1、raising standards worldwideNO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAWBSI Standards PublicationBS ISO 3951-4:2011BS 6002-5Sampling procedures for inspection by variablesPart 4: Procedures for assessment of declared quality levelsBS ISO 3951-4:2011 BRITISH STANDARDNational
2、forewordThis British Standard is the UK implementation of ISO 3951-4:2011.The UK participation in its preparation was entrusted to TechnicalCommittee SS/5, Acceptance sampling schemes.A list of organizations represented on this committee can beobtained on request to its secretary.This publication do
3、es not purport to include all the necessaryprovisions of a contract. Users are responsible for its correctapplication. BSI 2011ISBN 978 0 580 66142 6ICS 03.120.30Compliance with a British Standard cannot confer immunity fromlegal obligations.This British Standard was published under the authority of
4、 theStandards Policy and Strategy Committee on 31 August 2011.Amendments issued since publicationDate Text affectedBS ISO 3951-4:2011Reference numberISO 3951-4:2011(E)ISO 2011INTERNATIONAL STANDARD ISO3951-4First edition2011-08-15Sampling procedures for inspection by variables Part 4: Procedures for
5、 assessment of declared quality levels Rgles dchantillonnage pour les contrles par mesures Partie 4: Procdures pour lvaluation des niveaux dclars de qualit BS ISO 3951-4:2011ISO 3951-4:2011(E) COPYRIGHT PROTECTED DOCUMENT ISO 2011 All rights reserved. Unless otherwise specified, no part of this publ
6、ication 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 ISOs member body in the country of the requester. ISO copyright office Case postale 56 CH-1211 Gene
7、va 20 Tel. + 41 22 749 01 11 Fax + 41 22 749 09 47 E-mail copyrightiso.org Web www.iso.org Published in Switzerland ii ISO 2011 All rights reservedBS ISO 3951-4:2011ISO 3951-4:2011(E) ISO 2011 All rights reserved iiiContents Page Foreword iv Introduction.v 1 Scope1 2 Normative references2 3 Terms, d
8、efinitions, symbols and abbreviations.2 4 Principles3 5 Declared quality level (DQL).4 6 Sampling plans 5 7 Operating a sampling plan .8 8 Further information .15 Annex A (informative) Method of matching variables plans to attributes plans 20 Annex B (informative) Examples of use of the procedures21
9、 Bibliography25 BS ISO 3951-4:2011ISO 3951-4:2011(E) iv ISO 2011 All rights reservedForeword 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 thro
10、ugh 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 collabor
11、ates 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 Standa
12、rds. 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. Attention is drawn to the possibility that some of the elements of t
13、his document may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights. ISO 3951-4 was prepared by Technical Committee ISO/TC 69, Application of statistical methods, Subcommittee SC 5, Acceptance sampling. ISO 3951 consists of the following
14、parts, under the general title Sampling procedures for inspection by variables: Part 1: Specification for single sampling plans indexed by acceptance quality limit (AQL) for lot-by-lot inspection for a single quality characteristic and a single AQL Part 2: General specification for single sampling p
15、lans indexed by acceptance quality limit (AQL) for lot-by-lot inspection of independent quality characteristics Part 3: Double sampling schemes indexed by acceptance quality limit (AQL) for lot-by-lot inspection Part 4: Procedures for assessment of declared quality levels Part 5: Sequential sampling
16、 plans indexed by acceptance quality limit (AQL) for inspection by variables (known standard deviation) BS ISO 3951-4:2011ISO 3951-4:2011(E) ISO 2011 All rights reserved vIntroduction The procedures in this part of ISO 3951 differ in their scope from the procedures in ISO 3951 Parts 1, 2, 3 and 5. T
17、he acceptance sampling procedures that are specified in ISO 3951 Parts 1, 2, 3 and 5 are intended to be used in bilateral agreements between two parties. Those acceptance sampling procedures are intended to be used as simple, pragmatic rules for releasing product after inspection of only a limited s
18、ample of a consignment, and therefore the procedures do not make reference (either explicitly or implicitly) to any formally declared quality level. Under acceptance sampling, there is no sharp borderline between quality levels that should be considered acceptable and qualities that should be reject
19、ed by the procedure. For the procedures in ISO 3951 Parts 1, 2, 3 and 5, the two parties agree upon some limiting quality level (AQL) which is the worst tolerable process average when a continuing series of lots is submitted. The switching rules and the sampling schemes in those four standards are d
20、esigned to encourage the suppliers to have process averages consistently better than the AQL selected. In order to keep sample sizes moderate, the protection against accepting individual lots of inferior quality may be less than that provided by sampling plans targeted for sentencing individual lots
21、. Procedures in ISO 3951 Parts 1, 2, 3 and 5 are well suited for acceptance sampling purposes, but they should not be used in reviews, audits, etc. to verify a quality that has been declared for some entity. The main reason is that the procedures have been indexed in terms of quality levels that are
22、 relevant solely for the pragmatic purposes of acceptance sampling, and the various risks have been balanced accordingly. The procedures in this part of ISO 3951 have been developed as a response to the growing need for sampling procedures suitable for formal, systematic inspections such as reviews
23、or audits. When performing such a formal inspection, it is necessary for the authority to consider the risk of reaching an incorrect conclusion, and to take this risk into account in planning and executing the review/audit/testing, etc. This part of ISO 3951 provides guidance and rules to assist the
24、 user in taking this risk into account in an informed manner. The rules in this part of ISO 3951 have been devised such that there is only a small, limited risk of contradicting the declared quality level when in fact the actual level conforms to the declared level. If it were also desired that ther
25、e should be a similarly small risk of not contradicting the declared quality level when in fact the actual quality level does not conform to the declared quality level, then it would be necessary to investigate a rather large sample. Therefore, in order to obtain the benefit of a moderate sample siz
26、e, the procedures in this part of ISO 3951 have been devised in such a way that they allow a somewhat higher risk of failing to contradict the declared quality level when in fact the actual quality level does not conform to the declared quality level. The wording of the result of the assessment shou
27、ld reflect this unbalance between the risks of reaching incorrect conclusions. When the sample result contradicts the declared quality level, there is strong evidence of nonconformance to the declared quality level. When the sample result does not contradict the declared quality level, this should b
28、e understood as “we have not, in this limited sample, found strong evidence of nonconformance to the declared quality level”. BS ISO 3951-4:2011BS ISO 3951-4:2011INTERNATIONAL STANDARD ISO 3951-4:2011(E) ISO 2011 All rights reserved 1Sampling procedures for inspection by variables Part 4: Procedures
29、 for assessment of declared quality levels 1 Scope This part of ISO 3951 establishes sampling plans and procedures by variables that can be used to assess whether the quality level of an entity (lot, process, etc.) conforms to a declared value. The sampling plans have been devised so that their oper
30、ating characteristic curves match those of the corresponding attributes plans in ISO 2859-4 as closely as possible, so that the choice between using sampling by attributes and sampling by variables is not influenced by attempts to increase the chance of accepting an incorrectly declared quality leve
31、l. In this part of ISO 3951, there is a risk of between 1,4 % and 8,2 % of contradicting a correct declared quality level. The risk is 10 % of failing to contradict an incorrect declared quality level which is related to the limiting quality ratio (see Clause 4). Sampling plans are provided correspo
32、nding to three levels of discriminatory ability, and for the cases of unknown and known process standard deviation. In contrast to the procedures in the other parts of ISO 3951, the procedures in this part of ISO 3951 are not applicable to acceptance assessment of lots. Generally, the balancing of t
33、he risks of reaching incorrect conclusions in assessment procedures will differ from the balancing in the procedures for acceptance sampling. This part of ISO 3951 may be used for various forms of quality inspection in situations where objective evidence of conformity to some declared quality level
34、is to be provided by means of inspection of a sample. The procedures are applicable to entities such as lots, process output, etc. that allow random samples of individual items to be taken from the entity. The sampling plans provided in this part of ISO 3951 are applicable, but not limited, to inspe
35、ction of a variety of products such as end items, components and raw materials, operations, materials in process, supplies in storage, maintenance operations, data or records, and administrative procedures. The procedures are intended to be used when the quality characteristics are measurable variab
36、les that are independent and normally distributed, and where the quantity of interest is the fraction of items that are nonconforming. BS ISO 3951-4:2011ISO 3951-4:2011(E) 2 ISO 2011 All rights reserved2 Normative references The following referenced documents are indispensable for the application of
37、 this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. ISO 2859-4:2002, Sampling procedures for inspection by attributes Part 4: Procedures for assessment of declared quality leve
38、ls ISO 3534-1, Statistics Vocabulary and symbols Part 1: General statistical terms and terms used in probability ISO 3534-2, Statistics Vocabulary and symbols Part 2: Applied statistics ISO 3951-2: 2006, Sampling procedures for inspection by variables Part 2: General specification for single samplin
39、g plans indexed by acceptance quality limit (AQL) for lot-by-lot inspection of independent quality characteristics ISO 9000, Quality management systems Fundamentals and vocabulary 3 Terms, definitions, symbols and abbreviations 3.1 Terms and definitions For the purposes of this part of ISO 3951, the
40、 terms and definitions given in ISO 3534-1, ISO 3534-2, ISO 3951-2 and ISO 9000 and the following apply. 3.1.1 quality ratio ratio of the actual to the declared quality level of the entity under investigation 3.1.2 limiting quality ratio LQR value of the quality ratio that is limited to a small risk
41、 (10 % in this part of ISO 3951) of failing to contradict an incorrect declared quality level 3.2 Symbols and abbreviated terms The symbols and abbreviated terms used in this part of ISO 3951 are as follows: (.)vB Distribution function of the symmetric beta distribution with both parameters equal to
42、 v B(v,v) Beta function with both arguments equal to v, i.e. B(v,v)=(v)(v)/(v) where (v) is the gamma function (see below) D Declared quality level (as a symbol) DQL Declared Quality Level (as an acronym) ksForm k acceptability constant under the “s” method, used when the sample standard deviation i
43、s unknown kForm k acceptability constant under the “” method, used when the process standard deviation is presumed to be known BS ISO 3951-4:2011ISO 3951-4:2011(E) ISO 2011 All rights reserved 3L Lower specification limit (as a subscript, denotes the value at L) LQR Limiting Quality Ratio (as an acr
44、onym) m Number of quality characteristics, all assumed to be independent and normally distributed nsSample size under the “s” method nSample size under the “” method OC Operating Characteristic p Process fraction nonconforming in the entity p Estimate of the fraction nonconforming in the entity cp E
45、stimate of the combined fraction nonconforming at both specification limits, i.e. c LUp pp=+ *p Form p* acceptability constant (for both the “s” and “” methods) Q Quality statistic (see 7.2.2 and 7.3.2) s Sample standard deviation U Upper specification limit (as a subscript, denotes the value at U)
46、x Sample mean (.) Standard normal distribution function ()v Gamma function, defined by () ( )10exp dvvt tt= for 0 Process standard deviation 4 Principles In any assessment procedure based on sampling, there will be an inherent uncertainty due to possible sampling fluctuations. The procedures in this
47、 part of ISO 3951 have been conceived so as to lead to contradiction of the declared quality level only when there is sufficient evidence to support a conclusion that the actual quality is poorer than the declared quality level. The plans have been devised in such a way that their operating characte
48、ristic curves match those of the corresponding attributes plans ISO 2859-4 as closely as possible. Details of the matching method are given in Annex A. The attributes plans of ISO 2859-4 were selected such that when the actual quality level is equal to or better than the declared quality level, the
49、risk is less than 5 % of contradicting the declared value. It follows that when the actual quality level is worse than the declared quality level, there is a risk that the procedures will fail to contradict an incorrect declared quality level. Owing to the fact that the match between corresponding OC curves in ISO 2859-4 and ISO 3951-4 is imperfect, the corresponding risk in this part of ISO 3951 varies around 5 %. This risk depends on the value of the quality ratio, i.e. the r
