# ISO/TR 22514-4:2007

(Main)## Statistical methods in process management -- Capability and performance

## Statistical methods in process management -- Capability and performance

ISO/TR 22514-4:2007 describes process capability and performance measures that are commonly used.

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

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

Ta del ISO 22514 opisuje zmogljivost procesa in ukrepe za delovanje, ki se pogosto uporabljajo.

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TECHNICAL ISO/TR

REPORT 22514-4

First edition

2007-12-01

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/TR 22514-4:2007(E)

ISO 2007

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

ISO/TR 22514-4:2007(E)

PDF disclaimer

This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but

shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In

downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat

accepts no liability in this area.Adobe is a trademark of Adobe Systems Incorporated.

Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation

parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In

the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.

COPYRIGHT PROTECTED DOCUMENT© ISO 2007

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,

electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or

ISO's member body in the country of the requester.ISO copyright office

Case postale 56 • CH-1211 Geneva 20

Tel. + 41 22 749 01 11

Fax + 41 22 749 09 47

E-mail copyright@iso.org

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Published in Switzerland

ii © ISO 2007 – All rights reserved

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ISO/TR 22514-4:2007(E)

Contents Page

Foreword............................................................................................................................................................ iv

Introduction ........................................................................................................................................................ v

1 Scope ......................................................................................................................................................1

2 Terms and definitions ...........................................................................................................................1

2.1 Basic terms.............................................................................................................................................1

2.2 Process capability, estimates and indices..........................................................................................5

2.3 Process performance, measures and indices ....................................................................................8

3 Symbols and abbreviated terms ........................................................................................................10

3.1 Symbols ................................................................................................................................................10

3.2 Abbreviated terms ...............................................................................................................................12

4 Statistical measures used in process capability and performance ...............................................13

4.1 General..................................................................................................................................................13

4.2 Measures of location ...........................................................................................................................13

4.3 Measures of dispersion.......................................................................................................................13

4.4 Mean square error (MSE) ....................................................................................................................13

4.5 Reference limits ...................................................................................................................................13

4.6 Reference interval, also known as process spread .........................................................................13

4.7 Attributes ..............................................................................................................................................13

5 Capability..............................................................................................................................................14

5.1 General..................................................................................................................................................14

5.2 Process capability ...............................................................................................................................15

5.3 Process location ..................................................................................................................................16

5.4 Process capability indices for measured data .................................................................................17

5.5 Process capability indices for measured data (non-normal) ..........................................................19

5.6 Alternative method for describing and calculating process capability estimates .......................21

5.7 Other capability indices for measured data in other special cases ...............................................22

5.8 Assessment of proportion out-of-specification (normal distribution)...........................................23

5.9 Attributes ..............................................................................................................................................24

6 Performance .........................................................................................................................................25

6.1 General..................................................................................................................................................25

6.2 Process performance indices for measured data (normal distribution)........................................26

6.3 Process performance indices for measured data (non-normal distribution)................................27

6.4 Other performance indices for measured data.................................................................................28

6.5 Assessment of proportion out-of-specification (normal distribution)...........................................28

6.6 Attributes ..............................................................................................................................................28

Annex A (informative) Estimating standard deviations.................................................................................29

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

Procedure and example ......................................................................................................................31

Annex C (informative) Distribution identification ..........................................................................................39

Annex D (informative) Confidence intervals...................................................................................................44

Annex E (informative) Example of the output from computer software......................................................46

Bibliography ......................................................................................................................................................48

© ISO 2007 – All rights reserved iii---------------------- Page: 3 ----------------------

ISO/TR 22514-4:2007(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.

International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.

The main task of technical committees is to prepare International Standards. Draft International Standards

adopted by the technical committees are circulated to the member bodies for voting. Publication as an

International Standard requires approval by at least 75 % of the member bodies casting a vote.

In exceptional circumstances, when a technical committee has collected data of a different kind from that

which is normally published as an International Standard (“state of the art”, for example), it may decide by a

simple majority vote of its participating members to publish a Technical Report. A Technical Report is entirely

informative in nature and does not have to be reviewed until the data it provides are considered to be no

longer valid or useful.Attention is drawn to the possibility that some of the elements of this document may be the subject of patent

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

ISO/TR 22514-4 has been prepared by Technical Committee ISO/TC 69, Applications of statistical methods,

Subcommittee SC 4, Applications of statistical methods in process management.ISO 22514 consists of the following parts, under the general title Statistical methods in process management

— Capability and performance:⎯ Part 1: General principles and concepts

⎯ Part 3: Machine performance studies for measured data on discrete parts

⎯ Part 4: Process capability estimates and performance measures [Technical Report]

In the future, it is planned to revise ISO 21747:2006 (Statistical methods — Process performance and

capability statistics for measured quality characteristics) as Part 2.NOTE ISO/TR 22514-4 was initially prepared as ISO/DTR 12783. It was renumbered before publication to include it

in the ISO 22514 series.iv © ISO 2007 – All rights reserved

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ISO/TR 22514-4:2007(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 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 and this

report attempts to reflect the current position. The most fundamental shift has been to philosophically separate

what is named in this document 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 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, 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 indices'

confidence intervals are computed and reported. This part of ISO 22514 describes methods by which these

can be computed.© ISO 2007 – All rights reserved v

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TECHNICAL REPORT ISO/TR 22514-4:2007(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 Terms and definitionsFor the purposes of this document, the following terms and definitions apply.

2.1 Basic terms

2.1.1

product

result of a process

NOTE Process is defined in ISO 12207:1995, 3.17 and in ISO 9000:2005, 3.4.1.

2.1.2

characteristic

distinguishing feature

NOTE 1 A characteristic can be inherent or assigned.

NOTE 2 A characteristic can be qualitative or quantitative.

NOTE 3 There are various classes of characteristics, such as the following:

⎯ physical (e.g. mechanical, electrical, chemical or biological characteristics);

⎯ sensory (e.g. relating to smell, touch, taste, sight, hearing);⎯ behavioural (e.g. courtesy, honesty, veracity);

⎯ temporal (e.g. punctuality, reliability, availability);

⎯ ergonomic (e.g. physiological characteristic, or related to human safety);

⎯ functional (e.g. maximum speed of an aircraft).

[ISO 9000:2005, 3.5.1]

© ISO 2007 – All rights reserved 1

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ISO/TR 22514-4:2007(E)

2.1.3

quality characteristic

inherent characteristic (2.1.2) of a product (2.1.1), process or system related to a requirement

NOTE 1 Inherent means existing in something, especially as a permanent characteristic.

NOTE 2 A characteristic assigned to a product, process or system (e.g. the price of a product, the owner of a product)

is not a quality characteristic of that product, process or system.[ISO 9000:2005, 3.5.2]

2.1.4

specification limit

limiting value stated for a characteristic (2.1.2)

[ISO 3534-2:2006, 3.1.3]

2.1.5

specified tolerance

difference between the upper specification limits and lower specification limits (2.1.4)

[ISO 3534-2:2006, 3.1.6]2.1.6

target value

preferred or reference value of a characteristic (2.1.2) stated in a specification

[ISO 3534-2:2006, 3.1.2]2.1.7

distribution

〈of a characteristic〉 information on the probabilistic behaviour of a characteristic (2.1.2)

NOTE 1 The distribution of a characteristic (2.1.2) can be represented, for example, by ranking of the values of the

characteristic (2.1.2) and showing the resulting pattern of measures or scores in the form of a tally chart or histogram.

Such a pattern provides all of the numerical value information of the characteristic (2.1.2) except for the serial order in

which the data arises.NOTE 2 The distribution of a characteristic (2.1.2) is dependent on prevailing conditions. Thus, if meaningful

information about the distribution of a characteristic (2.1.2) is desired the conditions under which the data are collected

should be specified.NOTE 3 It is important to know the class of distributions (2.1.8), for instance, normal or log-normal, before predicting

or estimating process capability or performance measures and indices or fraction nonconforming.

[ISO 3534-2:2006, 2.5.1]2.1.8

class of distributions

particular family of distributions (2.1.7) each member of which has the same common attributes by which the

family is fully specifiedEXAMPLE 1 The two-parameter, symmetrical bell-shaped, normal distribution with parameters mean and standard

deviation.EXAMPLE 2 The three-parameter Weibull distribution with parameters location, shape and scale.

EXAMPLE 3 The unimodal continuous distributions.NOTE 1 The class of distributions can often be fully specified through the values of the appropriate parameters.

2 © ISO 2007 – All rights reserved---------------------- Page: 7 ----------------------

ISO/TR 22514-4:2007(E)

NOTE 2 Tests for the normality of data can be found in ISO 5479.

NOTE 3 Adapted from ISO 3534-2:2006, 2.5.2.

2.1.9

distribution model

specified distribution (2.1.7) or class of distributions (2.1.8)

EXAMPLE 1 A model for the distribution of a product characteristic, such as the diameter of a bolt, might be the

normal distribution with mean 15 mm and standard deviation 0,05 mm. Here the model is a fully specified one.

EXAMPLE 2 A model for the diameter of bolts as in Example 1 could be the class of normal distributions without

attempting to specify a particular distribution. Here the model is the class of normal distributions.

[ISO 3534-2:2006, 2.5.3]2.1.10

reference limits

nominated quantiles of the distribution (2.1.7) of the product characteristic

NOTE 1 The conditions of the distribution (2.1.7) of the product characteristic must be specified, see Notes 2 and 3 of

2.1.7.NOTE 2 Traditionally the 0,135 % and 99,865 % quantiles have been used.

EXAMPLE If the distribution (2.1.7) of the product characteristic is normal with mean µ and standard deviation σ,

the limits are µ ± 3σ when the traditional 0,135 % and 99,865 % quantiles are used.

2.1.11reference interval

interval bounded by the 99,865 % distribution quantile, X , and the 0,135 % distribution quantile,

99,865 %0,135 %

NOTE 1 The interval can be expressed by XX, and the length of the interval is

( )

99,865 % 0,135 %

XX− .

99,865 % 0,135 %

NOTE 2 This term is used only as an arbitrary, but standardized, basis for defining the process performance index

(2.3.3) and process capability index (2.2.3).NOTE 3 For a normal distribution (2.1.7), the reference interval may be expressed in terms of six standard deviations,

6σ, or 6S, when estimated from a sample.NOTE 4 For a non-normal distribution, the length of the reference interval can be estimated by means of appropriate

probability papers (e.g. log-normal) or from the sample kurtosis and sample skewness using, for example, Pearson

curves.NOTE 5 A quantile or fractile indicates division of a distribution into equal units or fractions, e.g. percentiles. Quantile is

defined in ISO 3534-1.[ISO 3534-2:2006, 2.5.7]

2.1.12

upper fraction nonconforming

fraction of the distribution (2.1.7) of a characteristic (2.1.2) that is greater than the upper specification limit

(2.1.4), U© ISO 2007 – All rights reserved 3

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ISO/TR 22514-4:2007(E)

EXAMPLE In a normal distribution (2.1.7), with mean, µ, and standard deviation σ :

UU−−µµ⎛⎞ ⎛⎞

p =−1ΦΦ=

U ⎜⎟ ⎜⎟

⎝⎠ ⎝⎠

where

p is the upper fraction nonconforming;

Φ is the distribution function of the standard normal distribution;

U is the upper specification limit.

NOTE 1 Tables (or functions in statistical computer packages) of the standard normal distribution are readily available

which give the proportion of process output expected beyond a particular value of interest, such as a specification limit

(2.1.4), in terms of standard deviations away from the process mean. This obviates the need to work out the statistical

distribution function given in the example.NOTE 2 The function relates to a theoretical distribution. In practice, with empirical distributions, the parameters are

replaced by estimates.[ISO 3534-2:2006, 2.5.4]

2.1.13

lower fraction nonconforming

fraction of the distribution (2.1.7) of a characteristic (2.1.2) that is less than the lower specification limit

(2.1.4), LEXAMPLE In a normal distribution (2.1.7), with mean, µ, and standard deviation, σ :

L − µp = Φ

L ⎜⎟

where

p is the lower fraction nonconforming;

Φ is the distribution function of the standard normal distribution;

L is the lower specification limit.

NOTE 1 Tables (or functions in statistical computer packages) of the standard normal distribution are readily available

which give the proportion of process output expected beyond a particular value of interest, such as a specification limit

(2.1.4), in terms of standard deviations away from the process mean. This obviates the need to work out the statistical

distribution function given in the example.NOTE 2 The function relates to a theoretical distribution. In practice, with empirical distributions, the parameters are

replaced by estimates.[ISO 3534-2:2006, 2.5.5]

4 © ISO 2007 – All rights reserved

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ISO/TR 22514-4:2007(E)

2.1.14

total fraction nonconforming

sum of upper fraction nonconforming (2.1.12) and lower fraction nonconforming (2.1.13)

EXAMPLE In a normal distribution (2.1.7), with mean, µ, and standard deviation, σ :

⎛⎞µµ−−UL⎛ ⎞p=+ΦΦ

t ⎜⎟ ⎜ ⎟

⎝⎠ ⎝ ⎠

where

p is the total fraction nonconforming;

Φ is the distribution function of the standard normal distribution;

U is the upper specification limit;

L is the lower specification limit.

[ISO 3534-2:2006, 2.5.6]

2.2 Process capability, estimates and indices

2.2.1

process capability

〈estimate〉 statistical estimate of the outcome of a characteristic from a process which has been demonstrated

to be in a state of statistical control and which describes that process’s ability to realize a characteristic that

will fulfil the requirements for that characteristicNOTE 1 The characteristic from the process needs to be documented to have been in statistical control.

NOTE 2 The outcome is a distribution (2.1.7), the class of which needs determination and its parameters estimated.

NOTE 3 In certain circumstances, the standard deviation, S , that represents only within subgroup variation can be

used as an estimator for S :∑∑j j

jj==11

S ≈ or or

dmc m

where

R is the average range calculated from a set of m subgroup ranges;

S is the sample standard deviation of the jth subgroup;

m is the number of subgroups of the same size, n;

d , c are constants based on subgroup size, n.

2 4

Alternatively, for a normal distribution, the process overall standard deviation σ , can be estimated using the formula for S .

t tThe value of the estimators S and S converge for a process in a state of statistical control. A comparison of the two gives

t wan indication of the degree of stability of the process. For an out-of-control process about a constant mean, or for a

process that is subject to systematic changes in the mean, the value of S is likely to significantly underestimate the

© ISO 2007 – All rights reserved 5---------------------- Page: 10 ----------------------

ISO/TR 22514-4:2007(E)

process standard deviation. Hence S should be used with extreme caution. Sometimes, too, the estimator S is preferred

w tto S because it has more tractable statistical properties (e.g. facilitating the calculation of confidence limits).

NOTE 4 For a normal distribution, process capability can be assessed from the expression:

X ± zSwhere

X = X

∑ j

j=1

and X is the observed mean of the jth subgroup.

The choice of z depends on the particular parts per million capability standard used. Typically z takes the value of 3, 4 or 5.

If the process capability meets the specified requirements, a z value of 3 indicates an expected 2 700 parts per million

outside of specification. Similarly, a z of 4 indicates an expected 64 parts per million and a z of 5 an expected 0,6 parts per

million outside of specification.NOTE 5 For a non-normal distribution, process capability can be assessed using, for example, an appropriate

probability paper or from the parameters of the distribution fitted to the data. The expression for process capability takes

the asymmetric form:The notation is in the same style as standard drawing office practice for expressing specified tolerances about a

nominal, or preferred, value for a characteristic when the preferred value is not equidistant from each limit. The equivalent

notation for limits symmetrical about the preferred value is ±. This enables a direct comparison to be made between the

dimensional performance of a characteristic and its specified requirements in terms of both location and dispersion.

NOTE 6 When S = is used, it needs to be appreciated that this estimator:⎯ becomes progressively less efficient as the subgroup size increases;

⎯ is very sensitive to the distribution of individual values;

⎯ makes it difficult to estimate confidence limits.

NOTE 7 Capability conditions are very restrictive and include:

⎯ the methods applied to demonstrate that the process is in control;

⎯ technical conditions (input batches, operators, tools, etc.);

⎯ the measurement process (discrimination, accuracy, repeatability, reproducibility, etc.); and

⎯ data collection (duration, frequency).NOTE 8 Adapted from ISO 3534-2:2006, 2.7.1.

2.2.2

process capability estimate

quantity that describes one or more properties of the distribution (2.1.7) of the product characteristic under

capability conditionsEXAMPLE 1 The standard deviation (ISO 3534-1:2006, 2.37) of the distribution (2.1.7) of the product characteristic

under capability conditions (see 2.2.1, Notes 1 and 7).6 © ISO 2007 – All rights reserved

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

ISO/TR 22514-4:2007(E)

EXAMPLE 2 The mean (ISO 3534-1:2006, 2.35.1) of the distribution (2.1.7) of the product characteristic under

capability conditions (see 2.2.1, Notes 1 and 7).EXAMPLE 3 The reference interval (2.1.11) of the distribution (2.1.7) of the product characteristic under capability

conditions (see 2.2.1, Notes 1 and 7).2.2.3

process capability index

index describing process capability (2.2.1) in relation to specified tolerance (2.1.5)

NOTE 1 Frequently, the process capability index is expressed as the value of the specified tolerance (2.1.5) divided

by a measure of the length of the reference interval (2.1.11) for a process in a state of statistical control, namely as:

UL−C =

XX−

99,865 % 0,135 %

NOTE 2 For a normal distribution (2.1.7), the reference interval (2.1.11) is equal to 6S (see 2.2.1, Notes).

NOTE 3 For a non-normal distribution (2.1.7), the reference interval (2.1.11) can be estimated, for example, using

the probability paper method or the Pearson curves method.NOTE 4 Adapted from ISO 3534-2:2006, 2.7.2.

2.2.4

upper process capability index

pkU

index describing process capability (2.2.1) in relation to the upper specification limit (2.1.4), U

NOTE 1 Frequently, the upper process capability index is expressed as the difference between the upper

specification limit (2.1.4) and the 50 % distribution quantile, X divided by a measure of the length of the upper

50 %reference interval (2.1

**...**

SLOVENSKI STANDARD

SIST-TP ISO/TR 22514-4:2010

01-julij-2010

6WDWLVWLþQHPHWRGH]DREYODGRYDQMHSURFHVRY=PRJOMLYRVWLQGHORYDQMHGHO

2FHQH]PRJOMLYRVWLSURFHVRYLQPHUHGHORYDQMD

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 performanceTa slovenski standard je istoveten z: ISO/TR 22514-4:2007

ICS:

03.120.30 8SRUDEDVWDWLVWLþQLKPHWRG Application of statistical

methods

SIST-TP ISO/TR 22514-4:2010 en

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

---------------------- Page: 1 ----------------------SIST-TP ISO/TR 22514-4:2010

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

SIST-TP ISO/TR 22514-4:2010

TECHNICAL ISO/TR

REPORT 22514-4

First edition

2007-12-01

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/TR 22514-4:2007(E)

ISO 2007

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

SIST-TP ISO/TR 22514-4:2010

ISO/TR 22514-4:2007(E)

PDF disclaimer

This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but

shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In

downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat

accepts no liability in this area.Adobe is a trademark of Adobe Systems Incorporated.

Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation

parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In

the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.

COPYRIGHT PROTECTED DOCUMENT© ISO 2007

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,

electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or

ISO's member body in the country of the requester.ISO copyright office

Case postale 56 • CH-1211 Geneva 20

Tel. + 41 22 749 01 11

Fax + 41 22 749 09 47

E-mail copyright@iso.org

Web www.iso.org

Published in Switzerland

ii © ISO 2007 – All rights reserved

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

SIST-TP ISO/TR 22514-4:2010

ISO/TR 22514-4:2007(E)

Contents Page

Foreword............................................................................................................................................................ iv

Introduction ........................................................................................................................................................ v

1 Scope ......................................................................................................................................................1

2 Terms and definitions ...........................................................................................................................1

2.1 Basic terms.............................................................................................................................................1

2.2 Process capability, estimates and indices..........................................................................................5

2.3 Process performance, measures and indices ....................................................................................8

3 Symbols and abbreviated terms ........................................................................................................10

3.1 Symbols ................................................................................................................................................10

3.2 Abbreviated terms ...............................................................................................................................12

4 Statistical measures used in process capability and performance ...............................................13

4.1 General..................................................................................................................................................13

4.2 Measures of location ...........................................................................................................................13

4.3 Measures of dispersion.......................................................................................................................13

4.4 Mean square error (MSE) ....................................................................................................................13

4.5 Reference limits ...................................................................................................................................13

4.6 Reference interval, also known as process spread .........................................................................13

4.7 Attributes ..............................................................................................................................................13

5 Capability..............................................................................................................................................14

5.1 General..................................................................................................................................................14

5.2 Process capability ...............................................................................................................................15

5.3 Process location ..................................................................................................................................16

5.4 Process capability indices for measured data .................................................................................17

5.5 Process capability indices for measured data (non-normal) ..........................................................19

5.6 Alternative method for describing and calculating process capability estimates .......................21

5.7 Other capability indices for measured data in other special cases ...............................................22

5.8 Assessment of proportion out-of-specification (normal distribution)...........................................23

5.9 Attributes ..............................................................................................................................................24

6 Performance .........................................................................................................................................25

6.1 General..................................................................................................................................................25

6.2 Process performance indices for measured data (normal distribution)........................................26

6.3 Process performance indices for measured data (non-normal distribution)................................27

6.4 Other performance indices for measured data.................................................................................28

6.5 Assessment of proportion out-of-specification (normal distribution)...........................................28

6.6 Attributes ..............................................................................................................................................28

Annex A (informative) Estimating standard deviations.................................................................................29

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

Procedure and example ......................................................................................................................31

Annex C (informative) Distribution identification ..........................................................................................39

Annex D (informative) Confidence intervals...................................................................................................44

Annex E (informative) Example of the output from computer software......................................................46

Bibliography ......................................................................................................................................................48

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Foreword

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

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

technical committees. Each member body interested in a subject for which a technical committee has been

established has the right to be represented on that committee. International organizations, governmental and

non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the

International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.

International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.

The main task of technical committees is to prepare International Standards. Draft International Standards

adopted by the technical committees are circulated to the member bodies for voting. Publication as an

International Standard requires approval by at least 75 % of the member bodies casting a vote.

In exceptional circumstances, when a technical committee has collected data of a different kind from that

which is normally published as an International Standard (“state of the art”, for example), it may decide by a

simple majority vote of its participating members to publish a Technical Report. A Technical Report is entirely

informative in nature and does not have to be reviewed until the data it provides are considered to be no

longer valid or useful.Attention is drawn to the possibility that some of the elements of this document may be the subject of patent

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

ISO/TR 22514-4 has been prepared by Technical Committee ISO/TC 69, Applications of statistical methods,

Subcommittee SC 4, Applications of statistical methods in process management.ISO 22514 consists of the following parts, under the general title Statistical methods in process management

— Capability and performance:⎯ Part 1: General principles and concepts

⎯ Part 3: Machine performance studies for measured data on discrete parts

⎯ Part 4: Process capability estimates and performance measures [Technical Report]

In the future, it is planned to revise ISO 21747:2006 (Statistical methods — Process performance and

capability statistics for measured quality characteristics) as Part 2.NOTE ISO/TR 22514-4 was initially prepared as ISO/DTR 12783. It was renumbered before publication to include it

in the ISO 22514 series.iv © ISO 2007 – All rights reserved

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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 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 and this

report attempts to reflect the current position. The most fundamental shift has been to philosophically separate

what is named in this document 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 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, 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 indices'

confidence intervals are computed and reported. This part of ISO 22514 describes methods by which these

can be computed.© ISO 2007 – All rights reserved v

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TECHNICAL REPORT ISO/TR 22514-4:2007(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 Terms and definitionsFor the purposes of this document, the following terms and definitions apply.

2.1 Basic terms

2.1.1

product

result of a process

NOTE Process is defined in ISO 12207:1995, 3.17 and in ISO 9000:2005, 3.4.1.

2.1.2

characteristic

distinguishing feature

NOTE 1 A characteristic can be inherent or assigned.

NOTE 2 A characteristic can be qualitative or quantitative.

NOTE 3 There are various classes of characteristics, such as the following:

⎯ physical (e.g. mechanical, electrical, chemical or biological characteristics);

⎯ sensory (e.g. relating to smell, touch, taste, sight, hearing);⎯ behavioural (e.g. courtesy, honesty, veracity);

⎯ temporal (e.g. punctuality, reliability, availability);

⎯ ergonomic (e.g. physiological characteristic, or related to human safety);

⎯ functional (e.g. maximum speed of an aircraft).

[ISO 9000:2005, 3.5.1]

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2.1.3

quality characteristic

inherent characteristic (2.1.2) of a product (2.1.1), process or system related to a requirement

NOTE 1 Inherent means existing in something, especially as a permanent characteristic.

NOTE 2 A characteristic assigned to a product, process or system (e.g. the price of a product, the owner of a product)

is not a quality characteristic of that product, process or system.[ISO 9000:2005, 3.5.2]

2.1.4

specification limit

limiting value stated for a characteristic (2.1.2)

[ISO 3534-2:2006, 3.1.3]

2.1.5

specified tolerance

difference between the upper specification limits and lower specification limits (2.1.4)

[ISO 3534-2:2006, 3.1.6]2.1.6

target value

preferred or reference value of a characteristic (2.1.2) stated in a specification

[ISO 3534-2:2006, 3.1.2]2.1.7

distribution

〈of a characteristic〉 information on the probabilistic behaviour of a characteristic (2.1.2)

NOTE 1 The distribution of a characteristic (2.1.2) can be represented, for example, by ranking of the values of the

characteristic (2.1.2) and showing the resulting pattern of measures or scores in the form of a tally chart or histogram.

Such a pattern provides all of the numerical value information of the characteristic (2.1.2) except for the serial order in

which the data arises.NOTE 2 The distribution of a characteristic (2.1.2) is dependent on prevailing conditions. Thus, if meaningful

information about the distribution of a characteristic (2.1.2) is desired the conditions under which the data are collected

should be specified.NOTE 3 It is important to know the class of distributions (2.1.8), for instance, normal or log-normal, before predicting

or estimating process capability or performance measures and indices or fraction nonconforming.

[ISO 3534-2:2006, 2.5.1]2.1.8

class of distributions

particular family of distributions (2.1.7) each member of which has the same common attributes by which the

family is fully specifiedEXAMPLE 1 The two-parameter, symmetrical bell-shaped, normal distribution with parameters mean and standard

deviation.EXAMPLE 2 The three-parameter Weibull distribution with parameters location, shape and scale.

EXAMPLE 3 The unimodal continuous distributions.NOTE 1 The class of distributions can often be fully specified through the values of the appropriate parameters.

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NOTE 2 Tests for the normality of data can be found in ISO 5479.

NOTE 3 Adapted from ISO 3534-2:2006, 2.5.2.

2.1.9

distribution model

specified distribution (2.1.7) or class of distributions (2.1.8)

EXAMPLE 1 A model for the distribution of a product characteristic, such as the diameter of a bolt, might be the

normal distribution with mean 15 mm and standard deviation 0,05 mm. Here the model is a fully specified one.

EXAMPLE 2 A model for the diameter of bolts as in Example 1 could be the class of normal distributions without

attempting to specify a particular distribution. Here the model is the class of normal distributions.

[ISO 3534-2:2006, 2.5.3]2.1.10

reference limits

nominated quantiles of the distribution (2.1.7) of the product characteristic

NOTE 1 The conditions of the distribution (2.1.7) of the product characteristic must be specified, see Notes 2 and 3 of

2.1.7.NOTE 2 Traditionally the 0,135 % and 99,865 % quantiles have been used.

EXAMPLE If the distribution (2.1.7) of the product characteristic is normal with mean µ and standard deviation σ,

the limits are µ ± 3σ when the traditional 0,135 % and 99,865 % quantiles are used.

2.1.11reference interval

interval bounded by the 99,865 % distribution quantile, X , and the 0,135 % distribution quantile,

99,865 %0,135 %

NOTE 1 The interval can be expressed by XX, and the length of the interval is

( )

99,865 % 0,135 %

XX− .

99,865 % 0,135 %

NOTE 2 This term is used only as an arbitrary, but standardized, basis for defining the process performance index

(2.3.3) and process capability index (2.2.3).NOTE 3 For a normal distribution (2.1.7), the reference interval may be expressed in terms of six standard deviations,

6σ, or 6S, when estimated from a sample.NOTE 4 For a non-normal distribution, the length of the reference interval can be estimated by means of appropriate

probability papers (e.g. log-normal) or from the sample kurtosis and sample skewness using, for example, Pearson

curves.NOTE 5 A quantile or fractile indicates division of a distribution into equal units or fractions, e.g. percentiles. Quantile is

defined in ISO 3534-1.[ISO 3534-2:2006, 2.5.7]

2.1.12

upper fraction nonconforming

fraction of the distribution (2.1.7) of a characteristic (2.1.2) that is greater than the upper specification limit

(2.1.4), U© ISO 2007 – All rights reserved 3

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EXAMPLE In a normal distribution (2.1.7), with mean, µ, and standard deviation σ :

UU−−µµ⎛⎞ ⎛⎞

p =−1ΦΦ=

U ⎜⎟ ⎜⎟

⎝⎠ ⎝⎠

where

p is the upper fraction nonconforming;

Φ is the distribution function of the standard normal distribution;

U is the upper specification limit.

NOTE 1 Tables (or functions in statistical computer packages) of the standard normal distribution are readily available

which give the proportion of process output expected beyond a particular value of interest, such as a specification limit

(2.1.4), in terms of standard deviations away from the process mean. This obviates the need to work out the statistical

distribution function given in the example.NOTE 2 The function relates to a theoretical distribution. In practice, with empirical distributions, the parameters are

replaced by estimates.[ISO 3534-2:2006, 2.5.4]

2.1.13

lower fraction nonconforming

fraction of the distribution (2.1.7) of a characteristic (2.1.2) that is less than the lower specification limit

(2.1.4), LEXAMPLE In a normal distribution (2.1.7), with mean, µ, and standard deviation, σ :

L − µp = Φ

L ⎜⎟

where

p is the lower fraction nonconforming;

Φ is the distribution function of the standard normal distribution;

L is the lower specification limit.

[ISO 3534-2:2006, 2.5.5]

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2.1.14

total fraction nonconforming

sum of upper fraction nonconforming (2.1.12) and lower fraction nonconforming (2.1.13)

EXAMPLE In a normal distribution (2.1.7), with mean, µ, and standard deviation, σ :

⎛⎞µµ−−UL⎛ ⎞p=+ΦΦ

t ⎜⎟ ⎜ ⎟

⎝⎠ ⎝ ⎠

where

p is the total fraction nonconforming;

Φ is the distribution function of the standard normal distribution;

U is the upper specification limit;

L is the lower specification limit.

[ISO 3534-2:2006, 2.5.6]

2.2 Process capability, estimates and indices

2.2.1

process capability

〈estimate〉 statistical estimate of the outcome of a characteristic from a process which has been demonstrated

to be in a state of statistical control and which describes that process’s ability to realize a characteristic that

will fulfil the requirements for that characteristicNOTE 1 The characteristic from the process needs to be documented to have been in statistical control.

NOTE 2 The outcome is a distribution (2.1.7), the class of which needs determination and its parameters estimated.

NOTE 3 In certain circumstances, the standard deviation, S , that represents only within subgroup variation can be

used as an estimator for S :∑∑j j

jj==11

S ≈ or or

dmc m

where

R is the average range calculated from a set of m subgroup ranges;

S is the sample standard deviation of the jth subgroup;

m is the number of subgroups of the same size, n;

d , c are constants based on subgroup size, n.

2 4

Alternatively, for a normal distribution, the process overall standard deviation σ , can be estimated using the formula for S .

t tThe value of the estimators S and S converge for a process in a state of statistical control. A comparison of the two gives

t wan indication of the degree of stability of the process. For an out-of-control process about a constant mean, or for a

process that is subject to systematic changes in the mean, the value of S is likely to significantly underestimate the

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process standard deviation. Hence S should be used with extreme caution. Sometimes, too, the estimator S is preferred

w tto S because it has more tractable statistical properties (e.g. facilitating the calculation of confidence limits).

NOTE 4 For a normal distribution, process capability can be assessed from the expression:

X ± zSwhere

X = X

∑ j

j=1

and X is the observed mean of the jth subgroup.

The choice of z depends on the particular parts per million capability standard used. Typically z takes the value of 3, 4 or 5.

If the process capability meets the specified requirements, a z value of 3 indicates an expected 2 700 parts per million

outside of specification. Similarly, a z of 4 indicates an expected 64 parts per million and a z of 5 an expected 0,6 parts per

million outside of specification.NOTE 5 For a non-normal distribution, process capability can be assessed using, for example, an appropriate

probability paper or from the parameters of the distribution fitted to the data. The expression for process capability takes

the asymmetric form:The notation is in the same style as standard drawing office practice for expressing specified tolerances about a

nominal, or preferred, value for a characteristic when the preferred value is not equidistant from each limit. The equivalent

notation for limits symmetrical about the preferred value is ±. This enables a direct comparison to be made between the

dimensional performance of a characteristic and its specified requirements in terms of both location and dispersion.

NOTE 6 When S = is used, it needs to be appreciated that this estimator:⎯ becomes progressively less efficient as the subgroup size increases;

⎯ is very sensitive to the distribution of individual values;

⎯ makes it difficult to estimate confidence limits.

NOTE 7 Capability conditions are very restrictive and include:

⎯ the methods applied to demonstrate that the process is in control;

⎯ technical conditions (input batches, operators, tools, etc.);

⎯ the measurement process (discrimination, accuracy, repeatability, reproducibility, etc.); and

⎯ data collection (duration, frequency).NOTE 8 Adapted from ISO 3534-2:2006, 2.7.1.

2.2.2

process capability estimate

quantity that describes one or more properties of the distribution (2.1.7) of the product characteristic under

capability conditionsEXAMPLE 1 The standard deviation (ISO 3534-1:2006, 2.37) of the distribution (2.1.7) of the product characteristic

under capability conditions (see 2.2.1, Notes 1 and 7).6 © ISO 2007 – All rights reserved

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EXAMPLE 2 The mean (ISO 3534-1:2006, 2.35.1) of the distribution (2.1.7) of the product char

**...**

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