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. ISBN 978-0-626-23813-1 SANS 16269-8:2010Edition 1ISO 16269-8:2004Edition 1SOUTH AFRICAN NATIONAL STANDARD Statistical interpretation of data Part 8: Dete
4、rmination of prediction intervals This national standard is the identical implementation of ISO 16269-8:2004 and is adopted with the permission of the International Organization for Standardization. Published by SABS Standards Division 1 Dr Lategan Road Groenkloof Private Bag X191 Pretoria 0001Tel:
5、+27 12 428 7911 Fax: +27 12 344 1568 www.sabs.co.za SABS SANS 16269-8:2010 Edition 1 ISO 16269-8:2004 Edition 1 Table of changes Change No. Date Scope National foreword This South African standard was approved by National Committee SABS TC 169, Applications of statistical methods, in accordance with
6、 procedures of the SABS Standards Division, in compliance with annex 3 of the WTO/TBT agreement. This SANS document was published in March 2010. Reference numberISO 16269-8:2004(E)ISO 2004INTERNATIONAL STANDARD ISO16269-8First edition2004-09-15Statistical interpretation of data Part 8: Determination
7、 of prediction intervals Interprtation statistique des donnes Partie 8: Dtermination des intervalles de prdiction SANS 16269-8:2010This s tandard may only be used and printed by approved subscription and freemailing clients of the SABS .ISO 16269-8:2004(E) PDF disclaimer This PDF file may contain em
8、bedded 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 downloading this file, parties accept therein the responsibility o
9、f 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 General Info relative to the file; the PDF-creation parameter
10、s 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 given below. ISO 2004 All rights reserved. Unless otherwise sp
11、ecified, 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 body in the country of the requester. ISO copyright office
12、 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 2004 All rights reservedSANS 16269-8:2010This s tandard may only be used and printed by approved subscription and freemailing clients of the SABS .I
13、SO 16269-8:2004(E) ISO 2004 All rights reserved iiiContents Page Foreword. v Introduction . vi 1 Scope 1 2 Normative references . 1 3 Terms, definitions and symbols 2 3.1 Terms and definitions. 2 3.2 Symbols . 2 4 Prediction intervals. 3 4.1 General. 3 4.2 Comparison with other types of statistical
14、interval 4 4.2.1 Choice of type of interval . 4 4.2.2 Comparison with a statistical tolerance interval . 4 4.2.3 Comparison with a confidence interval for the mean . 4 5 Prediction intervals for all observations in a further sample from a normally distributed population with unknown population stand
15、ard deviation 4 5.1 One-sided intervals. 4 5.2 Symmetric two-sided intervals 5 5.3 Prediction intervals for non-normally distributed populations that can be transformed to normality 5 5.4 Determination of a suitable initial sample size, n, for a given maximum value of the prediction interval factor,
16、 k 6 5.5 Determination of the confidence level corresponding to a given prediction interval . 6 6 Prediction intervals for all observations in a further sample from a normally distributed population with known population standard deviation 6 6.1 One-sided intervals. 6 6.2 Symmetric two-sided interva
17、ls 7 6.3 Prediction intervals for non-normally distributed populations that can be transformed to normality 7 6.4 Determination of a suitable initial sample size, n, for a given value of k. 7 6.5 Determination of the confidence level corresponding to a given prediction interval . 8 7 Prediction inte
18、rvals for the mean of a further sample from a normally distributed population 8 8 Distribution-free prediction intervals 8 8.1 General. 8 8.2 One-sided intervals. 8 8.3 Two-sided intervals. 9 Annex A (normative) Tables of one-sided prediction interval factors, k, for unknown population standard devi
19、ation 13 Annex B (normative) Tables of two-sided prediction interval factors, k, for unknown population standard deviation 31 Annex C (normative) Tables of one-sided prediction interval factors, k, for known population standard deviation. 49 Annex D (normative) Tables of two-sided prediction interva
20、l factors, k, for known population standard deviation. 67 SANS 16269-8:2010This s tandard may only be used and printed by approved subscription and freemailing clients of the SABS .ISO 16269-8:2004(E) iv ISO 2004 All rights reservedAnnex E (normative) Tables of sample sizes for one-sided distributio
21、n-free prediction intervals .85 Annex F (normative) Tables of sample sizes for two-sided distribution-free prediction intervals91 Annex G (normative) Interpolating in the tables .97 Annex H (informative) Statistical theory underlying the tables .101 Bibliography108 SANS 16269-8:2010This s tandard ma
22、y only be used and printed by approved subscription and freemailing clients of the SABS .ISO 16269-8:2004(E) ISO 2004 All rights reserved vForeword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of prepari
23、ng 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-governmental, in lia
24、ison 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. The main task of
25、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 vote. Attention is
26、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 16269-8 was prepared by Technical Committee ISO/TC 69, Application of statistical methods. ISO 16269 consists
27、of the following parts, under the general title Statistical interpretation of data: Part 6: Determination of statistical tolerance intervals Part 7: Median Estimation and confidence intervals Part 8: Determination of prediction intervals SANS 16269-8:2010This s tandard may only be used and printed b
28、y approved subscription and freemailing clients of the SABS .ISO 16269-8:2004(E) vi ISO 2004 All rights reservedIntroduction Prediction intervals are of value wherever it is desired or required to predict the results of a future sample of a given number of discrete items from the results of an earli
29、er sample of items produced under identical conditions. They are of particular use to engineers who need to be able to set limits on the performance of a relatively small number of manufactured items. This is of increasing importance with the recent shift towards small-scale production in some indus
30、tries. Despite the first review article on prediction intervals and their applications being published as long ago as 1973, there is still a surprising lack of awareness of their value, perhaps due in part to the inaccessibility of the research work for the potential user, and also partly due to con
31、fusion with confidence intervals and statistical tolerance intervals. The purpose of this part of ISO 16269 is therefore twofold: to clarify the differences between prediction intervals, confidence intervals and statistical tolerance intervals; to provide procedures for some of the more useful types
32、 of prediction interval, supported by extensive, newly-computed tables. For information on prediction intervals that are outside the scope of this part of ISO 16269, the reader is referred to the Bibliography. SANS 16269-8:2010This s tandard may only be used and printed by approved subscription and
33、freemailing clients of the SABS .INTERNATIONAL STANDARD ISO 16269-8:2004(E) ISO 2004 All rights reserved 1Statistical interpretation of data Part 8: Determination of prediction intervals 1 Scope This part of ISO 16269 specifies methods of determining prediction intervals for a single continuously di
34、stributed variable. These are ranges of values of the variable, derived from a random sample of size n, for which a prediction relating to a further randomly selected sample of size m from the same population may be made with a specified confidence. Three different types of population are considered
35、, namely: a) normally distributed with unknown standard deviation; b) normally distributed with known standard deviation; c) continuous but of unknown form. For each of these three types of population, two methods are presented, one for one-sided prediction intervals and one for symmetric two-sided
36、prediction intervals. In all cases, there is a choice from among six confidence levels. The methods presented for cases a) and b) may also be used for non-normally distributed populations that can be transformed to normality. For cases a) and b) the tables presented in this part of ISO 16269 are res
37、tricted to prediction intervals containing all the further m sampled values of the variable. For case c) the tables relate to prediction intervals that contain at least m r of the next m values, where r takes values from 0 to 10 or 0 to m 1, whichever range is smaller. For normally distributed popul
38、ations a procedure is also provided for calculating prediction intervals for the mean of m further observations. 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 referen
39、ces, 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, Statistics Vocabulary and symbols Part 2: Statistical quality control SANS 16269-8:2010This s tandard may
40、 only be used and printed by approved subscription and freemailing clients of the SABS .ISO 16269-8:2004(E) 2 ISO 2004 All rights reserved3 Terms, definitions and symbols 3.1 Terms and definitions For the purposes of this document, the terms and definitions given in ISO 3534-1 and ISO 3534-2 and the
41、 following apply. 3.1.1 prediction interval interval determined from a random sample from a population in such a way that one may have a specified level of confidence that no fewer than a given number of values in a further random sample of a given size from the same population will fall NOTE In thi
42、s context, the confidence level is the long-run proportion of intervals constructed in this manner that will have this property. 3.1.2 order statistics sample values identified by their position after ranking in non-decreasing order of magnitude NOTE The sample values in order of selection are denot
43、ed in this part of ISO 16269 by x1, x2, , xn. After arranging in non-decreasing order, they are denoted by x1, x2, , xn, where x1u x2u u xn. The word “non-decreasing” is used in preference to “increasing” to include the case where two or more values are equal, at least to within measurement error. S
44、ample values that are equal to one another are assigned distinct, contiguous integer subscripts in square brackets when represented as order statistics. 3.2 Symbols a lower limit to the values of the variable in the population nominal maximum probability that more than r observations from the furthe
45、r random sample of size m will lie outside the prediction interval b upper limit to the values of the variable in the population C confidence level expressed as a percentage: C = 100 (1 ) k prediction interval factor m size of further random sample to which the prediction applies n size of random sa
46、mple from which the prediction interval is derived s sample standard deviation: ()()211niisxxn=r specified maximum number of observations from the further random sample of size m that will not lie in the prediction interval T1lower prediction limit T2upper prediction limit xiith observation in a ran
47、dom sample xiith order statistic SANS 16269-8:2010This s tandard may only be used and printed by approved subscription and freemailing clients of the SABS .ISO 16269-8:2004(E) ISO 2004 All rights reserved 3x sample mean: 1niixxn=4 Prediction intervals 4.1 General A two-sided prediction interval is a
48、n interval of the form (T1, T2), where T10. This is illustrated in Table 1 for a 95 % confidence level for one-sided and two-sided intervals when r/m = 0,1. However, there is no such analogy between statistical tolerance interval constants and prediction interval constants for r = 0, the case on whi
49、ch this part of ISO 16269 is primarily focussed. Table 1 Example of prediction interval constants r 1 2 5 10 20 50 100 1 000 m 10 20 50 100 200 500 1 000 10 000 Prediction interval constantsStatistical tolerance interval constants for a minimum proportion of 0,9 of the population covered One-sided intervals 1,887 1,846 1,767 1,718 1,686 1,663 1,655 1,647 1,646 Two-sided intervals 2,208 2,172 2,103 2,061 2,034 2,014 2,007 2,000 2,000 NOTE 2 The case r = 0 is particularly important in app
