SIST ISO 24153:2010
Random sampling and randomization procedures
Random sampling and randomization procedures
ISO 24153:2009 defines procedures for random sampling and randomization. Several methods are provided, including approaches based on mechanical devices, tables of random numbers, and portable computer algorithms.
ISO 24153:2009 is applicable whenever a regulation, contract, or other standard requires random sampling or randomization to be used. The methods are applicable to such situations as
a) acceptance sampling of discrete units presented for inspection in lots,
b) sampling for survey purposes,
c) auditing of quality management system results, and
d) selecting experimental units, allocating treatments to them, and determining evaluation order in the conduct of designed experiments.
Information is also included to facilitate auditing or other external review of random sampling or randomization results where this is required by quality management personnel or regulatory bodies.
ISO 24153:2009 does not provide guidance as to the appropriate random sampling or randomization procedures to be used for any particular experimental situation or give guidance with respect to possible sampling strategy selection or sample size determination. Other ISO International Standards (such as ISO 2859, ISO 3951, ISO 8422, ISO 8423, ISO 13448, ISO 14560, ISO 18414, ISO 21247 and ISO 11648) or authoritative references should be consulted for guidance in such areas.
Modes opératoires d'échantillonnage et de répartition aléatoires
Naključno vzorčenje in postopki za doseganje naključnosti
Ta mednarodni standard opredeljuje postopke naključnega vzorčenja in doseganja naključnosti. Na voljo je več metod, vključno s pristopi, osnovanimi na mehanskih napravah, preglednicah naključnih številk in prenosnih računalniških algoritmih. Ta mednarodni standard velja, kadar predpis, pogodba ali drug standard zahteva uporabo naključnega vzorčenja ali doseganja naključnosti. Te metode veljajo v situacijah, kot je a) prevzemno vzorčenje diskretnih enot, predstavljenih za kontrolo po partijah, b) vzorčenje za namene študije, c) revizija rezultatov sistema vodenja kakovosti ter d) izbiranje eksperimentalnih enot, razporejanje njihovih obdelav in določevanje vrste vrednotenja pri izvajanju zasnovanih eksperimentov. Vključene so tudi informacije, ki olajšajo revizijo ali drug zunanji pregled rezultatov naključnega vzorčenja oziroma doseganja naključnosti, kjer to zahteva osebje za vodenje kakovosti ali regulatorni organi. Ta mednarodni standard ne določa vodila glede primernega naključnega vzorčenja oziroma postopkov za doseganje naključnosti za uporabo v kakršni koli posebni eksperimentalni situaciji in ne podaja vodila v zvezi z možno izbiro strategije vzorčenja ali določevanjem velikosti vzorca. Pri drugih ISO standardih (kot tistih, ki so navedeni v uvodu) ali veljavnih sklicih se je potrebno posvetovati glede vodila na takšnih področjih.
General Information
Standards Content (Sample)
SLOVENSKI STANDARD
01-julij-2010
1DNOMXþQRY]RUþHQMHLQSRVWRSNL]DGRVHJDQMHQDNOMXþQRVWL
Random sampling and randomization procedures
Modes opératoires d'échantillonnage et de répartition aléatoires
Ta slovenski standard je istoveten z: ISO 24153:2009
ICS:
03.120.30 8SRUDEDVWDWLVWLþQLKPHWRG Application of statistical
methods
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
INTERNATIONAL ISO
STANDARD 24153
First edition
2009-12-01
Random sampling and randomization
procedures
Modes opératoires d'échantillonnage et de répartition aléatoires
Reference number
©
ISO 2009
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's 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 of not infringing Adobe's 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
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 given below.
© ISO 2009
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
ISO's member 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 copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2009 – All rights reserved
Contents Page
Foreword .iv
Introduction.v
1 Scope.1
2 Normative references.1
3 Terms, definitions, and symbols .1
4 General .5
5 Random sampling — Mechanical device methods.6
6 Pseudo-independent random sampling — Table method.7
7 Pseudo-independent random sampling — Computer method.7
8 Applications to common sampling situations .11
Annex A (normative) Random number tables.18
Annex B (informative) Random number generation algorithm computer code .22
Annex C (informative) Random sampling and randomization computer code .25
Bibliography.31
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.
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 24153 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 5, Acceptance sampling.
iv © ISO 2009 – All rights reserved
Introduction
Random sampling and randomization procedures are the cornerstone to the validity of many statistical
methods used in experimentation, whether for industrial quality control and improvement purposes or for
designed experiments in the medical, biological, agricultural, or other scientific fields. Many statistical
standards address the conduct of such experimentation. In particular, all of the following acceptance-sampling
standards have been designed on the premise that random sampling is employed to select the required
sampling units for lot disposition purposes:
ISO 2859 (all parts), Sampling procedures for inspection by attributes
ISO 3951 (all parts), Sampling procedures for inspection by variables
ISO 8422, Sequential sampling plans for inspection by attributes
ISO 8423, Sequential sampling plans for inspection by variables for percent nonconforming (known
standard deviation)
ISO 13448 (all parts), Acceptance sampling procedures based on the allocation of priorities principle
(APP)
ISO 14560, Acceptance sampling procedures by attributes — Specified quality levels in nonconforming
items per million
ISO 18414, Acceptance sampling procedures by attributes — Accept-zero sampling system based on
credit principle for controlling outgoing quality
ISO 21247, Combined accept-zero sampling systems and process control procedures for product
acceptance
In addition, ISO 2859-3 and ISO 21247 include provisions for random sampling to be applied to determine
whether a lot should be inspected or not under skip-lot sampling procedures, and to decide which units require
inspection from a production process under continuous sampling plans, respectively. Consequently, it is of
great importance to the valid operation of all of the above standards that sampling be effectively random in its
application.
Although the principles of this International Standard are universally applicable where random sampling is
required and the sampling units can be clearly defined, preferably on the basis of discrete items, there are
many situations in which the material of interest does not lend itself to being quantified on a discrete-item
basis, as in the case of a bulk material. In such situations, the user is advised to consult the following ISO
International Standards for appropriate guidance:
ISO 11648 (all parts), Statistical aspects of sampling from bulk materials
INTERNATIONAL STANDARD ISO 24153:2009(E)
Random sampling and randomization procedures
1 Scope
This International Standard defines procedures for random sampling and randomization. Several methods are
provided, including approaches based on mechanical devices, tables of random numbers, and portable
computer algorithms.
This International Standard is applicable whenever a regulation, contract, or other standard requires random
sampling or randomization to be used. The methods are applicable to such situations as
a) acceptance sampling of discrete units presented for inspection in lots,
b) sampling for survey purposes,
c) auditing of quality management system results, and
d) selecting experimental units, allocating treatments to them, and determining evaluation order in the
conduct of designed experiments.
Information is also included to facilitate auditing or other external review of random sampling or randomization
results where this is required by quality management personnel or regulatory bodies.
This International Standard does not provide guidance as to the appropriate random sampling or
randomization procedures to be used for any particular experimental situation or give guidance with respect to
possible sampling strategy selection or sample size determination. Other ISO standards (such as those listed
in the Introduction) or authoritative references should be consulted for guidance in such areas.
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 references, the latest edition of the referenced
document (including any amendments) applies.
ISO 3534-1, Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in
probability
ISO 3534-2, Statistics — Vocabulary and symbols — Part 2: Applied statistics
ISO 3534-3, Statistics — Vocabulary and symbols — Part 3: Design of experiments
ISO 80000-2, Quantities and units — Part 2: Mathematical signs and symbols to be used in the natural
sciences and technology
3 Terms, definitions, and symbols
For the purposes of this document, the terms and definitions given in ISO 3534-1, ISO 3534-2, ISO 3534-3,
and the following apply.
3.1 Terms and definitions
3.1.1
cluster
part of a population (3.1.6) divided into mutually exclusive groups of sampling units (3.1.13) related in a
certain manner
[ISO 3534-2:2006, definition 1.2.28]
3.1.2
cluster sampling
sampling (3.1.12) in which a random sample (3.1.8) of clusters (3.1.1) is selected and all the sampling
units (3.1.13) which constitute the clusters are included in the sample (3.1.11)
[ISO 3534-2:2006, definition 1.3.9]
3.1.3
derangement
complete permutation
permutation of elements where no element remains in its original position in the set (e.g. {3, 1, 2} is a
derangement of {1, 2, 3})
3.1.4
lot
definite part of a population (3.1.6) constituted under essentially the same conditions as the population with
respect to the sampling (3.1.12) purpose
NOTE The sampling purpose can, for example, be to determine lot acceptability, or to estimate the mean value of a
particular characteristic.
[ISO 3534-2:2006, definition 1.2.4]
3.1.5
multistage sampling
sampling (3.1.12) in which the sample (3.1.11) is selected by stages, the sampling units (3.1.13) at each
stage being sampled from the larger sampling units chosen at the previous stage
NOTE Multistage sampling is different from multiple sampling. Multiple sampling is sampling by several criteria at the
same time.
[ISO 3534-2:2006, definition 1.3.10]
3.1.6
population
〈reference〉 totality of items under consideration
[ISO 3534-2:2006, definition 1.2.1]
3.1.7
pseudo-independent random sampling
sampling (3.1.12) where a sample (3.1.11) of n sampling units (3.1.13) is taken from a population (3.1.6)
in accordance with a table of random numbers or a computer algorithm designed such that each of the
possible combinations of n sampling units has a particular probability of being taken (see also 4.4)
3.1.8
random sample
sample (3.1.11) selected by random sampling (3.1.9)
[ISO 3534-2:2006, definition 1.2.25]
2 © ISO 2009 – All rights reserved
3.1.9
random sampling
sampling (3.1.12) where a sample (3.1.11) of n sampling units (3.1.13) is taken from a population (3.1.6)
in such a way that each of the possible combinations of n sampling units has a particular probability of being
taken
[ISO 3534-2:2006, definition 1.3.5]
3.1.10
randomization
process by which a set of items are set into a random order
NOTE If, from a population (3.1.6) consisting of the natural numbers 1 to n, numbers are drawn at random (i.e. in
such a way that all numbers have the same chance of being drawn), one by one, successively, without replacement, until
the population is exhausted, the numbers are said to be drawn "in random order".
If these n numbers have been associated in advance with n distinct units or n distinct treatments that are then re-arranged
in the order in which the numbers are drawn, the order of the units or treatments is said to be randomized.
3.1.11
sample
subset of a population (3.1.6) made up of one or more sampling units (3.1.13)
[ISO 3534-2:2006, definition 1.2.17]
3.1.12
sampling
act of drawing or constituting a sample (3.1.11)
[ISO 3534-2:2006, definition 1.3.1]
3.1.13
sampling unit
unit
one of the individual parts into which a population (3.1.6) is divided
NOTE 1 A sampling unit can contain one or more items, for example, a box of matches, but one test result will be
obtained for it.
NOTE 2 A sampling unit can consist of discrete items or a defined amount of bulk material.
[ISO 3534-2:2006, definition 1.2.14]
3.1.14
sampling with replacement
sampling (3.1.12) in which each sampling unit (3.1.13) taken and observed is returned to the
...
INTERNATIONAL ISO
STANDARD 24153
First edition
2009-12-01
Random sampling and randomization
procedures
Modes opératoires d'échantillonnage et de répartition aléatoires
Reference number
©
ISO 2009
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's 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 of not infringing Adobe's 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
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 given below.
© ISO 2009
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
ISO's member 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 copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2009 – All rights reserved
Contents Page
Foreword .iv
Introduction.v
1 Scope.1
2 Normative references.1
3 Terms, definitions, and symbols .1
4 General .5
5 Random sampling — Mechanical device methods.6
6 Pseudo-independent random sampling — Table method.7
7 Pseudo-independent random sampling — Computer method.7
8 Applications to common sampling situations .11
Annex A (normative) Random number tables.18
Annex B (informative) Random number generation algorithm computer code .22
Annex C (informative) Random sampling and randomization computer code .25
Bibliography.31
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.
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 24153 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 5, Acceptance sampling.
iv © ISO 2009 – All rights reserved
Introduction
Random sampling and randomization procedures are the cornerstone to the validity of many statistical
methods used in experimentation, whether for industrial quality control and improvement purposes or for
designed experiments in the medical, biological, agricultural, or other scientific fields. Many statistical
standards address the conduct of such experimentation. In particular, all of the following acceptance-sampling
standards have been designed on the premise that random sampling is employed to select the required
sampling units for lot disposition purposes:
ISO 2859 (all parts), Sampling procedures for inspection by attributes
ISO 3951 (all parts), Sampling procedures for inspection by variables
ISO 8422, Sequential sampling plans for inspection by attributes
ISO 8423, Sequential sampling plans for inspection by variables for percent nonconforming (known
standard deviation)
ISO 13448 (all parts), Acceptance sampling procedures based on the allocation of priorities principle
(APP)
ISO 14560, Acceptance sampling procedures by attributes — Specified quality levels in nonconforming
items per million
ISO 18414, Acceptance sampling procedures by attributes — Accept-zero sampling system based on
credit principle for controlling outgoing quality
ISO 21247, Combined accept-zero sampling systems and process control procedures for product
acceptance
In addition, ISO 2859-3 and ISO 21247 include provisions for random sampling to be applied to determine
whether a lot should be inspected or not under skip-lot sampling procedures, and to decide which units require
inspection from a production process under continuous sampling plans, respectively. Consequently, it is of
great importance to the valid operation of all of the above standards that sampling be effectively random in its
application.
Although the principles of this International Standard are universally applicable where random sampling is
required and the sampling units can be clearly defined, preferably on the basis of discrete items, there are
many situations in which the material of interest does not lend itself to being quantified on a discrete-item
basis, as in the case of a bulk material. In such situations, the user is advised to consult the following ISO
International Standards for appropriate guidance:
ISO 11648 (all parts), Statistical aspects of sampling from bulk materials
INTERNATIONAL STANDARD ISO 24153:2009(E)
Random sampling and randomization procedures
1 Scope
This International Standard defines procedures for random sampling and randomization. Several methods are
provided, including approaches based on mechanical devices, tables of random numbers, and portable
computer algorithms.
This International Standard is applicable whenever a regulation, contract, or other standard requires random
sampling or randomization to be used. The methods are applicable to such situations as
a) acceptance sampling of discrete units presented for inspection in lots,
b) sampling for survey purposes,
c) auditing of quality management system results, and
d) selecting experimental units, allocating treatments to them, and determining evaluation order in the
conduct of designed experiments.
Information is also included to facilitate auditing or other external review of random sampling or randomization
results where this is required by quality management personnel or regulatory bodies.
This International Standard does not provide guidance as to the appropriate random sampling or
randomization procedures to be used for any particular experimental situation or give guidance with respect to
possible sampling strategy selection or sample size determination. Other ISO standards (such as those listed
in the Introduction) or authoritative references should be consulted for guidance in such areas.
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 references, the latest edition of the referenced
document (including any amendments) applies.
ISO 3534-1, Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in
probability
ISO 3534-2, Statistics — Vocabulary and symbols — Part 2: Applied statistics
ISO 3534-3, Statistics — Vocabulary and symbols — Part 3: Design of experiments
ISO 80000-2, Quantities and units — Part 2: Mathematical signs and symbols to be used in the natural
sciences and technology
3 Terms, definitions, and symbols
For the purposes of this document, the terms and definitions given in ISO 3534-1, ISO 3534-2, ISO 3534-3,
and the following apply.
3.1 Terms and definitions
3.1.1
cluster
part of a population (3.1.6) divided into mutually exclusive groups of sampling units (3.1.13) related in a
certain manner
[ISO 3534-2:2006, definition 1.2.28]
3.1.2
cluster sampling
sampling (3.1.12) in which a random sample (3.1.8) of clusters (3.1.1) is selected and all the sampling
units (3.1.13) which constitute the clusters are included in the sample (3.1.11)
[ISO 3534-2:2006, definition 1.3.9]
3.1.3
derangement
complete permutation
permutation of elements where no element remains in its original position in the set (e.g. {3, 1, 2} is a
derangement of {1, 2, 3})
3.1.4
lot
definite part of a population (3.1.6) constituted under essentially the same conditions as the population with
respect to the sampling (3.1.12) purpose
NOTE The sampling purpose can, for example, be to determine lot acceptability, or to estimate the mean value of a
particular characteristic.
[ISO 3534-2:2006, definition 1.2.4]
3.1.5
multistage sampling
sampling (3.1.12) in which the sample (3.1.11) is selected by stages, the sampling units (3.1.13) at each
stage being sampled from the larger sampling units chosen at the previous stage
NOTE Multistage sampling is different from multiple sampling. Multiple sampling is sampling by several criteria at the
same time.
[ISO 3534-2:2006, definition 1.3.10]
3.1.6
population
〈reference〉 totality of items under consideration
[ISO 3534-2:2006, definition 1.2.1]
3.1.7
pseudo-independent random sampling
sampling (3.1.12) where a sample (3.1.11) of n sampling units (3.1.13) is taken from a population (3.1.6)
in accordance with a table of random numbers or a computer algorithm designed such that each of the
possible combinations of n sampling units has a particular probability of being taken (see also 4.4)
3.1.8
random sample
sample (3.1.11) selected by random sampling (3.1.9)
[ISO 3534-2:2006, definition 1.2.25]
2 © ISO 2009 – All rights reserved
3.1.9
random sampling
sampling (3.1.12) where a sample (3.1.11) of n sampling units (3.1.13) is taken from a population (3.1.6)
in such a way that each of the possible combinations of n sampling units has a particular probability of being
taken
[ISO 3534-2:2006, definition 1.3.5]
3.1.10
randomization
process by which a set of items are set into a random order
NOTE If, from a population (3.1.6) consisting of the natural numbers 1 to n, numbers are drawn at random (i.e. in
such a way that all numbers have the same chance of being drawn), one by one, successively, without replacement, until
the population is exhausted, the numbers are said to be drawn "in random order".
If these n numbers have been associated in advance with n distinct units or n distinct treatments that are then re-arranged
in the order in which the numbers are drawn, the order of the units or treatments is said to be randomized.
3.1.11
sample
subset of a population (3.1.6) made up of one or more sampling units (3.1.13)
[ISO 3534-2:2006, definition 1.2.17]
3.1.12
sampling
act of drawing or constituting a sample (3.1.11)
[ISO 3534-2:2006, definition 1.3.1]
3.1.13
sampling unit
unit
one of the individual parts into which a population (3.1.6) is divided
NOTE 1 A sampling unit can contain one or more items, for example, a box of matches, but one test result will be
obtained for it.
NOTE 2 A sampling unit can consist of discrete items or a defined amount of bulk material.
[ISO 3534-2:2006, definition 1.2.14]
3.1.14
sampling with replacement
sampling (3.1.12) in which each sampling unit (3.1.13) taken and observed is returned to the population
(3.1.6) before the next sampling unit is taken
[ISO 3534-2:2006, definition 1.3.15]
3.1.15
sampling without replacement
sampling (3.1.12) in which each sampling unit (3.1.13) is taken from the population (3.1.6) once only
without being returned to the population
[ISO 3534-2:2006, definition 1.3.16]
3.1.16
seed
numerical value or set of values used to initialize a pseudo-independent random sampling (3.1.7) algorithm
or to establish a starting point in a table of random numbers
3.1.17
simple random sample
sample (3.1.11) selected by simple random sampling (3.1.18)
[ISO 3534-2:2006, definition 1.2.24]
3.1.18
simple random sampling
sampling (3.1.12) where a sample (3.1.11) of n sampling units (3.1.13) is taken from a population (3.1.
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.