ISO/TR 13425:2003

TECHNICAL ISO/TR
REPORT 13425
Second edition
2003-11-15

Guidelines for the selection of statistical
methods in standardization and
specification
Lignes directrices pour la sélection des méthodes statistiques en
normalisation et en spécifications




Reference number
ISO/TR 13425:2003(E)
©
ISO 2003

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ISO/TR 13425:2003(E)
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ISO/TR 13425:2003(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope. 1
2 Flowchart . 2
Annex A Content and use of the referenced standards and DIS . 3
Annex B List of Committee drafts, working drafts and new work item proposals in ISO/TC 69
work program . 27

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ISO/TR 13425:2003(E)
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 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 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.
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 requires approval by at least 75 % of the member bodies casting a vote.
In exceptional circumstances, when a technical committee has collected data of a different kind from that
which is normally published as an International Standard (“state of the art”, for example), it may decide by a
simple majority vote of its participating members to publish a Technical Report. A Technical Report is entirely
informative in nature and does not have to be reviewed until the data it provides are considered to be no
longer valid or useful.
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/TR 13425 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods.
This second edition cancels and replaces the first edition (ISO/TR 13425:1995), which has been technically
revised.
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ISO/TR 13425:2003(E)
Introduction
Statistical methods have numerous practical applications in the manufacturing and service industries,
marketing, research, laboratories and other spheres. Their effectiveness depends firstly on the suitability of
the chosen method for the intended purpose and secondly on the application for which it is used. Incorrect
choice or poor application can lead to improper deductions and therefore to crucial errors and inappropriate
decisions.
This is one of the reasons why ISO has produced a range of Standards for the application of statistical
methods.
This Technical Report should be seen as a descriptive catalogue of the available TC 69 International
Standards and Guides, published or in course of preparation, to assist the reader in selecting those most
suitable for his purpose, according to his needs, whether these be in decision making, problem solving or in
achieving a given purpose.

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TECHNICAL REPORT ISO/TR 13425:2003(E)

Guidelines for the selection of statistical methods in
standardization and specification
1 Scope
This Technical Report gives guidance on the selection and an overview of all the referenced standards,
guides, technical reports and DIS developed by ISO/TC 69 from a user prospective. DIS are drafts which can
be amended. Both categories are documents, which are available to the public. This Technical Report also
gives two descriptions of the content of the standards by two sets of abstracts: non-technical abstracts and
technical abstracts of all these documents. Each abstract presents a brief survey of the content of the actual
standard or DIS. It also gives some indications of the use of the document in different areas.
Annex A gives the non technical and technical abstracts. The non-technical abstracts are usually brief. In
these abstracts, the number of technical terms are kept to a minimum. They give brief outlines of the actual
documents. The technical abstracts are somewhat longer. More technical terms are used. The technical
abstracts also go more into depth with regard to the content and the use of the actual document than the non-
technical abstracts. For many documents, the two abstracts supplement each other.
Annex B lists the committee drafts, working drafts and new work item proposals in the ISO/TC 69 work
program.
The types of document are identified as follows:
Published International Standard: ISO xxxxxxx
Final draft International Standard: FDIS
Draft International Standard: DIS
Committee draft: CD
Working draft: WD
New work item proposal: NP
Draft Technical Specification: DTS
Technical Specification: TS
Draft Technical Report: DTR
Published Technical Report: TR
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ISO/TR 13425:2003(E)
2 Flowchart

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ISO/TR 13425:2003(E)
Annex A

Content and use of the referenced standards and DIS
A.1 Short non-technical abstracts of ISO/TC 69 Standards and DIS
ISO Guide 33: Uses of certified reference materials (Developed jointly by REMCO and ISO/TC 69)
A reference material (RM) is a substance or an artefact for which one or more properties are established
sufficiently well to validate a measurement system. There exist several kinds of RM:
 An internal reference material is a RM developed by a user for its own internal use.
 An external reference material is a RM provided by someone other than the user.
 A certified reference material (CRM) is a RM issued and certified by an organization recognized as
competent to do so. CRM are widely used in modern technology and the demand is expected to increase.
CRM must be used consistently in order to ensure reliable measurements.
The purpose of this Guide is to introduce basic concepts and practical aspects related to the use of CRM and
examine the conditions under which CRM are properly used and when they are misused.
ISO Guide 35: Certification of reference materials — General and statistical principles
(Developed jointly by REMCO and ISO/TC 69).
The purpose of this Guide is to provide a basic introduction to concepts and practical aspects related to the
certification of reference materials (RM). ISO Guide 33 (see above) more fully addresses concepts and
practical aspects related to their use. The present Guide is intended to describe the general and statistical
principles for the certification of RM. Another purpose of this Guide is to assist in understanding valid methods
for the certification of RM and also to help potential users to better define their technical requirements. The
Guide should be useful in establishing the full potential of certified reference materials as aids to assuring the
accuracy and interlaboratory compatibility of measurements on a national or international scale.
1)
ISO 2602:1980 Statistical interpretation of test results — Estimation of the mean — Confidence
interval
This International Standard is limited to the point and interval estimation of the mean of a normal population
on the basis of observations from a series of tests applied to a random sample of individuals drawn from such
a population. The intervals may be one- or two-sided. It deals only with the case where the variance is
unknown. Formulae are given for both ungrouped and grouped observations. It is not concerned with the
calculation of an interval containing, with a fixed probability, at least a given fraction of the population
(statistical tolerance limits).
1)
ISO 2854:1976 Statistical interpretation of data — Techniques of estimation and tests relating to
means and variances
This International Standard specifies the techniques required to estimate the mean and variance and to
examine certain hypotheses concerning the values of these parameters for samples of observations from one
or two normal populations drawn at random and independently. Methods to check the normality are provided.
Conditions for using the methods when the assumptions are not completely satisfied are discussed. Formulae
are given for ungrouped observations. The methods are illustrated by many examples.

1) Under revision as ISO 16269-5.
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ISO/TR 13425:2003(E)
ISO 2859-0:1995 Sampling procedures for inspection by attributes — Part 0: Introduction to the
ISO 2859 attribute sampling system
Part 0 of ISO 2859 is a guidance document, not a source of sampling schemes or plans. It consists of two
sections. Section 1: General introduction to acceptance sampling is essentially an introduction to the sampling
schemes employed in ISO 2859 and ISO 8422 but it treats the subject in a general way. It contains
explanations of terms, gives practical advice on sampling inspection and discusses some underlying concepts.
Section 2: The ISO 2859-1 system extends Section 1 and amplifies the introductory text and instructions
contained in ISO 2859-1, by giving detailed comments and examples to assist in using the procedures and
tables that make up the ISO 2859-1 system.
ISO 2859-1:1999 Sampling procedures for inspection by attributes — Part 1: Sampling schemes
indexed by acceptance quality limit (AQL) for lot-by-lot inspection
Part 1 of ISO 2859 specifies sampling plans and procedures for the case where lots consist of discrete items
and where all the product characteristics involved in the assessment of quality are attributes. It contains
sampling plans indexed by percent nonconforming and by nonconformities per 100 items. In addition to single
sampling plans it contains double sampling (i.e. two-stage) and multiple sampling (seven stage) plans.
ISO 2859-1 contains normal, tightened and reduced inspection plans that are intended for coordinated use on
a continuing series of lots, with switching between these different levels of sampling severity in response to
the recent sampling history. Through the economic and psychological pressure of potential non-acceptance, a
supplier is thereby encouraged to maintain a process average quality at least as good as that which has been
agreed with the customer.
2)
ISO 2859-2:1985 Sampling procedures for inspection by attributes — Part 2: Sampling plans
indexed by limiting quality (LQ) for isolated lot inspection
Part 2 of ISO 2859 establishes procedures that can be used when the switching rules of ISO 2859-1 cannot
be applied, with sampling plans indexed by limiting quality (LQ). Procedure A is used when both the supplier
and the customer wish to regard the lot in isolation. Procedure B is used when the supplier regards the lot as
one of a continuing series, but the customer considers the lot received in isolation. The LQ is used to indicate
a quality level at which there is usually less than a 10 % risk of the customer accepting the lot. The LQ is
expressed in terms of the percentage nonconforming in the submitted lots, but can also be used for the case
where quality is expressed in terms of nonconformities per 100 items.
2)
ISO 2859-3:1991 Sampling procedures for inspection by attributes — Part 3: Skip-lot sampling
procedures
Part 3 of ISO 2859 supplements the procedures contained in ISO 2859-1. It provides a procedure for reducing
the inspection effort on products submitted by suppliers who have demonstrated their ability to control all
facets of product quality effectively and to produce superior quality material consistently. However, the
procedure must not be used for the inspection of product characteristics that involve the safety of personnel.
Skip-lot sampling applies only to a continuing series of lots. Some lots in a series will be accepted without
inspection when the sampling results for a stated number of immediately preceding lots meet stated criteria.
The lots to be inspected are chosen randomly with a pre-determined frequency.
ISO 2859-4:2002 Sampling procedures for inspection by attributes — Part 4: Procedures for
assessment of declared quality levels
The procedures in ISO 2859-4 have been developed as a response to a growing need for sampling plans
suitable for formal, systematic inspections such as reviews and audits. The procedures in ISO 2859 Parts 1 to
3 are provided for acceptance sampling purposes only, and are not suitable for the verification of a quality that
has been declared for some entity. The sampling plans in ISO 2859-4 have been developed so that there is
no more than a 5 % risk of contradicting a declared quality level that is satisfied, and no more than a 10 %
probability of failing to contradict a declared quality level that is incorrect.

2) Under revision.
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ISO/TR 13425:2003(E)
3)
ISO 3207:1975 Statistical interpretation of data — Determination of a statistical tolerance interval
This International Standard specifies methods enabling a sample to be used as the basis for determining a
statistical tolerance interval, i.e. an interval such that there is a fixed probability (confidence level) that the
interval will contain at least a proportion p of the population from which the sample is taken. The statistical
tolerance interval may be two-sided or one-sided. The limits of the interval are called “statistical tolerance
limits” or “natural limits of the process”. These methods are applicable only where it may be assumed that in
the population under consideration the sample units have been selected at random and are independent and
the distribution of the characteristic being studied is normal. Several examples are illustrating the methods.
4)
ISO 3301:1975 Statistical interpretation of data — Comparison of two means in the case of
paired observations
This International Standard specifies a method for comparing the mean of a population of differences between
paired observations with zero or any other pre-assigned value. The method, known as the method of paired
observations, is a special case of a method described in ISO 2854, Statistical interpretation of data —
Techniques of estimation and tests relating to means and variances. The method can only be applied if the
following two conditions are satisfied: the series of differences of the observed pairs can be considered as a
series of independent random items, and the distribution of these differences is supposed to be normal or
approximately normal.
3)
ISO 3494:1976 Statistical interpretation of data — Power of tests relating to means and
variances
This International Standard is a further development of ISO 2854. In connection with statistical tests ISO 2854
considered the type I risk, i.e. the probability of rejecting a null hypothesis (tested hypothesis) if this
hypothesis is true. The present Standard puts forward notions of the type II risk, the probability of not rejecting
the null hypothesis if it is false. Furthermore, the power of the tests are given. The conditions are the same as
in ISO 2854 that the observations can be considered as independent and approximately distributed according
to the normal distribution.
5)
ISO 3534-1:1993 Statistics — Vocabulary and symbols — Part 1: Probability and general statistical
terms
This part of ISO 3534 defines probability and general statistical terms. They may be used in the drafting of
other International Standards. In addition, symbols are defined for many of the terms.
The terms are classified under four main headings:
a) Terms used in the theory of probability;
b) General statistical terms;
c) General terms relating to observations and test results;
d) General terms relating to methods of sampling.
The entries are arranged analytically and alphabetical indexes are provided. The standard includes a list of
symbols and abbreviations used in this part of ISO 3534.

3) Under revision as ISO 16269-6.
4) Under revision as ISO 16269-5.
5) Under revision.
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ISO/TR 13425:2003(E)
ISO/DIS 3534-2 Statistics — Vocabulary and symbols — Part 2: Statistical quality control
This part of ISO 3534 defines terms in five areas of applied statistics: data generation and collection; statistical
process management; specification, values and measurement and test results; inspection and general
acceptance sampling; and sampling of bulk material. A list of standard symbols is also given. The entries are
arranged thematically. Interrelationships between the different concepts are demonstrated by a number of
concept diagrams. ISO 3534-1 is compatible with ISO 3534-2. In both parts the mathematical level is
restricted as far as possible to attain correct and concise definitions.
ISO 3534-3:1999 Statistics — Vocabulary and symbols — Part 3: Design of experiments
This part of ISO 3534 defines the terms used in the field of design of experiments and may be used in the
drafting of other International Standards.
The terms are classified under three main headings:
a) general terms;
b) terms related to arrangements of experiments;
c) terms related to methods of analysis.
The entries are arranged analytically and alphabetical indexes are provided. A list of symbols and
abbreviations used in this part of ISO 3534 is provided.
6)
ISO 3951:1989 Sampling procedures and charts for inspection by variables for percent
nonconforming
ISO 3951 is a system of single sampling plans that is applicable where quality involves just one product
characteristic that is a variable having, at least approximately, a normal distribution. It applies when there is a
single upper or lower specification limit of the variable and also where there are both. A lot is judged as
unacceptable when sample measurements of the variable give grounds for believing that the proportion of the
items in the lot for which the variable lies outside specification is at an unacceptably high level. Assessment of
acceptability is made in terms of the sample mean and the sample standard deviation (or process standard
deviation, if known) of the variable. A choice is available between equivalent numerical and graphical
acceptance criteria.
ISO 5479:1997 Statistical interpretation of data — Tests for departure from the normal
distribution
Many statistical methods used in International Standards are based on the assumption that some basic
variable(s) are distributed according to the normal distribution. This assumption may be doubtful in many
cases. A large number of “tests of normality” have therefore been developed, each of which is more or less
sensitive to a particular feature of the distribution. In this draft International Standard graphical methods,
moment tests, regressions tests, and characteristic function tests are considered.

6) To be cancelled and replaced by ISO 3951-1, Sampling procedures for inspection by variables — Part 1: Specification
for single sampling plans indexed by acceptance quality limit (AQL) for lot-by-lot inspection for a single quality
characteristic and a single AQL, which is currently at DIS stage.
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ISO/TR 13425:2003(E)
ISO 5725-1:1994 Accuracy (trueness and precision) of measurement methods and results —
Part 1: General principles and definitions
Part 1 of ISO 5725 contains definitions of terms that are used to describe the accuracy of a measurement
method: “Trueness”, “repeatability”, “reproducibility” and “intermediate precision”. “Trueness” is a measure of
the closeness of agreement between the average of large series of measurement results and an accepted
reference value, whereas the others are used to describe the closeness of agreement between measurement
results. Part 1 also sets out the principles to be followed when planning experiments to estimate the values of
these parameters, and gives guidance on how the results of such experiments should be published in
standards.
ISO 5725-2:1994 Accuracy (trueness and precision) of measurement methods and results —
Part 2: Basic method for the determination of repeatability and reproducibility of
a standard measurement method
Part 2 of ISO 5725 describes in detail how to organize experiments to determine the repeatability and
reproducibility standard deviations for a standardized measurement method, it sets out the tasks to be
performed by personnel involved in the experiments, and gives guidance on how to prepare the samples of
materials that are required. It also specifies how to analyse the data obtained in such experiments, and how to
present and report the results. It contains several examples that illustrate the method of analysis.
ISO 5725-3:1994 Accuracy (trueness and precision) of measurement methods and results —
Part 3: Intermediate measures of the precision of a standard measurement
method
Part 2 of ISO 5725 is concerned with measurements that are obtained under repeatability and reproducibility
conditions. However, it is common in process control for measurements to be made under conditions that are
intermediate between those to which repeatability and reproducibility can be applied. Part 3 of ISO 5725
supplements Part 2 by introducing measures of precision that are appropriate under these intermediate
conditions. It also describes experiments to use to estimate their values.
ISO 5725-4:1994 Accuracy (trueness and precision) of measurement methods and results —
Part 4: Basic methods for the determination of the trueness of a standard
measurement method
Part 4 of ISO 5725 describes how to use the inter-laboratory experiment from Part 2 to determine the bias of a
standard measurement method. It also describes an experiment that may be carried out in a single laboratory
to determine the bias of that laboratory. Both experiments require materials for which an accepted reference
value has been established, e.g. reference materials, or by preparation of known samples, or by the use of
measurement standards or a reference measurement method.
ISO 5725-5:1998 Accuracy (trueness and precision) of measurement methods and results —
Part 5: Alternative methods for the determination of the precision of a standard
measurement method
Part 5 of ISO 5725 describes two experiments that may be used in circumstances where the experiment
described in Part 2 would give biased estimates of repeatability and reproducibility standard deviations. One is
appropriate when there is a risk that operators may allow the result of a measurement on one sample to
influence the result of a subsequent measurement on another sample of the same material. The other is
appropriate when the materials to be used in the experiment are such that one cannot be confident that
identical samples can be prepared. Part 5 also describes “robust” methods of analysing the data obtained
from the experiments described in Part 2 and 5.
ISO 5725-6:1994 Accuracy (trueness and precision) of measurement methods and results —
Part 6: Use in practice of accuracy values
Part 6 of ISO 5725 describes a number of practical applications of the values determined by the methods
described in Parts 2 to 5, including the calculation of repeatability and reproducibility limits, the use of these
limits to check the acceptability of measurement results, the assessment and control of the quality of
laboratory operations, and how to compare alternative measurement methods.
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ISO/TR 13425:2003(E)
7)
ISO 7870:1993 Control charts — General guide and introduction
This International Standard presents a discussion of key elements and the philosophy of statistical process
control by means of control charts, and identifies a wide variety of control charts, including those related to
Shewhart control charts and those with process acceptance or on-line predictive emphasis. An overview is
given over the basic principles and concepts and illustrates the relationship among various control charts
approaches. Statistical control methods for different charts are specified in ISO 7873, ISO 7966, and ISO 8258.
ISO/TR 7871:1997 Cumulative sum charts — Guidance on quality control and data analysis using
cusum techniques
This Technical Report gives an introduction to the use of the cumulative sum chart, usually called cusum chart,
in statistical process control. This is a highly informative graphical presentation of data which are ordered in a
logical sequence. A cusum chart monitor is intended to check a process for departure from a reference value.
The construction and applications are illustrated by means of number of examples. Different modifications for
special purposes are proposed. The performance of the cusum techniques are compared with the Shewhart
control charts and their relative merits are discussed. Generally, the cusum chart is found to be more efficient
for detecting small changes in the process level than the corresponding Shewhart chart.
7)
ISO 7873:1993 Control charts for arithmetic average with warning limits
The statistical control of processes using arithmetic average control charts with warning limits is a modification
of Shewhart control charts, see ISO 8258. Arithmetic average control charts with warning limits are able to
reveal smaller shifts of the mean value of the controlled quality measure because of additional information
obtained from the points being accumulated in the warning zone. In addition, sudden large shifts in process
level are detectable if sample average values fall beyond action limits.
7)
ISO 7966:1993 Acceptance control charts
This International Standard describes uses of acceptance control charts and gives methods of determining
action limits and decision criteria. Examples are included to illustrate a variety of circumstances under which
this technique has advantages, and to show details of sample-size determination and calculation of limits. A
comparison of this type and other types of control charts as well as the basic philosophy and concepts
regarding the use of control charts for statistical process control is given in ISO 7870.
ISO 8258:1991 Shewhart control charts
This International Standard is a guide to the use and understanding of the Shewhart control chart approach to
stat
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