《ISO-16269-6-2005.pdf》由会员分享，可在线阅读，更多相关《ISO-16269-6-2005.pdf（38页珍藏版）》请在三一文库上搜索。
1、 Reference number ISO 16269-6:2005(E) ISO 2005 INTERNATIONAL STANDARD ISO 16269-6 First edition 2005-04-01 Statistical interpretation of data Part 6: Determination of statistical tolerance intervals Interprtation statistique des donnes Partie 6: Dtermination des intervalles statistiques de tolrance
2、ISO 16269-6:2005(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 dow
3、nloading 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 th
4、e General 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
5、 given 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 me
6、mber 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 reserved ISO 16269-6:2005(E) ISO 2005 All rights reserved iii Content
7、s Page Forewordiv Introduction v 1 Scope1 2 Normative references .1 3 Terms, definitions and symbols1 3.1 Terms and definitions.1 3.2 Symbols .2 4 Procedures 3 4.1 Normal population with known variance and known mean3 4.2 Normal population with known variance and unknown mean.3 4.3 Normal population
8、 with unknown variance and unknown mean.3 4.4 Any continuous distribution of unknown type 3 5 Examples3 5.1 Data.3 5.2 Example 1: One-sided statistical tolerance interval under known variance.4 5.3 Example 2: Two-sided statistical tolerance interval under known variance 4 5.4 Example 3: One-sided st
9、atistical tolerance interval under unknown variance5 5.5 Example 4: Two-sided statistical tolerance interval under unknown variance6 5.6 Example 5: Distribution-free statistical tolerance interval for continuous distribution6 Annex A (informative) Forms for tolerance intervals8 Annex B (normative) O
10、ne-sided statistical tolerance limit factors, k1(n; p; 1 ), for known .14 Annex C (normative) Two-sided statistical tolerance limit factors, k2(n; p; 1 ), for known .17 Annex D (normative) One-sided statistical tolerance limit factors, k3(n; p; 1 ), for unknown .20 Annex E (normative) Two-sided stat
11、istical tolerance limit factors, k4(n; p; 1 ), for unknown .23 Annex F (normative) One-sided distribution-free statistical tolerance intervals.26 Annex G (normative) Two-sided distribution-free statistical tolerance intervals27 Annex H (informative) Construction of a distribution-free statistical to
12、lerance interval for any type of distribution28 Annex I (informative) Computation of factors for two-sided parametric statistical tolerance intervals29 Bibliography .30 ISO 16269-6:2005(E) iv ISO 2005 All rights reserved Foreword ISO (the International Organization for Standardization) is a worldwid
13、e 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
14、 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. International Standards are drafted in ac
15、cordance with the rules given in the ISO/IEC Directives, 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 req
16、uires approval by at least 75 % of the member bodies 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 16269-6 was prepared by Tech
17、nical Committee ISO/TC 69, Applications of statistical methods. This 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 st
18、atistical tolerance intervals Part 7: Median Estimation and confidence intervals Part 8: Determination of prediction intervals ISO 16269-6:2005(E) ISO 2005 All rights reserved v Introduction A statistical tolerance interval is an estimated interval, based on a sample, which can be asserted with conf
19、idence 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 tolerance interval constructed in the prescri
20、bed 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 intervals; a one-sided interval is cons
21、tructed 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 different samples. It is necessary that the o
22、bservations 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 characteristic being studied in the popu
23、lation 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, the statistical tolerance interval is
24、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 tolerance intervals may be constructed.
25、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 with one or two given specification lim
26、its, 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 which will be cancelled and replaced by t
27、his part of ISO 16269. Above the upper specification limit U there is the upper fraction nonconforming pU (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 pL (ISO 3534-2:, 3.2.5.6 and 3.3.1.5). The sum pU + pL = pT is called the t
28、otal fraction nonconforming. (ISO 3534-2:, 3.2.5.7). Between the specification limits U and L there is the fraction conforming 1 pT. In statistical process management the limits U and L are fixed in advance and the fractions pU, pL and pT are either calculated, if the distribution is assumed to be k
29、nown, 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 Meeker 10. In contrast, for the toleranc
30、e 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 estimated. These limits may be compared wit
31、h 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 limit L is relevant, while the two-sided in
32、tervals 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 limits” (see the terminology standard ISO 35
33、34-2:1993, 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 ISO 16269-6:2005(E) vi ISO 2005 All rights reserved revision of ISO 3534-2:, only the term specification limits have been kept for this concept. Furthermore, the
34、Guide for the expression of uncertainty in measurement 5 uses the term “coverage factor” defined as a “numerical factor used as a multiplier of the combined 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 1
35、6269. INTERNATIONAL STANDARD ISO 16269-6:2005(E) ISO 2005 All rights reserved 1 Statistical 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 propo
36、rtion 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 upper or a lower limit while a two-sided interval has both upper and lower limits. Two methods are provided, a parametric method
37、 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 except that it is continuous. 2 Normative references The following referenced documents are indispensable for the application of th
38、is 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 statistical terms ISO 3534-2:1), Statistics Vocab
39、ulary and symbols Part 2: Applied statistics 3 Terms, definitions and symbols 3.1 Terms and definitions For the purposes of this document, the terms and definition given in ISO 3534-1, ISO 3534-2 and the following apply. 3.1.1 statistical tolerance interval interval determined from a random sample i
40、n such a way that one may have a specified level of confidence that the interval covers at least a specified proportion of the sampled population NOTE The confidence level in this context is the long-run proportion of intervals constructed in this manner that will include at least the specified prop
41、ortion of the sampled population. 3.1.2 statistical tolerance limit statistic representing an end point of a statistical tolerance interval NOTE Statistical tolerance intervals can be either one-sided, in which case they have either an upper or a lower statistical tolerance limit, or two-sided, in w
42、hich case they have both. 1) To be published. (Revision of ISO 3534-2:1993) ISO 16269-6:2005(E) 2 ISO 2005 All rights reserved 3.1.3 coverage proportion of items in a population lying within a statistical tolerance interval NOTE This concept is not to be confused with the concept coverage factor use
43、d in the Guide for the expression of uncertainty in measurement (GUM ) 5. 3.1.4 normal population normally distributed population 3.2 Symbols For the purposes of this part of ISO 16269, the following symbols apply. i suffix of an observation k1 (n; p; 1 ) factor used to determine L x or U x when the
44、 value of is known for one-sided tolerance interval k2 (n; p; 1 ) factor used to determine L x and U x when the value of is known for two-sided tolerance interval k3 (n; p; 1 ) factor used to determine L x or U x when the value of is unknown for one-sided tolerance interval k4 (n; p; 1 ) factor used
45、 to determine L x and U x when the value of is unknown for two-sided tolerance interval n number of observations in the sample p minimum proportion of the population claimed to be lying in the statistical tolerance interval up p-fractile of the standard normal distribution xi ith observed value (1,
46、2,., )in= xmax maximum value of the observed values: xmax = max x1, x2, , xn xmin minimum value of the observed values: xmin = min x1, x2, , xn L x lower limit of the statistical tolerance interval U x upper limit of the statistical tolerance interval x sample mean, 1 1 n i i xx n = = s sample stand
47、ard deviation;() () 2 2 11 2 1 1 11 nn ii n ii i i nxx sxx nn n = = = 1 confidence level for the claim that the proportion of the population lying within the tolerance interval is greater than or equal to the specified level p population mean population standard deviation ISO 16269-6:2005(E) ISO 200
48、5 All rights reserved 3 4 Procedures 4.1 Normal population with known variance and known mean When the values of the mean, , and the variance, 2, of a normally distributed population are known, the distribution of the characteristic under investigation is fully determined. There is exactly a proport
49、ion p of the population: a) to the right of xL = p u (one-sided interval); b) to the left of xU = + p u (one-sided interval); c) between xL = (1)/2p u + and xU = + (1)/2p u + (two-sided interval). NOTE As such statements are known to be true, they are made with 100 % confidence. In the above equations, p u is p-fractile of the standard normal distribution. Numerical values of p u may be read from t