ISO 10928:2016

INTERNATIONAL ISO
STANDARD 10928
Third edition
2016-12-15
Plastics piping systems — Glass-
reinforced thermosetting plastics
(GRP) pipes and fittings — Methods
for regression analysis and their use
Systèmes de canalisation en matières plastiques — Tubes et raccords
plastiques thermodurcissables renforcés de verre (PRV) — Méthodes
pour une analyse de régression et leurs utilisations
Reference number
©
ISO 2016
© ISO 2016, Published in Switzerland
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ii © ISO 2016 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Principle . 1
5 Procedures for determining the linear relationships — Methods A and B .2
5.1 Procedures common to methods A and B . 2
5.2 Method A — Covariance method . 2
5.2.1 General. 2
5.2.2 Suitability of data . 3
5.2.3 Functional relationships . 3
5.2.4 Calculation of variances . 4
5.2.5 Check for the suitability of data for extrapolation . 5
5.2.6 Validation of statistical procedures by an example calculation . 6
5.3 Method B — Regression with time as the independent variable .10
5.3.1 General.10
5.3.2 Suitability of data .10
5.3.3 Functional relationships .11
5.3.4 Check for the suitability of data for extrapolation .11
5.3.5 Validation of statistical procedures by an example calculation .11
6 Application of methods to product design and testing .12
6.1 General .12
6.2 Product design.13
6.3 Comparison to a specified value .13
6.4 Declaration of a long-term value .13
Annex A (informative) Second-order polynomial relationships .14
Annex B (informative) Non-linear relationships .19
Annex C (normative) Calculation of lower confidence and prediction limits for method A .45
Bibliography .47
Foreword
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
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electrotechnical standardization.
The procedures used to develop this document and 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, Part 2 (see www.iso.org/directives).
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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, Plastics 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 incorporates 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 reserved

Introduction
This document describes the procedures 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 require 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
tests was investigated. Many of these simple techniques require the logarithms of the data to
a) be normally distributed,
b) produce a regression line having a negative slope, and
c) have a sufficiently high regression correlation (see Table 1).
While the last two conditions can be satisfied, analysis shows 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-destructive 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 product 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 the 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-linear 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.
INTERNATIONAL STANDARD ISO 10928:2016(E)
Plastics piping systems — Glass-reinforced thermosetting
plastics (GRP) pipes and fittings — Methods for regression
analysis and their use
1 Scope
This document specifies procedures suitable for the analysis of data which, when converted into
logarithms of the values, have either a normal or 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 the 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 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 references
There are no normative references in this document.
3 Terms and definitions
No 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 browsing platform: available at http://www.iso.org/obp
4 Principle
Data 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 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.
5 Procedures for determining the linear relationships — Methods A and B
5.1 Procedures common to methods A and B
Use method A (see 5.2) or method B (see 5.3) to fit a straight line of the form given in Formula (1):
ya=+ bx× (1)
where
y is the logarithm, lg, of the property 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 method
5.2.1 General
For method A, calculate the following variables in accordance with 5.2.2 to 5.2.5, using Formulae (2),
(3) and (4):
yY−
()
∑
i
Q = (2)
y
n
xX−
()
∑
i
Q = (3)
x
n
 
xX− ×−yY
() ()
∑
ii
 
Q = (4)
xy
n
where
Q is the sum of the squared residuals parallel to the y-axis, divided by n;
y
Q is the sum of the squared residuals parallel to the x-axis, divided by n;
x
Q is the sum of the squared residuals perpendicular to the line, divided by n;
xy
Y is the arithmetic mean of the y data, i.e. given as Formula (5):
y
∑
i
Y = (5)
n
X is the arithmetic mean of the x
...