SANS 16269-6-2006 Statistical interpretation of data Part 6 Determination of statistical tolerance intervals《统计数据解释 第6部分 统计公差区间确定》.pdf

1、 Collection of SANS standards in electronic format (PDF) 1. Copyright This standard is available to staff members of companies that have subscribed to the complete collection of SANS standards in accordance with a formal copyright agreement. This document may reside on a CENTRAL FILE SERVER or INTRA

2、NET SYSTEM only. Unless specific permission has been granted, this document MAY NOT be sent or given to staff members from other companies or organizations. Doing so would constitute a VIOLATION of SABS copyright rules. 2. Indemnity The South African Bureau of Standards accepts no liability for any

3、damage whatsoever than may result from the use of this material or the information contain therein, irrespective of the cause and quantum thereof. ICS 03.120.30 ISBN 0-626-17983-1 SANS 16269-6:2006 Edition 1 ISO 16269-6:2005 Edition 1SOUTH AFRICAN NATIONAL STANDARD Statistical interpretation of data

4、 Part 6: Determination of statistical tolerance intervals This national standard is the identical implementation of ISO 16269-6:2005 and is adopted with the permission of the International Organization for Standardization. Published by Standards South Africa 1 dr lategan road groenkloof private bag

5、x191 pretoria 0001 tel: 012 428 7911 fax: 012 344 1568 international code +27 12 www.stansa.co.za Standards South Africa This standard may only be used and printed by approved subscription and freemailing clients of the SABS. SANS 16269-6:2006 Edition 1 ISO 16269-6:2005 Edition 1 Table of changes Ch

6、ange No. Date Scope Abstract Describes procedures for establishing tolerance intervals that include at least a specified proportion of the population with a specified confidence level. Both one-sided and two-sided statistical tolerance intervals are provided, a one-sided interval having either an up

7、per or a lower limit while a two-sided interval has both upper and lower limits. Two methods are provided, a parametric method for the case where the characteristic being studied has a normal distribution and a distribution-free method for the case where nothing is known about the distribution excep

8、t that it is continuous. Keywords data processing, definitions, distribution, estimation, functions (mathematics), instruments, interpretations, mathematical calculations, mathematical entities, measurement, measurement techniques, normal distributions, statistical analysis, statistical data, statis

9、tical methods of analysis, statistical tolerance intervals, statistical tolerances (measurement), statistics, testing, tolerances (measurement). National foreword This South African standard was approved by National Committee StanSA TC 169, Applications of statistical methods, in accordance with pro

10、cedures of Standards South Africa, in compliance with annex 3 of the WTO/TBT agreement. This standard may only be used and printed by approved subscription and freemailing clients of the SABS. Reference number ISO 16269-6:2005(E) ISO 2005INTERNATIONAL STANDARD ISO 16269-6 First edition 2005-04-01 St

11、atistical interpretation of data Part 6: Determination of statistical tolerance intervals Interprtation statistique des donnes Partie 6: Dtermination des intervalles statistiques de tolrance This standard may only be used and printed by approved subscription and freemailing clients of the SABS.ISO 1

12、6269-6:2005(E) PDF disclaimer This PDF file may contain embedded typefaces. In accordance with Adobes 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 download

13、ing this file, parties accept therein the responsibility of not infringing Adobes 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 Gen

14、eral 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 give

15、n below. ISO 2005 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 ISOs member

16、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 copyrightiso.org Web www.iso.org Published in Switzerland ii ISO 2005 All rights reservedThis standard may only be used and printed by approved subscriptio

17、n and freemailing clients of the SABS.ISO 16269-6:2005(E) ISO 2005 All rights reserved iiiContents Page Foreword iv Introduction v 1 Scope 1 2 Normative references . 1 3 Terms, definitions and symbols 1 3.1 Terms and definitions. 1 3.2 Symbols . 2 4 Procedures 3 4.1 Normal population with known vari

18、ance and known mean 3 4.2 Normal population with known variance and unknown mean . 3 4.3 Normal population with unknown variance and unknown mean. 3 4.4 Any continuous distribution of unknown type 3 5 Examples 3 5.1 Data. 3 5.2 Example 1: One-sided statistical tolerance interval under known variance

19、. 4 5.3 Example 2: Two-sided statistical tolerance interval under known variance 4 5.4 Example 3: One-sided statistical tolerance interval under unknown variance 5 5.5 Example 4: Two-sided statistical tolerance interval under unknown variance 6 5.6 Example 5: Distribution-free statistical tolerance

20、interval for continuous distribution 6 Annex A (informative) Forms for tolerance intervals 8 Annex B (normative) One-sided statistical tolerance limit factors, k 1 (n; p; 1 ), for known . 14 Annex C (normative) Two-sided statistical tolerance limit factors, k 2 (n; p; 1 ), for known . 17 Annex D (no

21、rmative) One-sided statistical tolerance limit factors, k 3 (n; p; 1 ), for unknown . 20 Annex E (normative) Two-sided statistical tolerance limit factors, k 4 (n; p; 1 ), for unknown . 23 Annex F (normative) One-sided distribution-free statistical tolerance intervals. 26 Annex G (normative) Two-sid

22、ed distribution-free statistical tolerance intervals 27 Annex H (informative) Construction of a distribution-free statistical tolerance interval for any type of distribution 28 Annex I (informative) Computation of factors for two-sided parametric statistical tolerance intervals 29 Bibliography . 30

23、This standard may only be used and printed by approved subscription and freemailing clients of the SABS.ISO 16269-6:2005(E) iv ISO 2005 All rights reservedForeword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The

24、 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-gove

25、rnmental, 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. T

26、he 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 vot

27、e. 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 16269-6 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods. Th

28、is first edition of ISO 16269-6 cancels and replaces ISO 3207:1975, which has been technically revised. ISO 16269 consists of the following parts, under the general title Statistical interpretation of data: Part 6: Determination of statistical tolerance intervals Part 7: Median Estimation and confid

29、ence intervals Part 8: Determination of prediction intervals This standard may only be used and printed by approved subscription and freemailing clients of the SABS.ISO 16269-6:2005(E) ISO 2005 All rights reserved vIntroduction A statistical tolerance interval is an estimated interval, based on a sa

30、mple, which can be asserted with confidence 1 , for example 95 %, to contain at least a specified proportion p of the items in the population. The limits of a statistical tolerance interval are called statistical tolerance limits. The confidence level 1 is the probability that a statistical toleranc

31、e interval constructed in the prescribed manner will contain at least a proportion p of the population. Conversely, the probability that this interval will contain less than the proportion p of the population is . This part of ISO 16269 describes both one-sided and two-sided statistical tolerance in

32、tervals; a one-sided interval is constructed with an upper or a lower limit while a two-sided interval is constructed with both an upper and a lower limit. Tolerance intervals are functions of the observations of the sample, i.e. statistics, and they will generally take different values for differen

33、t samples. It is necessary that the observations be independent for the procedures provided in this part of ISO 16269 to be valid. Two types of tolerance interval are provided in this part of ISO 16269, parametric and distribution-free. The parametric approach is based on the assumption that the cha

34、racteristic being studied in the population has a normal distribution; hence the confidence that the calculated statistical tolerance interval contains at least a proportion p of the population can only be taken to be 1 if the normality assumption is true. For normally distributed characteristics, t

35、he statistical tolerance interval is determined using one of the Forms A, B, C or D given in Annex A. Parametric methods for distributions other than the normal are not considered in this part of ISO 16269. If departure from normality is suspected in the population, distribution-free statistical tol

36、erance intervals may be constructed. The procedure for the determination of a statistical tolerance interval for any continuous distribution is provided in Forms E and F of Annex A. The tolerance limits discussed in this part of ISO 16269 can be used to compare the natural capability of a process wi

37、th one or two given specification limits, either an upper one U or a lower one L or both in statistical process management. An indication of this is the fact that these tolerance limits have also been called natural process limits. See ISO 3534-2:1993, 3.2.4, and the general remarks in ISO 3207 whic

38、h will be cancelled and replaced by this part of ISO 16269. Above the upper specification limit U there is the upper fraction nonconforming p U(ISO 3534-2:, 3.2.5.5 and 3.3.1.4) and below the lower specification limit L there is the lower fraction nonconforming p L(ISO 3534-2:, 3.2.5.6 and 3.3.1.5).

39、 The sum p U+ p L= p Tis called the total fraction nonconforming. (ISO 3534-2:, 3.2.5.7). Between the specification limits U and L there is the fraction conforming 1 p T . In statistical process management the limits U and L are fixed in advance and the fractions p U , p Land p Tare either calculate

40、d, if the distribution is assumed to be known, or otherwise estimated. There are many applications of statistical tolerance intervals, although the above shows an example to a quality control problem. Wider applications and more statistical intervals are introduced in many textbooks such as Hahn and

41、 Meeker 10 . In contrast, for the tolerance intervals considered in this part of ISO 16269, the confidence level for the interval estimator and the proportion of the distribution within the interval (corresponding to the fraction conforming mentioned above) are fixed in advance, and the limits are e

42、stimated. These limits may be compared with U and L. Hence the appropriateness of the given specification limits U and L can be compared with the actual properties of the process. The one-sided tolerance intervals are used when only either the upper specification limit U or the lower specification l

43、imit L is relevant, while the two-sided intervals are used when both the upper and the lower specification limits are considered simultaneously. The terminology with regard to these different limits and intervals has been confusing as the “specification limits” were earlier also called “tolerance li

44、mits” (see the terminology standard ISO 3534-2:1993, 1.4.3, where both these terms as well as the term “limiting values” were all used as synonyms for this concept). In the latest This standard may only be used and printed by approved subscription and freemailing clients of the SABS.ISO 16269-6:2005

45、(E) vi ISO 2005 All rights reservedrevision of ISO 3534-2:, only the term specification limits have been kept for this concept. Furthermore, the Guide for the expression of uncertainty in measurement 5uses the term “coverage factor” defined as a “numerical factor used as a multiplier of the combined

46、 standard uncertainty in order to obtain an expanded uncertainty”. This use of “coverage” differs from the use of the term in this part of ISO 16269. This standard may only be used and printed by approved subscription and freemailing clients of the SABS.INTERNATIONAL STANDARD ISO 16269-6:2005(E) ISO

47、 2005 All rights reserved 1Statistical interpretation of data Part 6: Determination of statistical tolerance intervals 1 Scope This part of ISO 16269 describes procedures for establishing tolerance intervals that include at least a specified proportion of the population with a specified confidence l

48、evel. Both one-sided and two-sided statistical tolerance intervals are provided, a one-sided interval having either an upper or a lower limit while a two-sided interval has both upper and lower limits. Two methods are provided, a parametric method for the case where the characteristic being studied

49、has a normal distribution and a distribution-free method for the case where nothing is known about the distribution except that it is continuous. 2 Normative references The following referenced documents are indispensable for the application of 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 3534-1, Statistics Vocabulary and symbols Part 1: Probability and general sta