1、raising standards worldwideNO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAWBSI Standards PublicationBS ISO 22514-6:2013Statistical methods in process management Capability and performancePart 6: Process capability statistics for characteristics following a multivariate normal d
2、istributionBS ISO 22514-6:2013 BRITISH STANDARDNational forewordThis British Standard is the UK implementation of ISO 22514-6:2013. The UK participation in its preparation was entrusted toT e c h n i c a l Committee SS/4, Statistical Process Management.A list of organizations represented on this com
3、mittee can be obtained 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 2013. Published by BSI Standards Limited 2013.ISBN 978 0 580 67345 0 ICS 03
4、.120.30 Compliance with a British Standard cannot confer immunityfrom legal obligations.This British Standard was published under the authority of the Standards Policy and Strategy Committee on 31 March 2013.Amendments issued since publicationDate T e x t a f f e c t e dBS ISO 22514-6:2013 ISO 2013S
5、tatistical methods in process management Capability and performance Part 6: Process capability statistics for characteristics following a multivariate normal distributionMthodes statistiques dans la gestion des processus Capabilit et performance Partie 6: Statistiques de capabilit pour un processus
6、caractris par une distribution normale multivarieINTERNATIONAL STANDARDISO22514-6First edition2013-02-15Reference numberISO 22514-6:2013(E)BS ISO 22514-6:2013ISO 22514-6:2013(E)ii ISO 2013 All rights reservedCOPYRIGHT PROTECTED DOCUMENT ISO 2013All rights reserved. Unless otherwise specified, no par
7、t 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 ISOs member bo
8、dy in the country of the requester.ISO copyright officeCase postale 56 CH-1211 Geneva 20Tel. + 41 22 749 01 11Fax + 41 22 749 09 47E-mail copyrightiso.orgWeb www.iso.orgPublished in SwitzerlandBS ISO 22514-6:2013ISO 22514-6:2013(E) ISO 2013 All rights reserved iiiContents PageForeword ivIntroduction
9、 v1 Scope . 12 Normative references 13 Terms and definitions . 14 Abbreviated terms 35 Process analysis . 46 Use of multivariate process capability and performance assessment . 47 Calculation of process capability and process performance 47.1 Description of Types I and II . 47.2 Designation and symb
10、ols of the indices 57.3 Types c and c process capability index . 87.4 Types a and Type b process capability index .108 Examples 118.1 Two-dimensional position tolerances . 118.2 Position and dimension of a slot . 16Annex A (informative) Derivation of formulae .20Annex B (informative) Shaft imbalance
11、 example .25Annex C (informative) Hole position example .29Annex D (informative) Construction of the quality function 33Bibliography .34BS ISO 22514-6:2013ISO 22514-6:2013(E)ForewordISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO m
12、ember 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, governm
13、ental 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 Dire
14、ctives, 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 bodi
15、es casting a vote.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 22514-6 was prepared by Technical Committee ISO/TC 69, Applications of statistic
16、al 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 2: Process capability and per
17、formance of time-dependent process models Part 3: Machine performance studies for measured data on discrete parts Part 4: Process capability estimates and performance measures Technical Report Part 5: Process capability statistics for attribute characteristics Part 6: Process capability statistics f
18、or characteristics following a multivariate normal distribution Part 7: Capability of measurement processes Part 8: Machine performance of a multi-state production processiv ISO 2013 All rights reservedBS ISO 22514-6:2013ISO 22514-6:2013(E)IntroductionDue to the increased complexity of the productio
19、n methods and the increasing quality requirements for products and processes, a process analysis based on univariate quantities is in many cases not sufficient.Instead, it may be necessary to analyse the process on the basis of multivariate product quantities. This can, for instance, be in such case
20、s where geometric tolerances, dynamic magnitudes such as imbalance, correlated quantities of materials or other procedural products are observed.By analogy with ISO 22514-2, ISO 22514-6 provides calculation formulae for process performance and process capability indices, which take into consideratio
21、n process dispersion as well as process location as an extension to the corresponding indices for univariate quantities. The indices proposed are indeed based on the classical Cpand Cpkindices for the one-dimensional case. The motivation for the extension to the multivariate case is explained in Ann
22、ex A.Examples of possible applications are two-dimensional or three-dimensional positions, imbalance or several correlated quantities of chemical products.The dispersion of the measuring results comprises the dispersion of the product realization process and the precision of the measuring process. I
23、t is assumed that the capability of the used measuring system was demonstrated prior to the determination of the capability of the product realization process.The calculation method described here should be used to support an unambiguous decision, especially if limiting values for process capability
24、 indices for multivariate, continuous product quantities are specified as part of a contract between customers and suppliers, or the capabilities of different constructions, production methods or suppliers are to be compared, or production processes are to be approved, or problems are to be analysed
25、 and decisions made in complaint cases or damage events.NOTE Product realization processes include e.g. manufacturing processes, service processes, product assembly processes. ISO 2013 All rights reserved vBS ISO 22514-6:2013BS ISO 22514-6:2013Statistical methods in process management Capability and
26、 performance Part 6: Process capability statistics for characteristics following a multivariate normal distribution1 ScopeThis part of ISO 22514 provides methods for calculating performance and capability statistics for process or product quantities where it is necessary or beneficial to consider a
27、family of singular quantities in relation to each other. The methods provided here mostly are designed to describe quantities that follow a bivariate normal distribution.NOTE In principle, this part of ISO 22514 can be used for multivariate cases.This part of ISO 22514 does not offer an evaluation o
28、f the different provided methods with respect to different situations of possible application of each method. For the current state, the selection of one preferable method might be done following the users preferences.The purpose is to give definitions for different approaches of index calculation f
29、or performance and capability in the case of a multiple process or product quantity description.2 Normative referencesThe following documents, in whole or in part, are normatively referenced in this document and are indispensable for its application. For dated references, only the edition cited appl
30、ies. For undated references, the latest edition of the referenced document (including any amendments) applies.ISO 22514-1, Statistical methods in process management Capability and performance Part 1: General principles and conceptsISO 22514-2, Statistical methods in process management Capability and
31、 performance Part 2: Process capability and performance of time-dependent process models3 Terms and definitionsFor the purpose of this document, the terms and definitions given in ISO 22514-1 and ISO 22514-2 and the following apply.3.1quantityproperty of a phenomenon, body, or substance, where the p
32、roperty has a magnitude that can be expressed as a number and a referenceISO/IEC Guide 99:2007, 1.13.2multivariate quantityset of distinguishing featuresNote 1 to entry: The set can be expressed by a d-tuple, i.e. an ordered set consisting of d elements.INTERNATIONAL STANDARD ISO 22514-6:2013(E) ISO
33、 2013 All rights reserved 1BS ISO 22514-6:2013ISO 22514-6:2013(E)Note 2 to entry: If the single quantities in the set are denoted by xiwhere i = 1, 2d, the multivariate quantity is expressed as the vector x = (x1, x2, xd)T. Thus, a multivariate quantity can be considered as a feature vector of a pro
34、duct. The value of the multivariate quantity is represented by a point in the d-dimensional feature space.Note 3 to entry: The selection of the quantities in a vector is made for specific technical reason.Note 4 to entry: All single quantities combined in the vector of a multivariate must be measura
35、ble in the same product or object.Note 5 to entry: If the multivariate quantity is to be described by means of statistics, the vector is to be considered as a random vector following a d-dimensional multivariate distribution.EXAMPLE 1 A number of d = 3 quantities like x1= colour, x2= mass and x3= nu
36、mber of defects are combined in order to use only one statistic for process assessment. The dimension of vector x is d = 3.EXAMPLE 2 In order to evaluate a boring process, the position of the borehole axis is measured in an x-coordinate and y-coordinate. The coordinates are combined to the two-dimen
37、sional multivariate quantity x where the component x1is the x-coordinate and x2is the y-coordinate.EXAMPLE 3 Imbalance of a wheel.3.3tolerance regionregion in the feature space that contains all permitted values of the multivariate quantity (3.2)Note 1 to entry: The region is limited by lines, surfa
38、ces or hyper-surfaces in the d-dimensional space and not necessarily closed. The form and extension of the region are specified by one or more parameters.Note 2 to entry: Typical shapes of tolerance regions are rectangles, ellipses (or circles) in the two-dimensional case, cuboids or hyper-cuboids,
39、ellipsoids or hyper-ellipsoids or composite prismatic shapes. Figure 1 shows examples of tolerance regions in the two-dimensional space.Note 3 to entry: The tolerance region is specified based on the required function of the product. Products showing values outside the region are assumed to not fulf
40、il functional requirements. Those products are considered to be nonconforming parts.Note 4 to entry: In order to assess a product with respect to the limits of the tolerance region, the order of the single quantity in the multivariate quantity and the number d of dimension must be equal to that of t
41、he tolerance region description.EXAMPLE A tolerance zone as it is defined in ISO 1101 for geometrical product features can be considered as a tolerance region. In that case, limiting geometrically perfect lines or surfaces correspond to the boundary and the tolerance correspond to the parameter of t
42、he tolerance region.2 ISO 2013 All rights reservedBS ISO 22514-6:2013ISO 22514-6:2013(E)A)xa2yC)a1xa2byX2X1B)dxya1KeyA rectangular tolerance region with parameters a1, a2, x and yB circular tolerance region with parameters d, x and yC triangularly extended rectangular region with parameters a1, a2,
43、b, x and yFigure 1 Examples of tolerance regions in the two-dimensional space of the bivariate quantity (x1, x2)T3.4process capabilitydistribution of measured quantity (3.1) values from a process that has been demonstrated to be in statistical control and which describes the ability of a process to
44、produce quantity values that will fulfil the requirements for that quantityNote 1 to entry: The process capability index provides the ability to meet requirements of the measured quantity.Note 2 to entry: The abbreviation for process capability index is PCI.3.5estimated process capabilitystatistical
45、 description of a process capability (3.4)3.6process performancedistribution of measured quantity (3.1) values from a processNote 1 to entry: The process may not have been demonstrated to be in statistical control.3.7estimated process performancestatistical description of a process performance (3.6)
46、4 Abbreviated termsMMC maximum material conditionPCI process capability index ISO 2013 All rights reserved 3BS ISO 22514-6:2013ISO 22514-6:2013(E)5 Process analysisThe purpose of process analysis is to obtain sound knowledge of a process. This knowledge is necessary for controlling the process effic
47、iently, so that the products realized by the process fulfil the quality requirement.A process analysis is always an analysis of one or more quantities that are considered to be important to the process.Product quantities can often be analysed instead of process quantities because product quantities
48、not only characterize the products, but due to their correlation with process quantities they also characterize the process creating these products.The values of the quantities under consideration are typically determined on the basis of samples taken from the process flow. The sample size and frequ
49、ency should be chosen depending on the type of process and the type of product so that all important changes are detected in time. The samples should be representative for the multivariate quantities under consideration. (Univariate quantity values are considered in ISO 22514-2.) This part of ISO 22514 describes multivariate capability statistics.To estimate the PCI, the sample size should preferably be at least 125.6 Use of multivariate process capability and performance assessmentThe purpose of a process c
