1、BS ISO 10928:2016Plastics piping systems Glass-reinforced thermosettingplastics (GRP) pipes and fittings Methods for regressionanalysis and their useBSI Standards PublicationWB11885_BSI_StandardCovs_2013_AW.indd 1 15/05/2013 15:06BS ISO 10928:2016 BRITISH STANDARDNational forewordThis British Standa
2、rd is the UK implementation of ISO 10928:2016. It supersedes BS ISO 10928:2009+A1:2013 which is withdrawn.The UK participation in its preparation was entrusted to TechnicalCommittee PRI/88/2, Plastics piping for pressure applications.A list of organizations represented on this committee can beobtain
3、ed on request to its secretary.This publication does not purport to include all the necessaryprovisions of a contract. Users are responsible for its correctapplication. The British Standards Institution 2016. Published by BSI Standards Limited 2016ISBN 978 0 580 92474 3ICS 23.040.20; 23.040.45Compli
4、ance with a British Standard cannot confer immunity fromlegal obligations.This British Standard was published under the authority of theStandards Policy and Strategy Committee on 31 December 2016.Amendments/Corrigenda issued since publicationDate Text affectedBS ISO 10928:2016 ISO 2016Plastics pipin
5、g systems Glass-reinforced thermosetting plastics (GRP) pipes and fittings Methods for regression analysis and their useSystmes de canalisation en matires plastiques Tubes et raccords plastiques thermodurcissables renforcs de verre (PRV) Mthodes pour une analyse de rgression et leurs utilisationsINT
6、ERNATIONAL STANDARDISO10928Third edition2016-12-15Reference numberISO 10928:2016(E)BS ISO 10928:2016ISO 10928:2016(E)ii ISO 2016 All rights reservedCOPYRIGHT PROTECTED DOCUMENT ISO 2016, Published in SwitzerlandAll rights reserved. Unless otherwise specified, no part of this publication may be repro
7、duced 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 body in the country of the requester
8、.ISO copyright officeCh. de Blandonnet 8 CP 401CH-1214 Vernier, Geneva, SwitzerlandTel. +41 22 749 01 11Fax +41 22 749 09 47copyrightiso.orgwww.iso.orgBS ISO 10928:2016ISO 10928:2016(E)Foreword ivIntroduction v1 Scope . 12 Normative references 13 Terms and definitions . 14 Principle 15 Procedures fo
9、r determining the linear relationships Methods A and B . 25.1 Procedures common to methods A and B . 25.2 Method A Covariance method 25.2.1 General 25.2.2 Suitability of data 35.2.3 Functional relationships . 35.2.4 Calculation of variances . 45.2.5 Check for the suitability of data for extrapolatio
10、n 55.2.6 Validation of statistical procedures by an example calculation 65.3 Method B Regression with time as the independent variable .105.3.1 General. 105.3.2 Suitability of data .105.3.3 Functional relationships 115.3.4 Check for the suitability of data for extrapolation .115.3.5 Validation of st
11、atistical procedures by an example calculation .116 Application of methods to product design and testing 126.1 General 126.2 Product design 136.3 Comparison to a specified value . 136.4 Declaration of a long-term value 13Annex A (informative) Second-order polynomial relationships 14Annex B (informat
12、ive) Non-linear relationships 19Annex C (normative) Calculation of lower confidence and prediction limits for method A 45Bibliography .47 ISO 2016 All rights reserved iiiContents PageBS ISO 10928:2016ISO 10928:2016(E)ForewordISO (the International Organization for Standardization) is a worldwide fed
13、eration 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 comm
14、ittee. 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.The procedures used to develop this document an
15、d those intended for its further maintenance are described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the different types of ISO documents should be noted. This document was drafted in accordance with the editorial rules of the ISO/IEC Directives, Par
16、t 2 (see www.iso.org/directives).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. Details of any patent rights identified during the development of th
17、e document will be in the Introduction and/or on the ISO list of patent declarations received (see www.iso.org/patents).Any trade name used in this document is information given for the convenience of users and does not constitute an endorsement.For an explanation on the meaning of ISO specific term
18、s and expressions related to conformity assessment, as well as information about ISOs adherence to the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see the following URL: www.iso.org/iso/foreword.html.The committee responsible for this document is ISO/TC 138, Pl
19、astics pipes, fittings and valves for the transport of fluids, Subcommittee SC 6, Reinforced plastics pipes and fittings for all applications.This third edition cancels and replaces the second edition (ISO 10928:2009), which has been technically revised and includes the following changes. It also in
20、corporates the Amendment ISO 10928:2009/Amd 1:2013: Annex A (GRP pressure pipe design procedure) has been removed from the document; several bibliographical references have been removed.iv ISO 2016 All rights reservedBS ISO 10928:2016ISO 10928:2016(E)IntroductionThis document describes the procedure
21、s intended for analysing the regression of test data, usually with respect to time and the use of the results in design and assessment of conformity with performance requirements. Its applicability is limited to use with data obtained from tests carried out on samples. The referring standards requir
22、e estimates to be made of the long-term properties of the pipe for such parameters as circumferential tensile strength, long-term ring deflection, strain corrosion and creep or relaxation stiffness.A range of statistical techniques that could be used to analyse the test data produced by destructive
23、tests was investigated. Many of these simple techniques require the logarithms of the data toa) be normally distributed,b) produce a regression line having a negative slope, andc) have a sufficiently high regression correlation (see Table 1).While the last two conditions can be satisfied, analysis s
24、hows that there is a skew to the distribution and hence this primary condition is not satisfied. Further investigation into techniques that can handle skewed distributions resulted in the adoption of the covariance method of analysis of such data for this document.However, the results from non-destr
25、uctive tests, such as long-term creep or relaxation stiffness, often satisfy all three conditions and hence a simpler procedure, using time as the independent variable, can also be used in accordance with this document.These data analysis procedures are limited to analysis methods specified in ISO p
26、roduct standards or test methods. However, other analysis procedures can be useful for the extrapolation and prediction of long-term behaviour of some properties of glass-reinforced thermosetting plastics (GRP) piping products. For example, a second-order polynomial analysis is sometimes useful in t
27、he extrapolation of creep and relaxation data. This is particularly the case for analysing shorter term data, where the shape of the creep or relaxation curve can deviate considerably from linear. A second-order polynomial analysis is included in Annex A. In Annex B, there is an alternative non-line
28、ar analysis method. These non-linear methods are provided only for information and the possible use in investigating the behaviour of a particular piping product or material therefore they might not be generally applicable to other piping products. ISO 2016 All rights reserved vBS ISO 10928:2016BS I
29、SO 10928:2016Plastics piping systems Glass-reinforced thermosetting plastics (GRP) pipes and fittings Methods for regression analysis and their use1 ScopeThis document specifies procedures suitable for the analysis of data which, when converted into logarithms of the values, have either a normal or
30、a skewed distribution. It is intended for use with the test methods and referring standards for glass-reinforced thermosetting plastics (GRP) pipes or fittings for the analysis of properties as a function of time. However, it can be used for the analysis of other data.Depending upon the nature of th
31、e data, two methods are specified. The extrapolation using these techniques typically extends the trend from data gathered over a period of approximately 10 000 h to a prediction of the property at 50 years, which is the typical maximum extrapolation time.This document only addresses the analysis of
32、 data. The test procedures to collect the data, the number of samples required and the time period over which data are collected are covered by the referring standards and/or test methods. Clause 6 discusses how the data analysis methods are applied to product testing and design.2 Normative referenc
33、esThere are no normative references in this document.3 Terms and definitionsNo terms and definitions are listed in this document.ISO and IEC maintain terminological databases for use in standardization at the following addresses: IEC Electropedia: available at http:/www.electropedia.org/ ISO Online
34、browsing platform: available at http:/www.iso.org/obp4 PrincipleData are analysed for regression using methods based on least squares analysis which can accommodate the incidence of a skew and/or a normal distribution. The two methods of analysis used are the following: method A: covariance using a
35、first-order relationship; method B: least squares, with time as the independent variable using a first-order relationship.The methods include statistical tests for the correlation of the data and the suitability for extrapolation.INTERNATIONAL STANDARD ISO 10928:2016(E) ISO 2016 All rights reserved
36、1BS ISO 10928:2016ISO 10928:2016(E)5 Procedures for determining the linear relationships Methods A and B5.1 Procedures common to methods A and BUse method A (see 5.2) or method B (see 5.3) to fit a straight line of the form given in Formula (1):yabx=+ (1)wherey is the logarithm, lg, of the property
37、being investigated;a is the intercept on the y-axis;b is the slope;x is the logarithm, lg, of the time, in hours.5.2 Method A Covariance method5.2.1 GeneralFor method A, calculate the following variables in accordance with 5.2.2 to 5.2.5, using Formulae (2), (3) and (4):QyYniy2=()(2)QxXnix=()2(3)QxX
38、 yYniixy=()()(4)whereQyis the sum of the squared residuals parallel to the y-axis, divided by n;Qxis the sum of the squared residuals parallel to the x-axis, divided by n;Qxyis the sum of the squared residuals perpendicular to the line, divided by n;Y is the arithmetic mean of the y data, i.e. given
39、 as Formula (5):Yyni=(5)X is the arithmetic mean of the x data, i.e. given as Formula (6):Xxni=(6)2 ISO 2016 All rights reservedBS ISO 10928:2016ISO 10928:2016(E)xi, yiare individual values;n is the total number of results (pairs of readings for xi, yi).NOTE If the value of Qxyis greater than zero,
40、the slope of the line is positive and if the value of Qxy is less than zero, then the slope is negative.5.2.2 Suitability of dataCalculate the linear coefficient of correlation, r, using Formulae (7) and (8):rQQQ2xy2xy=(7)rr=()20,5(8)If the value of r is less than StudentsStudentstfntf()+()22, then
41、the data are unsuitable for analysis.Table 1 gives the minimum acceptable values of the correlation coefficient, r, as a function of the number of variables, n. The Students t value is based on a two-sided 0,01 level of significance.Table 1 Minimum values of the correlation coefficient, r, for accep
42、table data from n pairs of dataNumber of variablesnDegrees of freedomn 2Students t(0,01)Minimum rNumber of variablesnDegrees of freedomn 2Students t(0,01)Minimum r13 11 3,106 0,683 5 26 24 2,797 0,495 814 12 3,055 0,661 4 27 25 2,787 0,486 915 13 3,012 0,641 1 32 30 2,750 0,448 716 14 2,977 0,622 6
43、37 35 2,724 0,418 217 15 2,947 0,605 5 42 40 2,704 0,393 218 16 2,921 0,589 7 47 45 2,690 0,372 119 17 2,898 0,575 1 52 50 2,678 0,354 220 18 2,878 0,561 4 62 60 2,660 0,324 821 19 2,861 0,548 7 72 70 2,648 0,301 722 20 2,845 0,536 8 82 80 2,639 0,283 023 21 2,831 0,525 6 92 90 2,632 0,267 324 22 2,
44、819 0,515 1 102 100 2,626 0,254 025 23 2,807 0,505 25.2.3 Functional relationshipsFind a and b for the functional relationship line using Formula (1). ISO 2016 All rights reserved 3BS ISO 10928:2016ISO 10928:2016(E)First, set as given in Formula (9): =QQyx(9)then calculate a and b using Formulae (10
45、) and (11):b =()05,(10)aYbX= (11)5.2.4 Calculation of variancesIf tuis the applicable time to failure, then set xuas given in Formula (12):xtuulg= (12)Using Formulae (13), (14) and (15) respectively, calculate for i = 1 to n, the following sequence of statistics: the best fit xi for true xi; the bes
46、t fit yi for true yi; the error variance, 2for x.xxbyaiii=+()2(13)yabxii=+ (14)2222=()+ ()()yy xxnii ii(15)Calculate quantities E and D using Formulae (16) and (17):EbQ=22xy(16)DbnQ=22xy(17)Calculate the variance, C, of the slope b, using Formula (18):CD E=+()1 (18)4 ISO 2016 All rights reservedBS I
47、SO 10928:2016ISO 10928:2016(E)5.2.5 Check for the suitability of data for extrapolationIf it is intended to extrapolate the line, calculate T using Formula (19):TbbbC=()=var 05 05,(19)If the absolute value, |T| (i.e. ignoring signs), of T is equal to or greater than the applicable value for Students
48、 t, tv, shown in Table 2 for (n 2) degrees of freedom, then consider the data suitable for extrapolation.Calculation of confidence limits is not required by the test methods or referring standards; however, the calculation of lower confidence limit, LCL, and lower prediction limit, LPL, is given in
49、Annex C.Table 2 Percentage points of Students t distribution (upper 2,5 % points; two-sided 5 % level of confidence; tvfor 97,5 %)Degree of freedom(n 2)Students t valuetvDegree of freedom(n 2)Students t valuetvDegree of freedom(n 2)Students t valuetv1234512,706 24,302 73,182 42,776 42,570 636373839402,028 12,026 22,024 42,022 72,021 171727374751,993 91,993 51,993 01,992 51,992 16789102,446 92,364 62,306 02,262 22,228 1
