- Page: 6 ----------------------

SIST ISO 22514-4:2017

ISO 22514-4:2016(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 WTO principles in the Technical

Barriers to Trade (TBT) see the following URL: Foreword - Supplementary information.

The committee responsible for this document is Technical Committee ISO/TC 69, Applications of

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

This first edition of ISO 22514-4 cancels and replaces ISO/TR 22514-4:2007, which has been technically

revised.

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 estimates and performance for attributive 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

© ISO 2016 – All rights reserved v

---------------------- Page: 7 ----------------------

SIST ISO 22514-4:2017

ISO 22514-4:2016(E)

Introduction

Many organizations have embarked upon a continuous improvement strategy. To comply with such a

strategy, any organization will need to evaluate the capability and performance of its key processes.

The methods described in this part of ISO 22514 are intended to assist any management in this respect.

These evaluations need to be constantly reviewed by the management so that actions compatible with

continuous improvement can be taken when required.

The content of this part of ISO 22514 has been subject to large shifts of opinion during recent times. The

most fundamental shift has been to philosophically separate what is named in this part of ISO 22514 as

capability conditions from performance conditions, the primary difference being whether statistical

stability has been obtained (capability) or not (performance). This naturally leads onto the two sets of

indices that are to be found in their relevant clauses. It has become necessary to draw a firm distinction

between these since it has been observed in the industry that companies have been deceived about

their true capability position due to inappropriate indices being calculated and published.

The progression of this part of ISO 22514 is from the general condition to the specific and this approach

leads to general formulae being presented before their more usual, but specific manifestations.

There exist numerous references that describe the importance of understanding the processes at

work within any organization, be it a manufacturing process or an information handling process. As

organizations compete for sales with each other, it has become increasingly apparent that it is not only

the price paid for a product or service that matters so much, but also what costs will be incurred by the

purchaser from using such a product or service. The objective for any supplier is to continually reduce

variability and not to just satisfy specification.

Continual improvement leads to reductions in the costs of failure and assists in the drive for survival in

an increasingly more competitive world. There will also be savings in appraisal costs for as variation is

reduced, the need to inspect product might disappear or the frequency of sampling might be reduced.

Process capability and performance evaluations are necessary to enable organizations to assess the

capability and performance of their suppliers. Those organizations will find the indices contained

within this part of ISO 22514 useful in this endeavour.

Quantifying the variation present within a process enables judgement of its suitability and ability

to meet some given requirement. The following paragraphs and clauses provide an outline of the

philosophy required to be understood to determine the capability or performance of any process.

All processes will be subject to certain inherent variability. This part of ISO 22514 does not attempt

to explain what is meant by inherent variation, why it exists, where it comes from nor how it affects a

process. This part of ISO 22514 starts from the premise that it exists and is stable.

Process owners should endeavour to understand the sources of variation in their processes. Methods

such as flowcharting the process and identifying the inputs and outputs from a process assist in

identification of these variations together with the appropriate use of cause and effect (fishbone)

diagrams.

It is important for the user of this part of ISO 22514 to appreciate that variations exist that will be of a

short-term nature, as well as those that will be of a long-term nature and that capability determinations

using only the short-term variation might be greatly different to those which have used the long-term

variability.

When considering short-term variation, a study that uses only the shortest-term variation, sometimes

known as a machine study and described in ISO 22514-3, might be carried out. The method required to

carry out such a study will be outside the scope of this part of ISO 22514; however, it should be noted

that such studies are important and useful.

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

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indices’ confidence intervals are computed and reported. This part of ISO 22514 describes methods by

which these can be computed.

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INTERNATIONAL STANDARD ISO 22514-4:2016(E)

Statistical methods in process management — Capability

and performance —

Part 4:

Process capability estimates and performance measures

1 Scope

This part of ISO 22514 describes process capability and performance measures that are commonly used.

2 Symbols and abbreviated terms

2.1 Symbols

In addition to the symbols listed below, some symbols are defined where they are used within the text.

α fraction or proportion

β shape parameter in a Weibull distribution

β coefficient of kurtosis

2

c constant based on subgroup size, n (see ISO 7870-2)

4

C process capability index

p

C minimum process capability index

pk

lower process capability index

C

pk

L

upper process capability index

C

pk

U

C alternative process capability index

pm

C process capability fraction (PCF)

R

d constant based on subgroup size, n (see ISO 7870-2)

2

e Eulers’s number (approximately 2,718), mathematical constant

Φ distribution function of the standard normal distribution

γ location parameter in a Weibull distribution

γ coefficient of skewness

1

m number of subgroups

K , K multipliers for estimating the confidence limits for a process capability index

l u

L lower specification limit

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P lower 0,135 % percentile

0,135 %

μ location of the process; population mean value

N total sample size

n number of values or subgroup size (for a control chart)

P α percentile

α %

p lower fraction nonconforming

L

P process performance index

p

P minimum process performance index

pk

lower process performance index

P

pk

L

upper process performance index

P

pk

U

p total fraction nonconforming

t

p upper fraction nonconforming

U

P upper 99,865 % percentile

99,865 %

π geometric constant

Q process variation index

k

θ parameter required for the Rayleigh distribution

average subgroup range

R

S standard deviation, sample statistic

S standard deviation, with the subscript ‘t’ indicating total

t

average sample standard deviation

S

th

S observed sample standard deviation of the j subgroup

j

σ standard deviation, population

estimated standard deviation, total

ˆ

σ

t

T target value

U upper specification limit

X α % percentile

α %

th

X i value in a sample

i

arithmetic mean value, sample

X

arithmetic mean, of a number of sample arithmetic means

X

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ξ scale parameter in a Weibull distribution

Y , Y values read from a graph

1 2

z quantile of the standardized normal distribution from −∞ to α

α

2.2 Abbreviated terms

MSE mean square error

PCF process capability fraction

PCI process capability index

3 Basic concepts used for process capability and performance

3.1 General

The measures referred to in 4.2 to 4.6 refer only to measured data. They are unsuitable for count or

attributes data and information concerning the expression of measures for such data will be found in

ISO 22514-5.

3.2 Location

The characterization of location is the mean, μ, or the median, X . Although for symmetric

50 %

distributions the mean is the most natural selection, with non-symmetric distributions the median is

the preferred selection.

3.3 Dispersion

3.3.1 Inherent dispersion

The preferred selection to quantify inherent dispersion is the standard deviation σ. This is often

estimated from the mean range value, R , taken from a range (R) chart or S from a standard deviation

(S) chart when the process is stable and in a state of statistical control as indicated in 4.1. Methods used

to estimate the process standard deviation are given in Annex A.

3.3.2 Total dispersion

It is necessary to differentiate between a standard deviation that measures only short-term variation

and that which measures longer-term variation. The total dispersion is the dispersion that is inherent in

the long-term variation. Methods of calculating the standard deviations representing these variations

are given in Annex A. Very often, when data are gathered over a long period of time, the standard

deviation is made larger by the effects of fluctuations in the process, σ .

t

3.3.3 Short-term dispersion

A process may have a short-term dispersion effect that is a part of the total dispersion. Figure 1

illustrates this. The short-term dispersion includes the inherent dispersion and can also include some

short-term instability effect.

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Key

1 short-term dispersion

2 overall dispersion

Figure 1 — Short-term dispersion and its relationship to the total dispersion

The total dispersion can be any shape and not necessarily normal as illustrated here.

3.4 Mean square error (MSE)

When minimizing variation, some practitioners use the mean square error as the preferred measure. It

is compatible with the methods used in off-line quality techniques.

3.5 Reference limits

The lower and upper reference limits are respectively defined as the 0,135 % and the 99,865 %

percentiles of the distribution that describe the output of the process characteristic. They are written

as X and X .

0,135 5 % 99,865 %

3.6 Reference interval (also known as process spread)

The reference interval is the interval between the upper and the lower reference limits. The reference

interval includes 99,73 % of the individuals in the population from a process that is in a state of

statistical control.

4 Capability

4.1 General

Process capability is a measure of inherent process variability. The variability that is inherent in a

process when operating in a state of statistical control is known as the inherent process variability. It

represents the variation that remains after all known removable assignable causes have been eliminated.

If the process is monitored using a control chart, the control chart will show an in control state.

Capability is often regarded as being related to the proportion of output that will occur within the

product specification tolerances. Since a process in statistical control should be described by a

predictable distribution, the proportion of out-of-specification outputs can be estimated. As long

as the process remains in statistical control, it will continue to produce the same proportion out-of-

specification.

Management actions to reduce the variation from random causes are required to improve the process’

ability to consistently meet the specification requirements.

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In short, the following will be necessary:

— define the process and its operating conditions. If there is a change to those conditions, it will

necessitate a new process study;

— assess the short-term and long-term measurement variabilities as percentages of the total variability

and minimize them;

— preserve the process stability and maintain its statistical control;

— estimate the remaining inherent variation;

— select an appropriate measure of capability.

The following are the conditions that will apply for capability:

— all technical conditions, e.g. temperature and humidity, shall be clearly stated;

— the uncertainty of the measurement system shall be estimated and judged appropriate (see

ISO 22514-7);

— multi-factor, multi-level aspects of the process should be allowed;

— the duration over which the data has been gathered shall be recorded;

— the frequency of sampling and sample size shall be specified and the start and finish dates of data

collection;

— the process shall be controlled with a control chart;

— the process shall be in a state of statistical control.

It is necessary to check the control chart from which the data have been taken for statistical control

and to examine a histogram of the data with any specification limits superimposed upon it. A valid

[15]

test for normality should be used in assessing the data such as the Anderson-Darling test or any

other suitable method. This test is powerful in detecting departures from normality in the tails of

the distribution and is suggested here as this is the region of interest for capability and performance

indices. Additionally, a normal probability plot can be used to look for the following:

a) verification of normality;

b) outliers;

c) data beyond any specification limit;

d) whether the data are well inside the specification limit(s);

e) evidence of asymmetry (i.e. skewness);

f) evidence of “long tails” in the data (i.e. kurtosis);

g) off-centre distribution;

h) any unusual patterns.

Explanations of anomalies should be sought in relation to these mentioned features and appropriate

action taken on the data prior to the calculation of any measure. It would be inappropriate to just discard

data that do not appear to fit any preconceived pattern. Such departures might be very revealing about

the process’ behaviour and should be thoroughly investigated.

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4.2 Process capability

4.2.1 Normal distribution

Process capability is defined as a statistical measure of inherent process variability for a given

characteristic. The conventional method is to take the reference interva

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