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INTERNATIONAL STANDARD
ISO 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
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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 [email protected] www.iso.org
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ISO 22514-4:2016(E)
Contents
Page
Foreword...........................................................................................................................................................................................................................................v Introduction................................................................................................................................................................................................................................. vi 1 Scope.................................................................................................................................................................................................................................. 1 2 3
Symbols and abbreviated terms............................................................................................................................................................ 1 2.1 Symbols.......................................................................................................................................................................................................... 1 2.2 Abbreviated terms................................................................................................................................................................................ 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 Cp index (for the normal distribution)........................................................................................................... 9 4.4.3 Cpk index (for the normal distribution)..................................................................................................... 10 4.4.4 Cpk index for unilateral tolerances................................................................................................................. 10 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 Pp index.................................................................................................................................................................................. 16 5.2.2 Ppk index............................................................................................................................................................................... 17 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
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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
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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
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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
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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.
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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 β
fraction or proportion
β2
coefficient of kurtosis
shape parameter in a Weibull distribution
c4
constant based on subgroup size, n (see ISO 7870-2)
Cp
process capability index
Cpk
C pk
L
C pk
U
Cpm CR d2 e
Φ
minimum process capability index lower process capability index
upper process capability index
alternative process capability index process capability fraction (PCF)
constant based on subgroup size, n (see ISO 7870-2)
Eulers’s number (approximately 2,718), mathematical constant
γ
distribution function of the standard normal distribution
γ1 m
coefficient of skewness
Kl, Ku
multipliers for estimating the confidence limits for a process capability index
L
location parameter in a Weibull distribution number of subgroups
lower specification limit
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ISO 22514-4:2016(E) P0,135 %
lower 0,135 % percentile
N
total sample size
μ
n Pα %
location of the process; population mean value number of values or subgroup size (for a control chart)
pL
α percentile
Pp
process performance index
lower fraction nonconforming
Ppk Ppk
L
Ppk
U
pt
minimum process performance index lower process performance index
upper process performance index
pU
total fraction nonconforming
P99,865 %
upper 99,865 % percentile
π
Qk θ
upper fraction nonconforming geometric constant
process variation index
parameter required for the Rayleigh distribution
S
average subgroup range
St
standard deviation, with the subscript ‘t’ indicating total
R
S
Sj
standard deviation, sample statistic average sample standard deviation
σ
observed sample standard deviation of the jth subgroup
σˆ t
estimated standard deviation, total
T
U Xα % Xi X X
2
standard deviation, population target value
upper specification limit α % percentile
ith value in a sample
arithmetic mean value, sample
arithmetic mean, of a number of sample arithmetic means
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ISO 22514-4:2016(E) ξ
scale parameter in a Weibull distribution
Y1, Y2
values read from a graph
zα
quantile of the standardized normal distribution from −∞ to α
2.2 Abbreviated terms MSE
mean square error
PCI
process capability index
PCF
process capability fraction
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, X50 % . Although for symmetric 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, σt . 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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