1、BS ISO 22514-2:2017Statistical methods in process management Capability and performancePart 2: Process capability and performance of time-dependent process modelsBSI Standards PublicationWB11885_BSI_StandardCovs_2013_AW.indd 1 15/05/2013 15:06BS ISO 22514-2:2017 BRITISH STANDARDNational forewordThis
2、 British Standard is the UK implementation of ISO 22514-2:2017. It supersedes BS ISO 22514-2:2013 which is withdrawn. The UK participation in its preparation was entrusted to Technical Committee SS/4, Statistical Process Management.A list of organizations represented on this committee can be obtaine
3、d on request to its secretary.This publication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application. The British Standards Institution 2017.Published by BSI Standards Limited 2017ISBN 978 0 580 94907 4 ICS 03.120.30 Compliance with
4、 a British Standard cannot confer immunity from legal obligations.This British Standard was published under the authority of the Standards Policy and Strategy Committee on 28 February 2017.Amendments/corrigenda issued since publicationDate T e x t a f f e c t e dBS ISO 22514-2:2017 ISO 2017Statistic
5、al methods in process management Capability and performance Part 2: Process capability and performance of time-dependent process modelsMthodes statistiques dans la gestion de processus Aptitude et performance Partie 2: Aptitude de processus et performance des modles de processus dpendants du tempsIN
6、TERNATIONAL STANDARDISO22514-2Second edition2017-02Reference numberISO 22514-2:2017(E)BS ISO 22514-2:2017ISO 22514-2:2017(E)ii ISO 2017 All rights reservedCOPYRIGHT PROTECTED DOCUMENT ISO 2017, Published in SwitzerlandAll rights reserved. Unless otherwise specified, no part of this publication may b
7、e 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 ISOs member body in the country of the re
8、quester.ISO copyright officeCh. de Blandonnet 8 CP 401CH-1214 Vernier, Geneva, SwitzerlandTel. +41 22 749 01 11Fax +41 22 749 09 47copyrightiso.orgwww.iso.orgBS ISO 22514-2:2017ISO 22514-2:2017(E)Foreword ivIntroduction v1 Scope . 12 Normative references 13 Terms definitions, symbols and abbreviated
9、 terms 13.1 Symbols . 13.2 Abbreviated terms . 24 Process analysis . 35 Time-dependent distribution models 36 Process capability and performance indices .146.1 Methods for determination of performance and capability indices Overview .146.1.1 General. 146.1.2 Calculation of location 156.1.3 Calculati
10、on of dispersion . 166.1.4 Calculation of X0,135 %and X99,865 %176.2 One-sided specification limits. 186.3 Use of different calculation methods 197 Reporting process performance/capability indices 20Bibliography .21 ISO 2017 All rights reserved iiiContents PageBS ISO 22514-2:2017ISO 22514-2:2017(E)F
11、orewordISO (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 tec
12、hnical 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 o
13、f 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
14、 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 suc
15、h 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 d
16、oes 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 ISOs adherence to the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see the following URL: www
17、 .iso .org/ iso/ foreword .htmlThe committee responsible for this document is ISO/TC 69, Applications of statistical methods, Subcommittee SC 4, Applications of statistical methods in process management.This second edition of ISO 22514-2 cancels and replaces the corrected version of the first editio
18、n (ISO 22514-2:2013), of which it constitutes a minor revision.The changes compared to the previous edition are as follows: the symbols and indices in CLpk, CUpk, PLpkand PUpkhave been improved; in Table 2, row “Location”, column “C”, the letter “s” has been replaced by “s/r”; in Table 2, row “Locat
19、ion”, column “D”, the capital letter “S” has been replaced by “s/r”; in Table 3, row “Location method label”, rows “3” and “4” in Formulae (13) and (14) the usage of indices has been improved and it is more precise now; editorial adjustments have been made to comply with the latest edition of the IS
20、O/IEC Directives, Part 2, 2016.A list of all parts in the ISO 22514- series, published under the general title Statistical methods in process management Capability and performance, can be found on the ISO website.iv ISO 2017 All rights reservedBS ISO 22514-2:2017ISO 22514-2:2017(E)IntroductionMany s
21、tandards have been created concerning the quality capability/performance of processes by international, regional and national standardization bodies and also by industry. All of them assume that the process is in a state of statistical control, with stationary, normally distributed processes. Howeve
22、r, a comprehensive analysis of production processes shows that, over time, it is very rare for processes to remain in such a state.In recognition of this fact, this document provides a framework for estimating the quality capability/performance of industrial processes for an array of standard circum
23、stances. These circumstances are categorized based on the stability of the mean and variance, as to whether they are constant, changing systematically, or changing randomly. As such, the quality capability/performance can be assessed for very differently shaped distributions with respect to time.In
24、other parts of ISO 22514 more detailed information about calculations of indices can be found. It should be noted that where the capability indices given in this document are computed they only form point estimates of their true values. It is therefore recommended that wherever possible the indices
25、confidence intervals are computed and reported. ISO 2017 All rights reserved vBS ISO 22514-2:2017BS ISO 22514-2:2017Statistical methods in process management Capability and performance Part 2: Process capability and performance of time-dependent process models1 ScopeThis document describes a procedu
26、re for the determination of statistics for estimating the quality capability or performance of product and process characteristics. The process results of these quality characteristics are categorized into eight possible distribution types. Calculation formulae for the statistical measures are place
27、d with every distribution.The statistical methods described in this document only relate to continuous quality characteristics. They are applicable to processes in any industrial or economical sector.NOTE This method is usually applied in case of a great number of serial process results, but it can
28、also be used for small series (a small number of process results).2 Normative referencesThe following documents are referred to in the text in such a way that some or all of their content constitutes requirements of this document. For dated references, only the edition cited applies. For undated ref
29、erences, the latest edition of the referenced document (including any amendments) applies.ISO 5479, Statistical interpretation of data Tests for departure from the normal distribution3 Terms definitions, symbols and abbreviated termsFor the purposes of this document, the terms and definitions given
30、in ISO 3534-2 and ISO 22514-1, andthe symbols and abbreviated terms given below, apply.ISO and IEC maintain terminological databases for use in standardization at the following addresses: IEC Electropedia: available at h t t p :/ www .electropedia .org/ ISO Online browsing platform: available at h t
31、 t p :/ www .iso .org/ obp3.1 SymbolsCpprocess capability indexCpkminimum process capability indexCLpklower process capability indexCUpkupper process capability indexc4constant based on subgroup size nINTERNATIONAL STANDARD ISO 22514-2:2017(E) ISO 2017 All rights reserved 1BS ISO 22514-2:2017ISO 225
32、14-2:2017(E) dispersion of the processLdifference between Xmidand X0,135 %of the distribution of the product characteristicUdifference between X99,865 %and Xmidof the distribution of the product characteristicd2constant based on subgroup size nk number of subgroups of the same size n average locatio
33、n of the processL lower specification limitMl,dcalculation methods with location method label l and dispersion method label dN sample sizepLlower fraction nonconformingpttotal fraction nonconformingpUupper fraction nonconformingPpprocess performance indexPpkminimum process performance indexPLpklower
34、 process performance indexPUpkupper process performance indexRirange of the ith subgroups standard deviation, realized value standard deviation, populationS standard deviation, sample statisticSiobserved sample standard deviation of the ith subgroupStstandard deviation, with the subscript “t” indica
35、ting total standard deviationU upper specification limitX0,135 %0,135 % distribution quantileX99,865 %99,865 % distribution quantileX50 %50 % distribution quantileXmiddistribution midpoint3.2 Abbreviated termsANOVA analysis of varianceSPC statistical process control2 ISO 2017 All rights reservedBS I
36、SO 22514-2:2017ISO 22514-2:2017(E)4 Process analysisThe purpose of process analysis is to obtain knowledge of a process. This knowledge is necessary for controlling the process efficiently and effectively so that the products realized by the process fulfil the quality requirement. It is a general as
37、sumption of this document that a process analysis has been carried out and subsequent process improvements have been implemented.The behaviour of a characteristic under consideration can be described by the distribution, the location, the dispersion and the shape, parameters of which are time-depend
38、ent functions, in general. Different models of such resulting distributions the parameters of which are time-dependent functions are discussed in Clauses 6 and 7. To indicate whether a time-dependent distribution model fits, statistical methods e.g. estimating parameters, analysis of variance (ANOVA
39、) including graphical tools (e.g. probability plots, control charts) are used.The values of the characteristics under consideration are typically determined on the basis of samples taken from the process flow. The sample size and frequency should be chosen depending on the type of process and the ty
40、pe of product so that all important changes are detected in time. The samples should be representative for the characteristic under consideration. To asses the stability of the process a control chart should be used. Information on the use of control charts can be found in ISO 7870-2.5 Time-dependen
41、t distribution modelsThe instantaneous distribution characterizes the behaviour of the characteristic under investigation during a short interval. Usually, it is the time interval during which the sample (e.g. the subgroup) can be taken from the process. Observing the process continuously in time fo
42、r a longer time interval the output from the process is called the resulting process distribution and it is described by a corresponding time-dependent distribution model that reflects the instantaneous distribution of the characteristic under consideration, and the changes of its location, dispersi
43、on and shape parameters during the time interval of process observation.In practice, the resulting distribution can be represented by the whole data set, e.g. when SPC is applied, by all subgroups gained during the interval of the process observation.Time-dependent distribution models can be classif
44、ied into four groups according to whether the location and dispersion moments are constant or changing (see Table 1).a) A process whose location and dispersion are constant is in time-dependent distribution model A. In this case only, all the means and variances of the instantaneous distributions ar
45、e equal to each other and they are equal to the resulting distribution.b) If the dispersion of a process is changing with time, but the location stays constant, the process is said to be in time-dependent distribution model B.c) If the dispersion is constant, but the location is changing, we have ti
46、me-dependent distribution model C.d) Otherwise, we have time-dependent distribution model D. ISO 2017 All rights reserved 3BS ISO 22514-2:2017ISO 22514-2:2017(E)Table1 Classificationoftime-dependentdistributionmodelsProcess-standarddeviations(t)Processaverage(t)ConstantNot constantConstantACA1A2C1C2
47、C3C4ShorttimedistributionNormaldistributedNotnormaldistributedunimodalLocationRandomRandomSystematic(e.g.trend)Systematic and random(e.g. lot to lot)Shorttimedistribu-tionNormaldistributedNormaldistributedNormaldistributedNormaldistributedResultingdistributionNormaldistributedNotnormaldistrib-utedun
48、imodalAny shapeAny shape(e.g.multimodal)NotconstantResultingdistributionBResultingdistributionDAny shape unimodalAny shape4 ISO 2017 All rights reservedBS ISO 22514-2:2017ISO 22514-2:2017(E)For changing moments, the models can be classified according to whether the changes are random, systematic or
49、both.NOTE Model A2 is known as stationary in time-series analysis literature and model A1 is known as second order stationary.Table 2 summarizes the basic features of individual time-dependent distribution models; their graphical representations are given in Figures 1 to 8. There are subclasses of time-dependent distribution models A and C which are introduced due to their practical importance. They differ in the shape of the resulting distribution and in the cause of the process being in an out-of-control st
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