SIST ISO 2859-4:2021
(Main)Sampling procedures for inspection by attributes - Part 4: Procedures for assessment of declared quality levels
Sampling procedures for inspection by attributes - Part 4: Procedures for assessment of declared quality levels
This document establishes single sampling plans for conformance testing, i.e., for assessing whether the quality level of a relevant audit population (lot, process, inventory, file etc) conforms to a declared value. Sampling plans are provided corresponding to four levels of discriminatory ability. The limiting quality ratio (LQR) (see Clause 4) of each sampling plan is given for reference. For levels I-III, the sampling plans have been devised so as to obtain a risk no more than 5 % of contradicting a correct declared quality level. The risk of failing to contradict an incorrectly declared quality level which is related to the LQR is no more than 10 %. The sample sizes for level 0 are designed in a way that the LQR factors of the sampling plans are compatible with the LQR factors for level I.
In contrast to the procedures in the other parts of the ISO 2859 series, the procedures in this document are not applicable to acceptance assessment of lots. Generally, this document mainly focuses on controlling type I error, which differs from the balancing of the risks in the procedures for acceptance sampling.
This document can be used for various forms of quality inspection in situations where objective evidence of conformity to some declared quality level is to be provided by means of inspection of a sample. The procedures are applicable to entities such as lots, process output, etc. that allow random samples of individual items to be taken from the entity.
The sampling plans provided in this document are applicable, but not limited, to the inspection of a variety of targets such as:
— end items;
— components and raw materials;
— operations;
— materials in process;
— supplies in storage;
— maintenance operations;
— data or records;
— administrative procedures;
— accounting procedures or accounting entries;
— internal control procedures.
This document considers two types of quality models for discrete items and populations, as follows.
i) The conforming-nonconforming model, where each item is classified as conforming or nonconforming, and where the quality indicator of a population of items is the proportion p of nonconforming items, or, equivalently, the percentage 100 p of nonconforming items.
ii) The nonconformities model, where the number of nonconformities is counted on each item, and where the quality indicator of a population of items is the average number λ of nonconformities found on items in the population, or, equivalently, the percentage 100 λ of nonconformities on items in the population.
Règles d'échantillonnage pour les contrôles par attributs - Partie 4: Procédures pour l'évaluation des niveaux déclarés de qualité
Le présent document définit des plans d'échantillonnage individuels ŕ des fins d'essais de conformité, c'est-ŕ-dire afin d'évaluer si le niveau de qualité d'une population auditée donnée (lot, processus, inventaire, fichier, etc.) est conforme ŕ une valeur déclarée. Les plans d'échantillonnage correspondent ŕ quatre niveaux de capacité discriminante. Le ratio de qualité limite (RQL) (voir Article 4) de chaque plan d'échantillonnage est donné en référence. Pour les niveaux I ŕ III, les plans d'échantillonnage ont été conçus de sorte que le risque de rejet d'un niveau déclaré de qualité satisfaisant ne dépasse pas 5 %. Le risque de non-rejet d'un niveau déclaré de qualité insuffisant, qui est associé au RQL, ne dépasse pas 10 %. Les effectifs d'échantillon pour le niveau 0 sont planifiés de sorte que les facteurs RQL des plans d'échantillonnage soient compatibles avec les facteurs RQL du niveau I.
Contrairement aux procédures données dans les autres parties de la série ISO 2859, les procédures du présent document ne s'appliquent pas pour déterminer l'acceptation des lots. De maničre générale, le présent document porte principalement sur la maîtrise des erreurs de premičre espčce, qui est différente de la pondération des risques appliquée dans les procédures pour l'acceptation d'échantillons.
Le présent document peut ętre utilisé pour différentes modalités de contrôle de la qualité, dans des situations oů la preuve tangible de conformité ŕ un niveau déclaré de qualité est apportée en contrôlant un échantillon. Ces procédures s'appliquent ŕ des entités telles que des lots, des livrables de processus, etc., qui permettent de prélever des échantillons d'individus au hasard.
Les plans d'échantillonnage fournis dans le présent document s'appliquent, sans s'y limiter, au contrôle de différentes cibles telles que :
— les produits finis ;
— les composants et matičres premičres ;
— les opérations ;
— les matičres en cours d'élaboration ;
— les équipements stockés ;
— les opérations de maintenance ;
— les données ou enregistrements ;
— les procédures administratives ;
— les procédures ou saisies comptables ;
— les procédures de contrôle interne.
Le présent document étudie deux types de modčles d'acceptation de la qualité pour les individus distincts et les populations d'individus, présentés ci-aprčs :
i) Le modčle de conformité/non-conformité, dans lequel chaque individu est classé comme étant conforme ou non conforme, et oů l'indicateur de qualité d'une population d'individus correspond ŕ la proportion p d'individus non conformes, ce qui équivaut au pourcentage 100 p d'individus non conformes.
ii) Le modčle des non-conformités, dans lequel le nombre de non-conformités est comptabilisé pour chaque individu, et oů l'indicateur de qualité d'une population d'individus correspond au nombre moyen λ de non-conformités constatées sur les individus de la population, ce qui équivaut au pourcentage 100 λ de non-conformités constatées sur les individus de la population.
Postopki vzorčenja za kontrolo po opisnih spremenljivkah - 4. del: Postopki za ugotavljanje deklariranih ravni kakovosti
General Information
Relations
Buy Standard
Standards Content (Sample)
SLOVENSKI STANDARD
SIST ISO 2859-4:2021
01-oktober-2021
Nadomešča:
SIST ISO 2859-4:2010
Postopki vzorčenja za kontrolo po opisnih spremenljivkah - 4. del: Postopki za
ugotavljanje deklariranih ravni kakovosti
Sampling procedures for inspection by attributes - Part 4: Procedures for assessment of
declared quality levels
Règles d'échantillonnage pour les contrôles par attributs - Partie 4: Procédures pour
l'évaluation des niveaux déclarés de qualité
Ta slovenski standard je istoveten z: ISO 2859-4:2020
ICS:
03.120.30 Uporaba statističnih metod Application of statistical
methods
SIST ISO 2859-4:2021 en,fr
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST ISO 2859-4:2021
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SIST ISO 2859-4:2021
INTERNATIONAL ISO
STANDARD 2859-4
Third edition
2020-06
Sampling procedures for inspection by
attributes —
Part 4:
Procedures for assessment of declared
quality levels
Règles d'échantillonnage pour les contrôles par attributs —
Partie 4: Procédures pour l'évaluation des niveaux déclarés de qualité
Reference number
ISO 2859-4:2020(E)
©
ISO 2020
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SIST ISO 2859-4:2021
ISO 2859-4:2020(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2020
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting
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Published in Switzerland
ii © ISO 2020 – All rights reserved
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SIST ISO 2859-4:2021
ISO 2859-4:2020(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 2
3 Terms, definitions, symbols and abbreviated terms . 2
3.1 Terms and definitions . 2
3.2 Symbols and abbreviated terms. 3
4 Sampling and decision procedure . 3
4.1 Identifying a sampling plan. 3
4.2 Drawing of samples . 3
4.3 Decision objective . 4
4.4 Decision by sampling . 4
4.5 Disposition of nonconforming items. 4
5 Principles . 4
6 Declared quality level (DQL) . 5
7 Sampling plans . 5
7.1 General . 5
7.2 LQR level 0 . 6
7.3 LQR level I. 7
7.4 LQR level II . 7
7.5 LQR level III . 8
8 Further information . 9
8.1 Curves showing the approximate probability of contradiction . 9
8.2 Tables indicating discriminatory ability . 9
Annex A (informative) Examples of use of the procedures .13
Annex B (informative) Quality ratio related to β 100 % acceptance probability .16
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ISO 2859-4:2020(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.
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).
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 the 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 of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www .iso .org/
iso/ foreword .html.
This document was prepared by Technical Committee ISO/TC 69, Application of statistical methods,
Subcommittee SC 5, Acceptance sampling.
This third edition cancels and replaces the second edition (ISO 2859-4:2002), which has been technically
revised.
The main changes compared to the previous edition are as follows:
— the scope has been widened from testing for the percentage of nonconforming items to testing for
the percentage of nonconformities per item;
— the sampling and decision algorithm is more detailed and has been moved to an earlier position in
the document, so as to facilitate the operational use of the document;
— an LQR level 0 has been introduced, which can be used when a large probability of erroneously
contradicting a correctly declared quality level can be tolerated;
— an informative Annex B has been added to explain the mathematical-statistical background, and to
provide tables on quality ratios.
A list of all parts in the ISO 2859 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www .iso .org/ members .html.
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Introduction
The procedures in this document differ in their scope from the procedures in ISO 2859-1 to ISO 2859-3.
The acceptance sampling systems specified in ISO 2859-1 to ISO 2859-3 are intended to be used in
bilateral agreements between two parties. The acceptance sampling procedures are supposed to be
used as simple, pragmatic rules for deciding on product release by inspection of only a limited sample
of a consignment, and therefore the procedures do not make reference (either explicitly or implicitly) to
any formally declared quality level.
Under acceptance sampling there is no sharp borderline between quality levels that should be
considered acceptable and qualities that should be rejected by the procedure. For the procedures in
ISO 2859-1, the two parties agree upon some acceptance quality limit (AQL) which is the worst tolerable
process average when a continuing series of lots is submitted. The switching rules and the sampling
schemes in ISO 2859-1 are designed to encourage the suppliers to have process averages consistently
better than the AQL selected. In order to keep sample sizes moderate, the protection against accepting
individual lots of inferior quality may be less than that provided by sampling plans targeted for
sentencing individual lots. The procedures in ISO 2859-2, on the contrary, are designed to provide good
protection against accepting individual lots of inferior quality (LQ), but at the expense of a possibly
high risk of not accepting lots of qualities that both parties actually would consider to be acceptable.
The procedures in ISO 2859-1 to ISO 2859-3 are well suited for acceptance sampling purposes, but they
should not be used in reviews, audits, systematic tests, etc. to verify a quality that has been declared for
some entity. The main reason is that the procedures have been indexed in terms of quality levels that
are relevant solely for the pragmatic purposes of acceptance sampling, and the various risks have been
balanced accordingly in a pragmatic attitude.
The procedures in this document have been developed as a response to the growing need for sampling
procedures suitable for formal, systematic inspections such as reviews or audits or systematic tests.
When performing such a formal inspection, it is necessary both for the inspecting authority and for the
body subject to inspection to consider the risks of reaching an incorrect conclusion. These risks have to
be accounted for explicitly in the design of review/auditing/testing procedures.
This document provides guidance and rules to assist the user in accounting for the risks of incorrect
conclusions in an informed manner.
The rules in this document have been devised such that there is only an acceptably small risk of
contradicting the declared quality level when in fact the actual level conforms to the declared level.
If it were also desired that there should be a similarly small risk of not contradicting the declared
quality level when in fact the actual quality level does not conform to the declared quality level, then it
would be necessary to investigate a rather large sample. Therefore, in order to obtain the benefit of a
moderate sample size, the procedures in this document have been devised in such a way that they allow
a somewhat higher risk of failing to contradict the declared quality level when in fact the actual quality
level does not conform to the declared quality level.
The wording of the result of the assessment should reflect this imbalance between the risks of reaching
incorrect conclusions. For the levels I, II, and III, when the sample result contradicts the declared quality
level, there is strong evidence of nonconformance to the declared quality level. When the sample result
does not contradict the declared quality level, this should be understood as “we have not, in this limited
sample, found strong evidence of nonconformance to the declared quality level”.
CAUTION — It should be noticed that, for sampling plans with very small sample sizes, one
should be aware of the poor discriminatory power under such sample sizes by referring to the
entries in Tables B.1, B.2, B.3 and B.4.
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SIST ISO 2859-4:2021
INTERNATIONAL STANDARD ISO 2859-4:2020(E)
Sampling procedures for inspection by attributes —
Part 4:
Procedures for assessment of declared quality levels
1 Scope
This document establishes single sampling plans for conformance testing, i.e., for assessing whether
the quality level of a relevant audit population (lot, process, inventory, file etc) conforms to a declared
value. Sampling plans are provided corresponding to four levels of discriminatory ability. The limiting
quality ratio (LQR) (see Clause 4) of each sampling plan is given for reference. For levels I-III, the
sampling plans have been devised so as to obtain a risk no more than 5 % of contradicting a correct
declared quality level. The risk of failing to contradict an incorrectly declared quality level which is
related to the LQR is no more than 10 %. The sample sizes for level 0 are designed in a way that the LQR
factors of the sampling plans are compatible with the LQR factors for level I.
In contrast to the procedures in the other parts of the ISO 2859 series, the procedures in this document
are not applicable to acceptance assessment of lots. Generally, this document mainly focuses on
controlling type I error, which differs from the balancing of the risks in the procedures for acceptance
sampling.
This document can be used for various forms of quality inspection in situations where objective
evidence of conformity to some declared quality level is to be provided by means of inspection of a
sample. The procedures are applicable to entities such as lots, process output, etc. that allow random
samples of individual items to be taken from the entity.
The sampling plans provided in this document are applicable, but not limited, to the inspection of a
variety of targets such as:
— end items;
— components and raw materials;
— operations;
— materials in process;
— supplies in storage;
— maintenance operations;
— data or records;
— administrative procedures;
— accounting procedures or accounting entries;
— internal control procedures.
This document considers two types of quality models for discrete items and populations, as follows.
i) The conforming-nonconforming model, where each item is classified as conforming or
nonconforming, and where the quality indicator of a population of items is the proportion p of
nonconforming items, or, equivalently, the percentage 100 p of nonconforming items.
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ISO 2859-4:2020(E)
ii) The nonconformities model, where the number of nonconformities is counted on each item, and
where the quality indicator of a population of items is the average number λ of nonconformities
found on items in the population, or, equivalently, the percentage 100 λ of nonconformities on items
in the population.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements 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 9000, Quality management systems — Fundamentals and vocabulary
3 Terms, definitions, symbols and abbreviated terms
3.1 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 3534-1, ISO 3534-2 and
ISO 9000 and the following apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
3.1.1
non-rejection number
c
largest number of nonconforming items or nonconformities, respectively, found in the sample from the
population under investigation that does not lead to contradiction of the declared quality level
3.1.2
quality ratio
QR
ratio of the actual quality level to the declared quality level of the entity under investigation
3.1.3
limiting quality ratio
LQR
value of the quality ratio that is limited to a small risk of failing to contradict an incorrect declared
quality level
Note 1 to entry: In this document, the risk of failing to contradict an incorrect declared quality level is no more
than 10 %.
3.1.4
audit population
totality of items under audit inspection
3.1.5
audit population conformance
state of the audit population fulfilling imposed requirements
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3.2 Symbols and abbreviated terms
c non-rejection number of a sampling plan
d number of nonconforming items or, respectively, nonconformities in the sample
n sample size of a sampling plan
DQL declared quality level
LQR limiting quality ratio
QR quality ratio
4 Sampling and decision procedure
4.1 Identifying a sampling plan
A single sampling plan (n, c) with sample size n and non-rejection number c is identified from Table 1 by
two characteristics:
a) the DQL, ranging from 0,01 percent to 10,00 percent;
b) the LQR level, ranging over 0, I, II, III.
Except a few exceptions for very small and very large DQL, the non-rejection numbers are constant
under each LQR level, with c = 0 under level 0, c = 1 under level I, c = 2 under level II, and c = 3 under
level III.
If the declared quality level is not one of the tabulated values, then the next higher tabulated value of
DQL shall be used to select the plan.
NOTE This results in an LQR that is somewhat higher, and to a probability of falsely contradicting a correct
declared quality level that is somewhat lower than the values given in Tables 2 to 5 (see 8.2).
EXAMPLE If an LQR level II is chosen with a DQL of 0,65 % nonconforming items, Table 1 yields a sampling
plan with a sample size n of 127, and a non-rejection number of nonconforming items c of 2, which provides an
LQR of 6,45 (see Table 4).
4.2 Drawing of samples
The sample shall be selected by simple random sampling or, where appropriate, by stratified or other
methods of random sampling from the entity.
When stratified sampling is used, the number of items from each stratum shall be selected in proportion
to the size of strata of the entity under investigation. The sub-sample from each stratum shall be
selected by simple random sampling from that stratum.
When sampling from a lot or a consignment, stratified sampling may be used with strata corresponding
to identifiable sub-lots.
When sampling from a process, stratified sampling may be used with strata corresponding to identified
sources of variation, for example tools, operators, shifts, etc.
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If the sample size exceeds the size of the entity under investigation, then all items of the entity shall be
inspected.
EXAMPLE If, in the example considered in 4.1, the entity under investigation is the computer records
of administrative transactions during five business days, and the number of transactions each day are
approximately equal, then the total sample of n = 127 transactions are selected as five sub-samples, three
consisting of 25 transactions and two consisting of 26 transactions, selected by simple random sampling from
the transactions on each of the five days.
4.3 Decision objective
The audit population is considered as conforming if the population quality indicator (percentage of
nonconforming units, or percentage of nonconformities per item, respectively) is smaller or equal to
the DQL. Otherwise, the audit population is considered as nonconforming. The inspection objective
shall decide on the conformance of the population by taking one of two mutually exclusive decisions:
i) rejection, i.e., contradict the quality declaration expressed by the DQL and classify the population as
nonconforming; ii) non-rejection or acceptance, i.e., do not contradict the quality declaration expressed
by the DQL and classify the population as conforming.
4.4 Decision by sampling
Each of the n items in the sample shall be inspected, and the total number d of nonconforming items or,
respectively, of the nonconformities on items in the sample shall be determined.
— If d is less than or equal to the non-rejection number c, the decision is non-rejection, i.e., the declared
quality level is not contradicted.
— If d exceeds the non-rejection number c, the decision is rejection, i.e., the declared quality level is
contradicted.
EXAMPLE Assume that, in the situation considered by the Example in 4.1, two or fewer nonconforming items
are found in the sample of 127 items. Then the sample result does not contradict the DQL of 0,65 % nonconforming
items. If three or more nonconforming items are found, the sample evidence contradicts the DQL.
4.5 Disposition of nonconforming items
Any nonconforming items or items exhibiting nonconformities found in the sample shall not be returned
to the rest of the items unless the nonconforming items are brought to a conforming condition and
applicable administrative rules are followed.
Examples for the use of the sampling and decision procedure in industrial practice are provided in
Annex A.
5 Principles
Any assessment procedure based on sampling is subject to sampling risk, i.e., the risk of taking an
erroneous decision due to the limited information conveyed by a sample. In the present context, there
are two types of erroneous conclusions on an audit population:
a) rejection although the population is actually conforming, i.e., the population quality indicator
(percentage of nonconforming units, or percentage of nonconformities per item, respectively) is
actually smaller or equal to the DQL;
b) non-rejection although the population is actually nonconforming, i.e., the population quality
indicator (percentage of nonconforming units, or percentage of nonconformities per item,
respectively) is actually exceeding the DQL.
The corresponding error risks are expressed by the respective error probabilities, namely a) the
probability of rejecting an actually conforming population; b) the probability of not rejecting an actually
nonconforming population. The latter two risks shall be balanced by the design of the sampling plans.
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The sampling plans for the LQR levels I, II and III are, with few exceptions for large DQLs, devised such
that the probability of contradicting an actually correct quality declaration is less than 5 %. For the
LQR level 0, the probability of contradicting an actually correct quality declaration is bounded by 20 %.
See Tables 2 through 5 for the detailed values.
For the inspection authority, it is vital to have a small probability of not detecting an incorrectly
declared quality level. The design of the sampling plans in this document focusses on the limiting
quality ratio (LQR): when the actual quality level is LQR×DQL, i.e., LQR times worse than the declared
quality level DQL, the procedures in this document have a risk of less than 10 % of failing to contradict
the declared quality level (corresponding to a 90 % probability of contradicting/rejecting the incorrect
declared quality level).
The ideal LQR would be close to 1,00. The latter ideal case cannot be achieved with practically feasible
sample sizes. This document considers four LQR levels 0, I, II and III. For all levels, the LQR values
range between 4 and 13, roughly. The sample sizes for level 0 are set to make sure that level 0 has
approximately the same LQR as level I at the same DQL value where the LQR ranges from 7,78 for the
largest DQL up to 12,34 for the smallest DQL. Under the latter design, it is inevitable that under level 0
the probabilities of contradicting an actually correct quality declaration are considerably higher than
under levels I, II, and III.
Technical details on the design of the sampling plans are provided in Annex B.
6 Declared quality level (DQL)
The DQL together with the LQR level is used for indexing the sampling plans provided in this document.
The values of DQL in the tables are known as preferred DQLs. The series of preferred DQL values
correspond to the series of preferred AQLs for inspection for nonconforming items given in ISO 2859-1.
There shall be a sound basis for the DQL used. The DQL shall not be deliberately overstated or
understated.
When a DQL is designated for a certain type quality characteristic, it indicates that the supplier has
good reason to believe that the quality is not worse than this designated value.
CAUTION — When the DQL is estimated from a sample taken from the entity of interest, the
procedures in this document shall not be used. Such a verification of an estimate from a sample
requires that the sample size and inspection result be taken into account in order to incorporate
the uncertainty associated with the estimate. This uncertainty affects the assessment of
the risks of making incorrect conclusions on the actual status of the entity of interest. Such
verification usually requires larger sample sizes than those used in the procedures described in
this document.
7 Sampling plans
7.1 General
The master Table 1 provides all single sampling plans (n, c) for the four LQR levels, indexed in the DQL
and the LQR level. Background on the choice of the LQR level and the properties of the corresponding
sampling plans are provided in 7.2 through 7.5.
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Table 1 — Master table of sampling plans
DQL LQR Level 0 LQR Level I LQR Level II LQR Level III
(% nonconforming items
n c n c n c n c
or % nonconformities per item)
0,010 1 866 0 3 153 1 ← ←
0,015 1 185 0 2 001 1 ← ←
0,025 743 0 1 255 1 3 154 2 ←
0,040 476 0 804 1 2 001 2 3 152 3
0,065 298 0 503 1 1 253 2 2 004 3
0,100 188 0 317 1 802 2 1 252 3
0,150 119 0 202 1 502 2 803 3
0,250 75 0 127 1 317 2 503 3
0,400 49 0 82 1 202 2 317 3
0,650 31 0 52 1 127 2 202 3
1,000 20 0 34 1 82 2 127 3
1,500 13 0 22 1 52 2 82 3
2,500 9 0 15 1 34 2 52 3
4,000 → 10 1 22 2 34 3
6,500 → 7 1 15 2 22 3
10,000 → 5 1 10 2 16 3
The plans are indexed by the declared quality level (DQL) of nonconforming product and the limiting quality ratio (LQR) levels.
“→” means: use the sampling plan to the right, which corresponds to a smaller limiting quality ratio
“←” means: use the sampling plan to the left, which corresponds to a higher limiting quality ratio
7.2 LQR level 0
Level 0 may be used when a large
...
INTERNATIONAL ISO
STANDARD 2859-4
Third edition
2020-06
Sampling procedures for inspection by
attributes —
Part 4:
Procedures for assessment of declared
quality levels
Règles d'échantillonnage pour les contrôles par attributs —
Partie 4: Procédures pour l'évaluation des niveaux déclarés de qualité
Reference number
ISO 2859-4:2020(E)
©
ISO 2020
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ISO 2859-4:2020(E)
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ISO 2859-4:2020(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 2
3 Terms, definitions, symbols and abbreviated terms . 2
3.1 Terms and definitions . 2
3.2 Symbols and abbreviated terms. 3
4 Sampling and decision procedure . 3
4.1 Identifying a sampling plan. 3
4.2 Drawing of samples . 3
4.3 Decision objective . 4
4.4 Decision by sampling . 4
4.5 Disposition of nonconforming items. 4
5 Principles . 4
6 Declared quality level (DQL) . 5
7 Sampling plans . 5
7.1 General . 5
7.2 LQR level 0 . 6
7.3 LQR level I. 7
7.4 LQR level II . 7
7.5 LQR level III . 8
8 Further information . 9
8.1 Curves showing the approximate probability of contradiction . 9
8.2 Tables indicating discriminatory ability . 9
Annex A (informative) Examples of use of the procedures .13
Annex B (informative) Quality ratio related to β 100 % acceptance probability .16
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ISO 2859-4:2020(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.
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).
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 the 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 of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www .iso .org/
iso/ foreword .html.
This document was prepared by Technical Committee ISO/TC 69, Application of statistical methods,
Subcommittee SC 5, Acceptance sampling.
This third edition cancels and replaces the second edition (ISO 2859-4:2002), which has been technically
revised.
The main changes compared to the previous edition are as follows:
— the scope has been widened from testing for the percentage of nonconforming items to testing for
the percentage of nonconformities per item;
— the sampling and decision algorithm is more detailed and has been moved to an earlier position in
the document, so as to facilitate the operational use of the document;
— an LQR level 0 has been introduced, which can be used when a large probability of erroneously
contradicting a correctly declared quality level can be tolerated;
— an informative Annex B has been added to explain the mathematical-statistical background, and to
provide tables on quality ratios.
A list of all parts in the ISO 2859 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www .iso .org/ members .html.
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ISO 2859-4:2020(E)
Introduction
The procedures in this document differ in their scope from the procedures in ISO 2859-1 to ISO 2859-3.
The acceptance sampling systems specified in ISO 2859-1 to ISO 2859-3 are intended to be used in
bilateral agreements between two parties. The acceptance sampling procedures are supposed to be
used as simple, pragmatic rules for deciding on product release by inspection of only a limited sample
of a consignment, and therefore the procedures do not make reference (either explicitly or implicitly) to
any formally declared quality level.
Under acceptance sampling there is no sharp borderline between quality levels that should be
considered acceptable and qualities that should be rejected by the procedure. For the procedures in
ISO 2859-1, the two parties agree upon some acceptance quality limit (AQL) which is the worst tolerable
process average when a continuing series of lots is submitted. The switching rules and the sampling
schemes in ISO 2859-1 are designed to encourage the suppliers to have process averages consistently
better than the AQL selected. In order to keep sample sizes moderate, the protection against accepting
individual lots of inferior quality may be less than that provided by sampling plans targeted for
sentencing individual lots. The procedures in ISO 2859-2, on the contrary, are designed to provide good
protection against accepting individual lots of inferior quality (LQ), but at the expense of a possibly
high risk of not accepting lots of qualities that both parties actually would consider to be acceptable.
The procedures in ISO 2859-1 to ISO 2859-3 are well suited for acceptance sampling purposes, but they
should not be used in reviews, audits, systematic tests, etc. to verify a quality that has been declared for
some entity. The main reason is that the procedures have been indexed in terms of quality levels that
are relevant solely for the pragmatic purposes of acceptance sampling, and the various risks have been
balanced accordingly in a pragmatic attitude.
The procedures in this document have been developed as a response to the growing need for sampling
procedures suitable for formal, systematic inspections such as reviews or audits or systematic tests.
When performing such a formal inspection, it is necessary both for the inspecting authority and for the
body subject to inspection to consider the risks of reaching an incorrect conclusion. These risks have to
be accounted for explicitly in the design of review/auditing/testing procedures.
This document provides guidance and rules to assist the user in accounting for the risks of incorrect
conclusions in an informed manner.
The rules in this document have been devised such that there is only an acceptably small risk of
contradicting the declared quality level when in fact the actual level conforms to the declared level.
If it were also desired that there should be a similarly small risk of not contradicting the declared
quality level when in fact the actual quality level does not conform to the declared quality level, then it
would be necessary to investigate a rather large sample. Therefore, in order to obtain the benefit of a
moderate sample size, the procedures in this document have been devised in such a way that they allow
a somewhat higher risk of failing to contradict the declared quality level when in fact the actual quality
level does not conform to the declared quality level.
The wording of the result of the assessment should reflect this imbalance between the risks of reaching
incorrect conclusions. For the levels I, II, and III, when the sample result contradicts the declared quality
level, there is strong evidence of nonconformance to the declared quality level. When the sample result
does not contradict the declared quality level, this should be understood as “we have not, in this limited
sample, found strong evidence of nonconformance to the declared quality level”.
CAUTION — It should be noticed that, for sampling plans with very small sample sizes, one
should be aware of the poor discriminatory power under such sample sizes by referring to the
entries in Tables B.1, B.2, B.3 and B.4.
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INTERNATIONAL STANDARD ISO 2859-4:2020(E)
Sampling procedures for inspection by attributes —
Part 4:
Procedures for assessment of declared quality levels
1 Scope
This document establishes single sampling plans for conformance testing, i.e., for assessing whether
the quality level of a relevant audit population (lot, process, inventory, file etc) conforms to a declared
value. Sampling plans are provided corresponding to four levels of discriminatory ability. The limiting
quality ratio (LQR) (see Clause 4) of each sampling plan is given for reference. For levels I-III, the
sampling plans have been devised so as to obtain a risk no more than 5 % of contradicting a correct
declared quality level. The risk of failing to contradict an incorrectly declared quality level which is
related to the LQR is no more than 10 %. The sample sizes for level 0 are designed in a way that the LQR
factors of the sampling plans are compatible with the LQR factors for level I.
In contrast to the procedures in the other parts of the ISO 2859 series, the procedures in this document
are not applicable to acceptance assessment of lots. Generally, this document mainly focuses on
controlling type I error, which differs from the balancing of the risks in the procedures for acceptance
sampling.
This document can be used for various forms of quality inspection in situations where objective
evidence of conformity to some declared quality level is to be provided by means of inspection of a
sample. The procedures are applicable to entities such as lots, process output, etc. that allow random
samples of individual items to be taken from the entity.
The sampling plans provided in this document are applicable, but not limited, to the inspection of a
variety of targets such as:
— end items;
— components and raw materials;
— operations;
— materials in process;
— supplies in storage;
— maintenance operations;
— data or records;
— administrative procedures;
— accounting procedures or accounting entries;
— internal control procedures.
This document considers two types of quality models for discrete items and populations, as follows.
i) The conforming-nonconforming model, where each item is classified as conforming or
nonconforming, and where the quality indicator of a population of items is the proportion p of
nonconforming items, or, equivalently, the percentage 100 p of nonconforming items.
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ISO 2859-4:2020(E)
ii) The nonconformities model, where the number of nonconformities is counted on each item, and
where the quality indicator of a population of items is the average number λ of nonconformities
found on items in the population, or, equivalently, the percentage 100 λ of nonconformities on items
in the population.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements 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 9000, Quality management systems — Fundamentals and vocabulary
3 Terms, definitions, symbols and abbreviated terms
3.1 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 3534-1, ISO 3534-2 and
ISO 9000 and the following apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
3.1.1
non-rejection number
c
largest number of nonconforming items or nonconformities, respectively, found in the sample from the
population under investigation that does not lead to contradiction of the declared quality level
3.1.2
quality ratio
QR
ratio of the actual quality level to the declared quality level of the entity under investigation
3.1.3
limiting quality ratio
LQR
value of the quality ratio that is limited to a small risk of failing to contradict an incorrect declared
quality level
Note 1 to entry: In this document, the risk of failing to contradict an incorrect declared quality level is no more
than 10 %.
3.1.4
audit population
totality of items under audit inspection
3.1.5
audit population conformance
state of the audit population fulfilling imposed requirements
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ISO 2859-4:2020(E)
3.2 Symbols and abbreviated terms
c non-rejection number of a sampling plan
d number of nonconforming items or, respectively, nonconformities in the sample
n sample size of a sampling plan
DQL declared quality level
LQR limiting quality ratio
QR quality ratio
4 Sampling and decision procedure
4.1 Identifying a sampling plan
A single sampling plan (n, c) with sample size n and non-rejection number c is identified from Table 1 by
two characteristics:
a) the DQL, ranging from 0,01 percent to 10,00 percent;
b) the LQR level, ranging over 0, I, II, III.
Except a few exceptions for very small and very large DQL, the non-rejection numbers are constant
under each LQR level, with c = 0 under level 0, c = 1 under level I, c = 2 under level II, and c = 3 under
level III.
If the declared quality level is not one of the tabulated values, then the next higher tabulated value of
DQL shall be used to select the plan.
NOTE This results in an LQR that is somewhat higher, and to a probability of falsely contradicting a correct
declared quality level that is somewhat lower than the values given in Tables 2 to 5 (see 8.2).
EXAMPLE If an LQR level II is chosen with a DQL of 0,65 % nonconforming items, Table 1 yields a sampling
plan with a sample size n of 127, and a non-rejection number of nonconforming items c of 2, which provides an
LQR of 6,45 (see Table 4).
4.2 Drawing of samples
The sample shall be selected by simple random sampling or, where appropriate, by stratified or other
methods of random sampling from the entity.
When stratified sampling is used, the number of items from each stratum shall be selected in proportion
to the size of strata of the entity under investigation. The sub-sample from each stratum shall be
selected by simple random sampling from that stratum.
When sampling from a lot or a consignment, stratified sampling may be used with strata corresponding
to identifiable sub-lots.
When sampling from a process, stratified sampling may be used with strata corresponding to identified
sources of variation, for example tools, operators, shifts, etc.
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ISO 2859-4:2020(E)
If the sample size exceeds the size of the entity under investigation, then all items of the entity shall be
inspected.
EXAMPLE If, in the example considered in 4.1, the entity under investigation is the computer records
of administrative transactions during five business days, and the number of transactions each day are
approximately equal, then the total sample of n = 127 transactions are selected as five sub-samples, three
consisting of 25 transactions and two consisting of 26 transactions, selected by simple random sampling from
the transactions on each of the five days.
4.3 Decision objective
The audit population is considered as conforming if the population quality indicator (percentage of
nonconforming units, or percentage of nonconformities per item, respectively) is smaller or equal to
the DQL. Otherwise, the audit population is considered as nonconforming. The inspection objective
shall decide on the conformance of the population by taking one of two mutually exclusive decisions:
i) rejection, i.e., contradict the quality declaration expressed by the DQL and classify the population as
nonconforming; ii) non-rejection or acceptance, i.e., do not contradict the quality declaration expressed
by the DQL and classify the population as conforming.
4.4 Decision by sampling
Each of the n items in the sample shall be inspected, and the total number d of nonconforming items or,
respectively, of the nonconformities on items in the sample shall be determined.
— If d is less than or equal to the non-rejection number c, the decision is non-rejection, i.e., the declared
quality level is not contradicted.
— If d exceeds the non-rejection number c, the decision is rejection, i.e., the declared quality level is
contradicted.
EXAMPLE Assume that, in the situation considered by the Example in 4.1, two or fewer nonconforming items
are found in the sample of 127 items. Then the sample result does not contradict the DQL of 0,65 % nonconforming
items. If three or more nonconforming items are found, the sample evidence contradicts the DQL.
4.5 Disposition of nonconforming items
Any nonconforming items or items exhibiting nonconformities found in the sample shall not be returned
to the rest of the items unless the nonconforming items are brought to a conforming condition and
applicable administrative rules are followed.
Examples for the use of the sampling and decision procedure in industrial practice are provided in
Annex A.
5 Principles
Any assessment procedure based on sampling is subject to sampling risk, i.e., the risk of taking an
erroneous decision due to the limited information conveyed by a sample. In the present context, there
are two types of erroneous conclusions on an audit population:
a) rejection although the population is actually conforming, i.e., the population quality indicator
(percentage of nonconforming units, or percentage of nonconformities per item, respectively) is
actually smaller or equal to the DQL;
b) non-rejection although the population is actually nonconforming, i.e., the population quality
indicator (percentage of nonconforming units, or percentage of nonconformities per item,
respectively) is actually exceeding the DQL.
The corresponding error risks are expressed by the respective error probabilities, namely a) the
probability of rejecting an actually conforming population; b) the probability of not rejecting an actually
nonconforming population. The latter two risks shall be balanced by the design of the sampling plans.
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ISO 2859-4:2020(E)
The sampling plans for the LQR levels I, II and III are, with few exceptions for large DQLs, devised such
that the probability of contradicting an actually correct quality declaration is less than 5 %. For the
LQR level 0, the probability of contradicting an actually correct quality declaration is bounded by 20 %.
See Tables 2 through 5 for the detailed values.
For the inspection authority, it is vital to have a small probability of not detecting an incorrectly
declared quality level. The design of the sampling plans in this document focusses on the limiting
quality ratio (LQR): when the actual quality level is LQR×DQL, i.e., LQR times worse than the declared
quality level DQL, the procedures in this document have a risk of less than 10 % of failing to contradict
the declared quality level (corresponding to a 90 % probability of contradicting/rejecting the incorrect
declared quality level).
The ideal LQR would be close to 1,00. The latter ideal case cannot be achieved with practically feasible
sample sizes. This document considers four LQR levels 0, I, II and III. For all levels, the LQR values
range between 4 and 13, roughly. The sample sizes for level 0 are set to make sure that level 0 has
approximately the same LQR as level I at the same DQL value where the LQR ranges from 7,78 for the
largest DQL up to 12,34 for the smallest DQL. Under the latter design, it is inevitable that under level 0
the probabilities of contradicting an actually correct quality declaration are considerably higher than
under levels I, II, and III.
Technical details on the design of the sampling plans are provided in Annex B.
6 Declared quality level (DQL)
The DQL together with the LQR level is used for indexing the sampling plans provided in this document.
The values of DQL in the tables are known as preferred DQLs. The series of preferred DQL values
correspond to the series of preferred AQLs for inspection for nonconforming items given in ISO 2859-1.
There shall be a sound basis for the DQL used. The DQL shall not be deliberately overstated or
understated.
When a DQL is designated for a certain type quality characteristic, it indicates that the supplier has
good reason to believe that the quality is not worse than this designated value.
CAUTION — When the DQL is estimated from a sample taken from the entity of interest, the
procedures in this document shall not be used. Such a verification of an estimate from a sample
requires that the sample size and inspection result be taken into account in order to incorporate
the uncertainty associated with the estimate. This uncertainty affects the assessment of
the risks of making incorrect conclusions on the actual status of the entity of interest. Such
verification usually requires larger sample sizes than those used in the procedures described in
this document.
7 Sampling plans
7.1 General
The master Table 1 provides all single sampling plans (n, c) for the four LQR levels, indexed in the DQL
and the LQR level. Background on the choice of the LQR level and the properties of the corresponding
sampling plans are provided in 7.2 through 7.5.
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ISO 2859-4:2020(E)
Table 1 — Master table of sampling plans
DQL LQR Level 0 LQR Level I LQR Level II LQR Level III
(% nonconforming items
n c n c n c n c
or % nonconformities per item)
0,010 1 866 0 3 153 1 ← ←
0,015 1 185 0 2 001 1 ← ←
0,025 743 0 1 255 1 3 154 2 ←
0,040 476 0 804 1 2 001 2 3 152 3
0,065 298 0 503 1 1 253 2 2 004 3
0,100 188 0 317 1 802 2 1 252 3
0,150 119 0 202 1 502 2 803 3
0,250 75 0 127 1 317 2 503 3
0,400 49 0 82 1 202 2 317 3
0,650 31 0 52 1 127 2 202 3
1,000 20 0 34 1 82 2 127 3
1,500 13 0 22 1 52 2 82 3
2,500 9 0 15 1 34 2 52 3
4,000 → 10 1 22 2 34 3
6,500 → 7 1 15 2 22 3
10,000 → 5 1 10 2 16 3
The plans are indexed by the declared quality level (DQL) of nonconforming product and the limiting quality ratio (LQR) levels.
“→” means: use the sampling plan to the right, which corresponds to a smaller limiting quality ratio
“←” means: use the sampling plan to the left, which corresponds to a higher limiting quality ratio
7.2 LQR level 0
Level 0 may be used when a large probability of erroneously contradicting a correct declared quality
level may be tolerated. For level 0 sampling plans, the probabilities of erroneously contradicting a
correct declared quality level in Table 2 range in value from 16,3 % to 20,4 %, see Table 2. For example,
if the actual quality level equals the declared quality level 2,50 %, the probability of erroneously
contradicting the declared quality level is 20,4 %.
Table 2 — LQR and probability of falsely contradicting a correct DQL — LQR level 0 plans
DQL
Probability of falsely
n c LQR contradicting a correct
(% nonconforming items
DQL %, α
or % nonconformities per item)
0,010 1 866 0 12,34 17,0
0,015 1 185 0 12,95 16,3
0,025 743 0 12,40 17,0
0,040 476 0 12,09 17,3
0,065 298 0 11,89 17,6
0,10 188 0 12,25 17,1
0,15 119 0 12,90 16,4
0,25 75 0 12,28 17,1
0,40 49 0 11,75 17,8
0,65 31 0 11,43 18,3
1,0 20 0 11,51 18,2
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ISO 2859-4:2020(E)
Table 2 (continued)
DQL
Probability of falsely
n c LQR contradicting a correct
(% nonconforming items
DQL %, α
or % nonconformities per item)
1,5 13 0 11,81 17,8
...
NORME ISO
INTERNATIONALE 2859-4
Troisième édition
2020-06
Règles d'échantillonnage pour les
contrôles par attributs —
Partie 4:
Procédures pour l'évaluation des
niveaux déclarés de qualité
Sampling procedures for inspection by attributes —
Part 4: Procedures for assessment of declared quality levels
Numéro de référence
ISO 2859-4:2020(F)
©
ISO 2020
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ISO 2859-4:2020(F)
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Publié en Suisse
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ISO 2859-4:2020(F)
Sommaire Page
Avant-propos .iv
Introduction .v
1 Domaine d’application . 1
2 Références normatives . 2
3 Termes, définitions, symboles et termes abrégés . 2
3.1 Termes et définitions . 2
3.2 Symboles et termes abrégés . 3
4 Procédure d’échantillonnage et procédure décisionnelle . 3
4.1 Identification d’un plan d’échantillonnage . 3
4.2 Prélèvement des échantillons . 3
4.3 Objectif de la décision . 4
4.4 Décision par échantillonnage . 4
4.5 Traitement des individus non conformes . 4
5 Principes . 4
6 Niveau déclaré de qualité (NDQ) . 5
7 Plans d’échantillonnage . 6
7.1 Généralités . 6
7.2 Niveau RQL 0. 6
7.3 Niveau RQL I . 7
7.4 Niveau RQL II . 8
7.5 Niveau RQL III . 9
8 Informations complémentaires . 9
8.1 Courbes présentant la probabilité approximative de rejet . 9
8.2 Tableaux indicateurs de la capacité discriminante . 9
Annexe A (informative) Exemples d’utilisation des procédures .14
Annexe B (informative) Association du ratio-qualité à une probabilité d’acceptation de β 100 % .17
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ISO 2859-4:2020(F)
Avant-propos
L’ISO (Organisation internationale de normalisation) est une fédération mondiale d’organismes
nationaux de normalisation (comités membres de l’ISO). L’élaboration des Normes internationales est
en général confiée aux comités techniques de l’ISO. Chaque comité membre intéressé par une étude
a le droit de faire partie du comité technique créé à cet effet. Les organisations internationales,
gouvernementales et non gouvernementales, en liaison avec l’ISO participent également aux travaux.
L’ISO collabore étroitement avec la Commission électrotechnique internationale (IEC) en ce qui
concerne la normalisation électrotechnique.
Les procédures utilisées pour élaborer le présent document et celles destinées à sa mise à jour sont
décrites dans les Directives ISO/IEC, Partie 1. Il convient, en particulier de prendre note des différents
critères d’approbation requis pour les différents types de documents ISO. Le présent document a été
rédigé conformément aux règles de rédaction données dans les Directives ISO/IEC, Partie 2 (voir www
.iso .org/ directives).
L’attention est attirée sur le fait que certains des éléments du présent document peuvent faire l’objet de
droits de propriété intellectuelle ou de droits analogues. L’ISO ne saurait être tenue pour responsable
de ne pas avoir identifié de tels droits de propriété et averti de leur existence. Les détails concernant
les références aux droits de propriété intellectuelle ou autres droits analogues identifiés lors de
l’élaboration du document sont indiqués dans l’Introduction et/ou dans la liste des déclarations de
brevets reçues par l’ISO (voir www .iso .org/ brevets).
Les appellations commerciales éventuellement mentionnées dans le présent document sont données
pour information, par souci de commodité, à l’intention des utilisateurs et ne sauraient constituer un
engagement.
Pour une explication de la nature volontaire des normes, la signification des termes et expressions
spécifiques de l’ISO liés à l’évaluation de la conformité, ou pour toute information au sujet de l’adhésion
de l’ISO aux principes de l’Organisation mondiale du commerce (OMC) concernant les obstacles
techniques au commerce (OTC), voir le lien suivant: www .iso .org/ iso/ fr/ avant -propos .html.
Le présent document a été élaboré par le comité technique ISO/TC 69, Application des méthodes
statistiques, sous-comité SC 5, Échantillonnage en vue d’acceptation.
Cette troisième édition annule et remplace la deuxième édition (ISO 2859-4:2002), qui a fait l’objet
d’une révision technique.
Les principales modifications par rapport à l’édition précédente sont les suivantes :
— le domaine d'application a été élargi afin d'inclure non seulement le pourcentage d'individus non
conformes, mais également le pourcentage de non-conformités par individu ;
— les règles liées à l'échantillonnage et à la prise de décision sont décrites de manière plus détaillée et
elles ont été déplacées en début de document afin de faciliter l'utilisation dudit document ;
— le niveau 0 de ratio de qualité limite (RQL) a été introduit en vue d'être utilisé lorsqu’une probabilité
élevée de rejet indu d’un niveau déclaré de qualité correct peut être tolérée ;
— l'Annexe B, informative, a été ajoutée afin d'apporter des explications d'un point de vue mathématique
et statistique et de fournir des tableaux sur les ratios de qualité.
Une liste de toutes les parties de la série ISO 2859 se trouve sur le site Web de l’ISO.
Il convient que l’utilisateur adresse tout retour d’information ou toute question concernant le présent
document à l’organisme national de normalisation de son pays. Une liste exhaustive desdits organismes
se trouve à l’adresse www .iso .org/ fr/ members .html.
iv © ISO 2020 – Tous droits réservés
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ISO 2859-4:2020(F)
Introduction
Les procédures du présent document diffèrent, de par leur domaine d’application, des procédures
énoncées dans les normes ISO 2859-1 à ISO 2859-3. Les systèmes d’échantillonnage pour acceptation
indiqués dans les normes ISO 2859-1 à ISO 2859-3 sont destinés à être utilisés dans le cadre d’accords
bilatéraux entre les deux parties. Les procédures d’échantillonnage pour acceptation sont supposées
être utilisées en tant que règles simples et pragmatiques, afin de décider de la sortie d’un produit
en s’appuyant sur un contrôle portant sur un nombre limité d’échantillons d’une expédition ; par
conséquent, ces procédures ne se réfèrent (soit explicitement, soit implicitement) à aucun niveau de
qualité formellement déclaré.
En ce qui concerne l’acceptation des échantillons, il n’y a pas de limite précise entre les niveaux de
qualité qu’il convient de considérer comme étant acceptables et ceux qu’il convient de rejeter en vertu
de la procédure. Concernant les procédures de l’ISO 2859-1, les deux parties se mettent d’accord sur un
niveau de qualité acceptable (NQA), qui, sur une série continue de lots, correspond au niveau moyen
le plus défavorable du processus acceptable. Les règles de modification du contrôle et les procédures
d’échantillonnage données dans l’ISO 2859-1 sont destinées à encourager les fournisseurs à utiliser
des moyennes de processus considérablement meilleures que le NQA fixé. Afin de limiter les effectifs
d’échantillon, la protection contre l’acceptation de lots individuels de qualité inférieure peut être
moins importante que celle qui est obtenue avec des plans d’échantillonnage destinés à évaluer des
lots individuels. En revanche, les procédures de l’ISO 2859-2 sont destinées à garantir un bon niveau
de protection contre l’acceptation de lots individuels de qualité inférieure (proche de la qualité limite
[QL]), au prix cependant d’un risque potentiellement élevé de rejet de lots que les deux parties auraient
jugés acceptables.
Les procédures énoncées dans les normes ISO 2859-1 à ISO 2859-3 sont bien adaptées à l’échantillonnage
pour acceptation, mais il convient de ne pas les utiliser dans le cas de révisions, d’audits, d’essais
systématiques, etc., destinés à vérifier le niveau déclaré de qualité pour un produit. La principale raison
est que les procédures ont été indexées en termes de niveaux de qualité qui ne sont applicables qu’à des
finalités pragmatiques d’échantillonnage pour acceptation et que les différents risques ont été évalués
de la même manière.
Les procédures du présent document ont été conçues pour répondre aux besoins croissants de
procédures d’échantillonnage applicables à des contrôles formels et systématiques, tels que des
révisions, des audits ou des essais systématiques. Lors de l’exécution de ces contrôles formels, il est
nécessaire que l’autorité de contrôle ainsi que l’entité soumise au contrôle envisagent la possibilité
d’aboutir à une conclusion erronée. Ces risques de conclusion erronée sont à prendre en compte de
manière explicite lors de la planification des procédures de révision, d’audit et d’essai.
Le présent document fournit des recommandations et autres règles qui visent à aider l’utilisateur à
tenir compte des risques de conclusions erronées de manière documentée.
Les règles du présent document ont été conçues de sorte que le risque de rejeter le niveau déclaré de
qualité, lorsque le niveau réel de qualité est conforme au niveau déclaré, soit faible et acceptable.
De façon similaire, s’il convient également qu’il n’y ait qu’un faible risque de non-rejet du niveau déclaré
de qualité, quand le niveau réel de qualité n’est pas conforme au niveau déclaré de qualité, il serait
nécessaire de vérifier un échantillon d’effectif plus important. Par conséquent, afin de tirer profit d’un
effectif d’échantillon de taille modérée, les procédures du présent document ont été élaborées de sorte
que le risque de non-rejet des produits dont le niveau déclaré de qualité n’est pas conforme au niveau
réel de qualité soit plus important.
Il convient que l’expression du résultat de l’évaluation reflète le déséquilibre entre les risques d’aboutir
à des conclusions erronées. Lorsque, pour les niveaux I, II et III, le résultat de l’échantillonnage conduit
au rejet du niveau déclaré de qualité, ceci constitue une preuve flagrante de non-conformité au niveau
de qualité déclaré. Lorsque le résultat de l’échantillonnage ne conduit pas au rejet du niveau déclaré de
qualité, il convient que cela soit compris au sens qu’« il n’a pas été trouvé de preuve flagrante, dans cet
échantillon limité, de non-conformité au niveau déclaré de qualité ».
© ISO 2020 – Tous droits réservés v
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ISO 2859-4:2020(F)
ATTENTION — Il convient de noter que, pour les plans d’échantillonnage avec de très petits
effectifs d’échantillon, il convient d’avoir conscience du faible pouvoir discriminant de tels
effectifs d’échantillon, en se référant aux entrées des Tableaux B.1, B.2, B.3 et B.4.
vi © ISO 2020 – Tous droits réservés
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NORME INTERNATIONALE ISO 2859-4:2020(F)
Règles d'échantillonnage pour les contrôles par
attributs —
Partie 4:
Procédures pour l'évaluation des niveaux déclarés de
qualité
1 Domaine d’application
Le présent document définit des plans d’échantillonnage individuels à des fins d’essais de conformité,
c’est-à-dire afin d’évaluer si le niveau de qualité d’une population auditée donnée (lot, processus,
inventaire, fichier, etc.) est conforme à une valeur déclarée. Les plans d’échantillonnage correspondent
à quatre niveaux de capacité discriminante. Le ratio de qualité limite (RQL) (voir Article 4) de chaque
plan d’échantillonnage est donné en référence. Pour les niveaux I à III, les plans d’échantillonnage ont
été conçus de sorte que le risque de rejet d’un niveau déclaré de qualité satisfaisant ne dépasse pas 5 %.
Le risque de non-rejet d’un niveau déclaré de qualité insuffisant, qui est associé au RQL, ne dépasse pas
10 %. Les effectifs d’échantillon pour le niveau 0 sont planifiés de sorte que les facteurs RQL des plans
d’échantillonnage soient compatibles avec les facteurs RQL du niveau I.
Contrairement aux procédures données dans les autres parties de la série ISO 2859, les procédures
du présent document ne s’appliquent pas pour déterminer l’acceptation des lots. De manière générale,
le présent document porte principalement sur la maîtrise des erreurs de première espèce, qui est
différente de la pondération des risques appliquée dans les procédures pour l’acceptation d’échantillons.
Le présent document peut être utilisé pour différentes modalités de contrôle de la qualité, dans des
situations où la preuve tangible de conformité à un niveau déclaré de qualité est apportée en contrôlant
un échantillon. Ces procédures s’appliquent à des entités telles que des lots, des livrables de processus,
etc., qui permettent de prélever des échantillons d’individus au hasard.
Les plans d’échantillonnage fournis dans le présent document s’appliquent, sans s’y limiter, au contrôle
de différentes cibles telles que :
— les produits finis ;
— les composants et matières premières ;
— les opérations ;
— les matières en cours d’élaboration ;
— les équipements stockés ;
— les opérations de maintenance ;
— les données ou enregistrements ;
— les procédures administratives ;
— les procédures ou saisies comptables ;
— les procédures de contrôle interne.
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ISO 2859-4:2020(F)
Le présent document étudie deux types de modèles d’acceptation de la qualité pour les individus
distincts et les populations d’individus, présentés ci-après :
i) Le modèle de conformité/non-conformité, dans lequel chaque individu est classé comme étant
conforme ou non conforme, et où l’indicateur de qualité d’une population d’individus correspond
à la proportion p d’individus non conformes, ce qui équivaut au pourcentage 100 p d’individus
non conformes.
ii) Le modèle des non-conformités, dans lequel le nombre de non-conformités est comptabilisé pour
chaque individu, et où l’indicateur de qualité d’une population d’individus correspond au nombre
moyen λ de non-conformités constatées sur les individus de la population, ce qui équivaut au
pourcentage 100 λ de non-conformités constatées sur les individus de la population.
2 Références normatives
Les documents suivants sont cités dans le texte de sorte qu’ils constituent, pour tout ou partie de leur
contenu, des exigences du présent document. Pour les références datées, seule l’édition citée s’applique.
Pour les références non datées, la dernière édition du document de référence s’applique (y compris les
éventuels amendements).
ISO 3534-1, Statistique — Vocabulaire et symboles — Partie 1: Termes statistiques généraux et termes
utilisés en calcul des probabilités
ISO 3534-2, Statistique — Vocabulaire et symboles — Partie 2: Statistique appliquée
ISO 9000, Systèmes de management de la qualité — Principes essentiels et vocabulaire
3 Termes, définitions, symboles et termes abrégés
3.1 Termes et définitions
Pour les besoins du présent document, les termes et définitions de ISO 3534-1, ISO 3534-2 et l’ISO 9000
ainsi que les suivants, s’appliquent.
L’ISO et l’IEC tiennent à jour des bases de données terminologiques destinées à être utilisées en
normalisation, consultables aux adresses suivantes :
— ISO Online browsing platform : disponible à l’adresse https:// www .iso .org/ obp.
— IEC Electropedia : disponible à l’adresse http:// www .electropedia .org/ ;
3.1.1
limite avant rejet
c
le plus grand nombre d’individus non conformes ou de non-conformités trouvés dans l’échantillon issu
de la population contrôlée, qui n’entraîne pas un rejet du niveau déclaré de qualité
3.1.2
ratio-qualité
RQ
rapport entre le niveau réel de qualité et le niveau déclaré de qualité pour l’entité contrôlée
2 © ISO 2020 – Tous droits réservés
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ISO 2859-4:2020(F)
3.1.3
ratio de qualité limite
RQL
valeur du ratio-qualité qui est limitée à un faible risque de non-rejet d’un niveau déclaré de qualité
insuffisant
Note 1 à l'article: à l’article : Dans le présent document, le risque de non-rejet d’un niveau déclaré de qualité
insuffisant ne dépasse pas 10 %.
3.1.4
population auditée
totalité des individus soumis à un contrôle par audit
3.1.5
conformité de la population auditée
état de la population auditée satisfaisant aux exigences imposées
3.2 Symboles et termes abrégés
c limite avant rejet d’un plan d’échantillonnage
d nombre d’individus non conformes ou de non-conformités dans l’échantillon
n effectif d’échantillon d’un plan d’échantillonnage
NDQ niveau déclaré de qualité
RQL ratio de qualité limite
RQ ratio-qualité
4 Procédure d’échantillonnage et procédure décisionnelle
4.1 Identification d’un plan d’échantillonnage
Un plan d’échantillonnage unique (n, c) présentant un effectif d’échantillon n et une limite avant rejet c
est identifié à partir du Tableau 1 par deux caractéristiques :
a) le NDQ, allant de 0,01 % à 10,00 % ;
b) le niveau RQL, défini comme étant le niveau RQL 0, I, II ou III.
Sauf quelques exceptions relatives à un NDQ soit très faible, soit très important, les limites avant rejet
sont constantes pour chaque niveau RQL, avec c = 0 pour le niveau 0, c = 1 pour le niveau I, c = 2 pour le
niveau II, et c = 3 pour le niveau III.
Si le niveau déclaré de qualité n’est pas l’un des niveaux repris dans les tableaux, alors la valeur de NDQ
immédiatement supérieure doit être utilisée pour la sélection du plan.
NOTE Il en résulte un RQL légèrement supérieur, et une probabilité de rejet indu d’un niveau déclaré de
qualité suffisant légèrement inférieure aux valeurs données dans les Tableaux 2 à 5 (voir 8.2).
EXEMPLE Si un niveau RQL II est choisi avec un NDQ de 0,65 % d’individus non conformes, le Tableau 1 donne
un plan d’échantillonnage avec un effectif d’échantillon n de 127 et une limite avant rejet c pour les individus non
conformes de 2, ce qui donne un RQL de 6,45 (voir Tableau 4).
4.2 Prélèvement des échantillons
L’échantillon doit être prélevé dans l’entité par échantillonnage aléatoire simple, ou, le cas échéant, par
échantillonnage stratifié ou d’autres méthodes de prélèvement aléatoire d’échantillons.
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ISO 2859-4:2020(F)
Quand l’échantillonnage stratifié est utilisé, le nombre d’individus dans chaque strate doit être choisi
proportionnellement à la taille de la strate dans l’entité contrôlée. Le sous-échantillon de chaque strate
doit être prélevé par échantillonnage aléatoire simple dans cette strate.
Quand l’échantillonnage est effectué dans un lot ou dans une livraison, l’échantillonnage stratifié peut
être utilisé avec des strates correspondant à des sous-lots identifiables.
Quand l’échantillonnage s’applique à un processus, l’échantillonnage stratifié peut être utilisé avec des
strates correspondant à des sources de variation identifiées, par exemple des outils, des opérateurs, des
postes, etc.
Si l’effectif d’échantillon dépasse l’effectif de l’entité contrôlée, alors tous les individus de l’entité doivent
être contrôlés.
EXEMPLE Si, dans l’exemple considéré en 4.1, l’entité contrôlée est le dossier informatique de transactions
administratives réalisées pendant cinq jours ouvrables et que le nombre de transactions quotidiennes est
à peu près le même, l’échantillon total de n = 127 transactions est prélevé en tant que cinq sous-échantillons :
trois sous-échantillons de 25 transactions et deux sous-échantillons de 26 transactions, sélectionnées par
échantillonnage aléatoire simple parmi les transactions de chacun de ces cinq jours.
4.3 Objectif de la décision
La population auditée est considérée comme étant conforme si son indicateur de qualité (pourcentage
d’individus non conformes, ou pourcentage de non-conformités par individu, respectivement) est
inférieur ou égal au NDQ. Sinon, la population auditée est considérée comme étant non conforme.
L’objectif du contrôle doit être de conclure sur la conformité de la population en prenant l’une des
deux décisions ci-après, mutuellement exclusives : i) rejet, c’est-à-dire rejeter la déclaration de qualité
exprimée par le NDQ et classer la population comme étant non conforme ; ii) non-rejet ou acceptation,
c’est-à-dire ne pas rejeter la déclaration de qualité exprimée par le NDQ et classer la population comme
étant conforme.
4.4 Décision par échantillonnage
Chacun des n individus de l’échantillon doit être contrôlé et le nombre total d d’individus non conformes
ou, respectivement, le nombre de non-conformités sur les individus de l’échantillon, doit être déterminé.
— Si d est inférieur ou égal à la limite avant rejet c, la décision est le non-rejet, c’est-à-dire que le niveau
déclaré de qualité n’est pas rejeté.
— Si d est supérieur à la limite avant rejet c, la décision est le rejet, c’est-à-dire que le niveau déclaré de
qualité est rejeté.
EXEMPLE Il est pris pour hypothèse que dans la situation étudiée dans l’exemple donné en 4.1, un
maximum de deux individus non conformes a été décelé dans l’échantillon de 127 individus. Dès lors, le résultat
de l’échantillonnage n’est pas contraire au NDQ de 0,65 % d’individus non conformes. Si trois individus non
conformes, ou davantage, sont décelés, la preuve d’échantillonnage conduit au rejet du NDQ.
4.5 Traitement des individus non conformes
Les individus non conformes ou individus présentant des non-conformités décelés dans l’échantillon
ne doivent pas être réintégrés au reste des individus sans avoir été mis en conformité et sans que les
règles administratives applicables aient été observées.
Des exemples d’utilisation de la procédure d’échantillonnage et de la procédure décisionnelle dans la
pratique industrielle sont présentés à l’Annexe A.
5 Principes
Une quelconque procédure d’évaluation fondée sur l’échantillonnage est soumise au risque
d’échantillonnage, c’est-à-dire le risque de prendre une décision erronée en raison des informations
4 © ISO 2020 – Tous droits réservés
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ISO 2859-4:2020(F)
limitées que fournit un échantillon. Il existe dans le présent contexte deux types de conclusions
erronées relatives à une population auditée :
a) rejet alors que la population est en fait conforme, c’est-à-dire que son indicateur de qualité
(pourcentage d’individus non conformes, ou pourcentage de non-conformités par individu,
respectivement) est en fait inférieur ou égal au NDQ ;
b) non-rejet alors que la population est en fait non conforme, c’est-à-dire que son indicateur de
qualité (pourcentage d’individus non conformes, ou pourcentage de non-conformités par individu,
respectivement) est en fait supérieur au NDQ.
Les risques d’erreur correspondants sont exprimés par les probabilités d’erreur respectives, à savoir a)
la probabilité de rejet d’une population qui s’avère en fait conforme ; b) la probabilité de non-rejet d’une
population qui s’avère en fait non conforme. Ces deux derniers risques doivent être équilibrés lors de la
planification des plans d’échantillonnage.
Les plans d’échantillonnage pour les niveaux RQL I, II et III, à l’exception des pourcentages élevés de
NDQ, sont conçus de sorte que la probabilité de rejet d’une déclaration de qualité qui s’avère en fait
suffisante soit inférieure à 5 %. Pour le niveau RQL 0, la probabilité de rejet d’une déclaration de qualité
qui s’avère en fait suffisante est bornée à 20 %. Les valeurs détaillées peuvent être consultées dans les
Tableaux 2 à 5.
Pour l’autorité de contrôle, il est essentiel de disposer d’une probabilité réduite de ne pas déceler un
niveau déclaré de qualité insuffisant. La planification des plans d’échantillonnage dans le présent
document cible le ratio de qualité limite (RQL) : lorsque le niveau réel de qualité correspond à la formule
RQL×NDQ, c’est-à-dire un niveau de qualité qui soit « RQL fois moins bon que le niveau déclaré de
qualité NDQ », les procédures du présent document présentent un risque inférieur à 10 % de non-rejet
du niveau déclaré de qualité (correspondant à une probabilité de rejet du niveau déclaré de qualité
incorrect de 90 %).
Le RQL idéal serait au voisinage de 1,00, mais ne peut pas être atteint avec les effectifs d’échantillon
envisageables dans la pratique. Le présent document étudie quatre niveaux RQL : 0, I, II et III. Pour tous
ces niveaux, les valeurs du RQL sont globalement comprises entre 4 et 13. Les effectifs d’échantillon
pour le niveau 0 sont définis de façon à s’assurer que le niveau 0 présente approximativement le même
RQL que le niveau I à la même valeur NDQ, pour un RQL allant de 7,78 pour le pourcentage de NDQ
le plus élevé, jusqu’à 12,34 pour le pourcentage de NDQ le plus faible. Avec cette planification, il est
inévitable que dans le niveau 0, la probabilité de rejet d’une déclaration de qualité réelle correcte soit
considérablement plus élevée que dans les niveaux I, II et III.
Les détails techniques de la planification des plans d’échantillonnage sont présentés à l’Annexe B.
6 Niveau déclaré de qualité (NDQ)
Le NDQ est utilisé conjointement avec le niveau RQL pour indexer les plans d’échantillonnage présentés
dans le présent document. Les valeurs de NDQ données dans les tableaux sont connues comme étant les
valeurs NDQ recommandées. Les séries de valeurs NDQ recommandées correspondent aux séries de
valeurs recommandées du NQA pour le contrôle d’individus non conformes, données dans l’ISO 2859-1.
Il doit y
...
INTERNATIONAL ISO
STANDARD 2859-4
Third edition
Sampling procedures for inspection by
attributes —
Part 4:
Procedures for assessment of declared
quality levels
Règles d'échantillonnage pour les contrôles par attributs —
Partie 4: Procédures pour l'évaluation des niveaux déclarés de qualité
PROOF/ÉPREUVE
Reference number
ISO 2859-4:2020(E)
©
ISO 2020
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ISO 2859-4:2020(E)
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Published in Switzerland
ii PROOF/ÉPREUVE © ISO 2020 – All rights reserved
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ISO 2859-4:2020(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 2
3 Terms, definitions, symbols and abbreviations . 2
3.1 Terms and definitions . 2
3.2 Symbols and abbreviated terms. 3
4 Sampling and decision procedure . 3
4.1 Identifying a sampling plan. 3
4.2 Drawing of samples . 3
4.3 Decision objective . 4
4.4 Decision by sampling . 4
4.5 Disposition of nonconforming items. 4
5 Principles . 4
6 Declared quality level (DQL) . 5
7 Sampling plans . 5
7.1 General . 5
7.2 LQR level 0 . 6
7.3 LQR level I. 7
7.4 LQR level II . 7
7.5 LQR level III . 8
8 Further information . 9
8.1 Curves showing the approximate probability of contradiction . 9
8.2 Tables indicating discriminatory ability . 9
Annex A (informative) Examples of use of the procedures .13
Annex B (informative) Quality ratio related to β 100 % acceptance probability .16
© ISO 2020 – All rights reserved PROOF/ÉPREUVE iii
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ISO 2859-4:2020(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.
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).
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 the 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 of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www .iso .org/
iso/ foreword .html.
This document was prepared by Technical Committee ISO/TC 69, Application of statistical methods,
Subcommittee SC 5, Acceptance sampling.
This third edition cancels and replaces the second edition (ISO 2859-4:2002), which has been technically
revised.
The main changes compared to the previous edition are as follows:
— xxx xxxxxxx xxx xxxx
A list of all parts in the ISO 2859 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www .iso .org/ members .html.
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ISO 2859-4:2020(E)
Introduction
The procedures in this document differ in their scope from the procedures in ISO 2859-1 to ISO 2859-3.
The acceptance sampling systems specified in ISO 2859-1 to ISO 2859-3 are intended to be used in
bilateral agreements between two parties. The acceptance sampling procedures are supposed to be
used as simple, pragmatic rules for deciding on product release by inspection of only a limited sample
of a consignment, and therefore the procedures do not make reference (either explicitly or implicitly) to
any formally declared quality level.
Under acceptance sampling there is no sharp borderline between quality levels that should be
considered acceptable and qualities that should be rejected by the procedure. For the procedures in
ISO 2859-1, the two parties agree upon some acceptance quality limit (AQL) which is the worst tolerable
process average when a continuing series of lots is submitted. The switching rules and the sampling
schemes in ISO 2859-1 are designed to encourage the suppliers to have process averages consistently
better than the AQL selected. In order to keep sample sizes moderate, the protection against accepting
individual lots of inferior quality may be less than that provided by sampling plans targeted for
sentencing individual lots. The procedures in ISO 2859-2, on the contrary, are designed to provide good
protection against accepting individual lots of inferior quality (LQ), but at the expense of a possibly
high risk of not accepting lots of qualities that both parties actually would consider to be acceptable.
The procedures in ISO 2859-1 to ISO 2859-3 are well suited for acceptance sampling purposes, but they
should not be used in reviews, audits, systematic tests, etc. to verify a quality that has been declared for
some entity. The main reason is that the procedures have been indexed in terms of quality levels that
are relevant solely for the pragmatic purposes of acceptance sampling, and the various risks have been
balanced accordingly in a pragmatic attitude.
The procedures in this document have been developed as a response to the growing need for sampling
procedures suitable for formal, systematic inspections such as reviews or audits or systematic tests.
When performing such a formal inspection, it is necessary both for the inspecting authority and for the
body subject to inspection to consider the risks of reaching an incorrect conclusion. These risks have to
be accounted for explicitly in the design of review/auditing/testing procedures.
This document provides guidance and rules to assist the user in accounting for the risks of incorrect
conclusions in an informed manner.
The rules in this document have been devised such that there is only an acceptably small risk of
contradicting the declared quality level when in fact the actual level conforms to the declared level.
If it were also desired that there should be a similarly small risk of not contradicting the declared
quality level when in fact the actual quality level does not conform to the declared quality level, then it
would be necessary to investigate a rather large sample. Therefore, in order to obtain the benefit of a
moderate sample size, the procedures in this document have been devised in such a way that they allow
a somewhat higher risk of failing to contradict the declared quality level when in fact the actual quality
level does not conform to the declared quality level.
The wording of the result of the assessment should reflect this imbalance between the risks of reaching
incorrect conclusions. For the levels I, II, and III, when the sample result contradicts the declared quality
level, there is strong evidence of nonconformance to the declared quality level. When the sample result
does not contradict the declared quality level, this should be understood as “we have not, in this limited
sample, found strong evidence of nonconformance to the declared quality level”.
CAUTION — It should be noticed that, for sampling plans with very small sample sizes, one
should be aware of the poor discriminatory power under such sample sizes by referring to the
entries in Tables B.1, B.2, B.3 and B.4.
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INTERNATIONAL STANDARD ISO 2859-4:2020(E)
Sampling procedures for inspection by attributes —
Part 4:
Procedures for assessment of declared quality levels
1 Scope
This document establishes single sampling plans for conformance testing, i.e., for assessing whether
the quality level of a relevant audit population (lot, process, inventory, file etc) conforms to a declared
value. Sampling plans are provided corresponding to four levels of discriminatory ability. The limiting
quality ratio (LQR) (see Clause 4) of each sampling plan is given for reference. For levels I-III, the
sampling plans have been devised so as to obtain a risk no more than 5 % of contradicting a correct
declared quality level. The risk of failing to contradict an incorrectly declared quality level which is
related to the LQR is no more than 10 %. The sample sizes for level 0 are designed in a way that the LQR
factors of the sampling plans are compatible with the LQR factors for level I.
In contrast to the procedures in the other parts of the ISO 2859 series, the procedures in this document
are not applicable to acceptance assessment of lots. Generally, this document mainly focuses on
controlling type I error, which differs from the balancing of the risks in the procedures for acceptance
sampling.
This document can be used for various forms of quality inspection in situations where objective
evidence of conformity to some declared quality level is to be provided by means of inspection of a
sample. The procedures are applicable to entities such as lots, process output, etc. that allow random
samples of individual items to be taken from the entity.
The sampling plans provided in this document are applicable, but not limited, to the inspection of a
variety of targets such as:
— end items;
— components and raw materials;
— operations;
— materials in process;
— supplies in storage;
— maintenance operations;
— data or records;
— administrative procedures;
— accounting procedures or accounting entries;
— internal control procedures.
This document considers two types of quality models for discrete items and populations, as follows.
i) The conforming-nonconforming model, where each item is classified as conforming or
nonconforming, and where the quality indicator of a population of items is the proportion p of
nonconforming items, or, equivalently, the percentage 100 p of nonconforming items.
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ii) The nonconformities model, where the number of nonconformities is counted on each item, and
where the quality indicator of a population of items is the average number λ of nonconformities
found on items in the population, or, equivalently, the percentage 100 λ of nonconformities on items
in the population.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements 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 9000, Quality management systems — Fundamentals and vocabulary
3 Terms, definitions, symbols and abbreviations
3.1 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 3534-1, ISO 3534-2 and
ISO 9000 and the following apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
3.1.1
non-rejection number
c
largest number of nonconforming items or nonconformities, respectively, found in the sample from the
population under investigation that does not lead to contradiction of the declared quality level
3.1.2
quality ratio
QR
ratio of the actual quality level to the declared quality level of the entity under investigation
3.1.3
limiting quality ratio
LQR
value of the quality ratio that is limited to a small risk of failing to contradict an incorrect declared
quality levelNote 1 to entry: In this document, the risk of failing to contradict an incorrect declared
quality level is no more than 10 %.
3.1.4
audit population
totality of items under audit inspection
3.1.5
audit population conformance
state of the audit population fulfilling imposed requirements
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3.2 Symbols and abbreviated terms
c non-rejection number of a sampling plan
d number of nonconforming items or, respectively, nonconformities in the sample
n sample size of a sampling plan
DQL declared quality level
LQR limiting quality ratio
QR quality ratio
4 Sampling and decision procedure
4.1 Identifying a sampling plan
A single sampling plan (n, c) with sample size n and non-rejection number c is identified from Table 1 by
two characteristics:
a) the DQL, ranging from 0,01 percent to 10,00 percent;
b) the LQR level, ranging over 0, I, II, III.
Except a few exceptions for very small and very large DQL, the non-rejection numbers are constant
under each LQR level, with c = 0 under level 0, c = 1 under level I, c = 2 under level II, and c = 3 under
level III.
If the declared quality level is not one of the tabulated values, then the next higher tabulated value of
DQL shall be used to select the plan.
NOTE This results in an LQR that is somewhat higher, and to a probability of falsely contradicting a correct
declared quality level that is somewhat lower than the values given in Tables 2 to 5 (see 8.2).
EXAMPLE If an LQR level II is chosen with a DQL of 0,65 % nonconforming items, Table 1 yields a sampling
plan with a sample size n of 127, and a non-rejection number of nonconforming items c of 2, which provides an
LQR of 6,45 (see Table 4).
4.2 Drawing of samples
The sample shall be selected by simple random sampling or, where appropriate, by stratified or other
methods of random sampling from the entity.
When stratified sampling is used, the number of items from each stratum shall be selected in proportion
to the size of strata of the entity under investigation. The sub-sample from each stratum shall be
selected by simple random sampling from that stratum.
When sampling from a lot or a consignment, stratified sampling may be used with strata corresponding
to identifiable sub-lots.
When sampling from a process, stratified sampling may be used with strata corresponding to identified
sources of variation, for example tools, operators, shifts, etc.
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If the sample size exceeds the size of the entity under investigation, then all items of the entity shall be
inspected.
EXAMPLE If, in the example considered in 4.1, the entity under investigation is the computer records
of administrative transactions during five business days, and the number of transactions each day are
approximately equal, then the total sample of n = 127 transactions are selected as five sub-samples, three
consisting of 25 transactions and two consisting of 26 transactions, selected by simple random sampling from
the transactions on each of the five days.
4.3 Decision objective
The audit population is considered as conforming if the population quality indicator (percentage of
nonconforming units, or percentage of nonconformities per item, respectively) is smaller or equal to
the DQL. Otherwise, the audit population is considered as nonconforming. The inspection objective
shall decide on the conformance of the population by taking one of two mutually exclusive decisions:
i) rejection, i.e., contradict the quality declaration expressed by the DQL and classify the population as
nonconforming; ii) non-rejection or acceptance, i.e., do not contradict the quality declaration expressed
by the DQL and classify the population as conforming.
4.4 Decision by sampling
Each of the n items in the sample shall be inspected, and the total number d of nonconforming items or,
respectively, of the nonconformities on items in the sample shall be determined.
— If d is less than or equal to the non-rejection number c, the decision is non-rejection, i.e., the declared
quality level is not contradicted.
— If d exceeds the non-rejection number c, the decision is rejection, i.e., the declared quality level is
contradicted.
EXAMPLE Assume that, in the situation considered by the Example in 4.1, two or fewer nonconforming items
are found in the sample of 127 items. Then the sample result does not contradict the DQL of 0,65 % nonconforming
items. If three or more nonconforming items are found, the sample evidence contradicts the DQL.
4.5 Disposition of nonconforming items
Any nonconforming items or items exhibiting nonconformities found in the sample shall not be returned
to the rest of the items unless the nonconforming items are brought to a conforming condition and
applicable administrative rules are followed.
Examples for the use of the sampling and decision procedure in industrial practice are provided in
Annex A.
5 Principles
Any assessment procedure based on sampling is subject to sampling risk, i.e., the risk of taking an
erroneous decision due to the limited information conveyed by a sample. In the present context, there
are two types of erroneous conclusions on an audit population:
a) rejection although the population is actually conforming, i.e., the population quality indicator
(percentage of nonconforming units, or percentage of nonconformities per item, respectively) is
actually smaller or equal to the DQL;
b) non-rejection although the population is actually nonconforming, i.e., the population quality
indicator (percentage of nonconforming units, or percentage of nonconformities per item,
respectively) is actually exceeding the DQL.
The corresponding error risks are expressed by the respective error probabilities, namely a) the
probability of rejecting an actually conforming population; b) the probability of not rejecting an actually
nonconforming population. The latter two risks shall be balanced by the design of the sampling plans.
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ISO 2859-4:2020(E)
The sampling plans for the LQR levels I, II and III are, with few exceptions for large DQLs, devised such
that the probability of contradicting an actually correct quality declaration is less than 5 %. For the
LQR level 0, the probability of contradicting an actually correct quality declaration is bounded by 20 %.
See Tables 2 through 5 for the detailed values.
For the inspection authority, it is vital to have a small probability of not detecting an incorrectly
declared quality level. The design of the sampling plans in this document focusses on the limiting
quality ratio (LQR): when the actual quality level is LQR×DQL, i.e., LQR times worse than the declared
quality level DQL, the procedures in this document have a risk of less than 10 % of failing to contradict
the declared quality level (corresponding to a 90 % probability of contradicting/rejecting the incorrect
declared quality level).
The ideal LQR would be close to 1,00. The latter ideal case cannot be achieved with practically feasible
sample sizes. This document considers four LQR levels 0, I, II and III. For all levels, the LQR values
range between 4 and 13, roughly. The sample sizes for level 0 are set to make sure that level 0 has
approximately the same LQR as level I at the same DQL value where the LQR ranges from 7,78 for the
largest DQL up to 12,34 for the smallest DQL. Under the latter design, it is inevitable that under level 0
the probabilities of contradicting an actually correct quality declaration are considerably higher than
under levels I, II, and III.
Technical details on the design of the sampling plans are provided in Annex B.
6 Declared quality level (DQL)
The DQL together with the LQR level is used for indexing the sampling plans provided in this document.
The values of DQL in the tables are known as preferred DQLs. The series of preferred DQL values
correspond to the series of preferred AQLs for inspection for nonconforming items given in ISO 2859-1.
There shall be a sound basis for the DQL used. The DQL shall not be deliberately overstated or
understated.
When a DQL is designated for a certain type quality characteristic, it indicates that the supplier has
good reason to believe that the quality is not worse than this designated value.
CAUTION — When the DQL is estimated from a sample taken from the entity of interest, the
procedures in this document shall not be used. Such a verification of an estimate from a sample
requires that the sample size and inspection result be taken into account in order to incorporate
the uncertainty associated with the estimate. This uncertainty affects the assessment of
the risks of making incorrect conclusions on the actual status of the entity of interest. Such
verification usually requires larger sample sizes than those used in the procedures described in
this document.
7 Sampling plans
7.1 General
The master Table 1 provides all single sampling plans (n, c) for the four LQR levels, indexed in the DQL
and the LQR level. Background on the choice of the LQR level and the properties of the corresponding
sampling plans are provided in 7.2 through 7.5.
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Table 1 — Master table of sampling plans
DQL LQR Level 0 LQR Level I LQR Level II LQR Level III
(% nonconforming items
n c n c n c n c
or % nonconformities per item)
0,010 1 866 0 3 153 1 ← ←
0,015 1 185 0 2 001 1 ← ←
0,025 743 0 1 255 1 3 154 2 ←
0,040 476 0 804 1 2 001 2 3 152 3
0,065 298 0 503 1 1 253 2 2 004 3
0,100 188 0 317 1 802 2 1 252 3
0,150 119 0 202 1 502 2 803 3
0,250 75 0 127 1 317 2 503 3
0,400 49 0 82 1 202 2 317 3
0,650 31 0 52 1 127 2 202 3
1,000 20 0 34 1 82 2 127 3
1,500 13 0 22 1 52 2 82 3
2,500 9 0 15 1 34 2 52 3
4,000 → 10 1 22 2 34 3
6,500 → 7 1 15 2 22 3
10,000 → 5 1 10 2 16 3
The plans are indexed by the declared quality level (DQL) of nonconforming product and the limiting quality ratio (LQR) levels.
“→” means: use the sampling plan to the right, which corresponds to a smaller limiting quality ratio
“←” means: use the sampling plan to the left, which corresponds to a higher limiting quality ratio
7.2 LQR level 0
Level 0 may be used when a large probability of erroneously contradicting a correct declared quality
level may be tolerated. For level 0 sampling plans, the probabilities of erroneously contradicting a
correct declared quality level in Table 2 range in value from 16,3 % to 20,4 %, see Table 2. For example,
if the actual quality level equals the declared quality level 2,50 %, the probability of erroneously
contradicting the declared quality level is 20,4 %.
Table 2 — LQR and probability of falsely contradicting a correct DQL — LQR level 0 plans
DQL
Probability of falsely
n c LQR contradicting a correct
(% nonconforming items
DQL %, α
or % nonconformities per item)
0,010 1 866 0 12,34 17,0
0,015 1 185 0 12,95 16,3
0,025 743 0 12,40 17,0
0,040 476 0 12,09 17,3
0,065 298 0 11,89 17,6
0,10 188 0 12,25 17,1
0,15 119 0 12,90 16,4
0,25 75 0 12,28 17,1
0,40 49 0 11,75 17,8
0,65 31 0 11,43 18,3
1,0 20 0 11,51 18,2
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Table 2 (continued)
DQL
Probability of falsely
n c LQR contradicting a correct
(% nonconforming items
DQL %, α
or % nonconformities per item)
1,5 13 0 11,81 17,8
2,5 9 0 10,23 20,4
EXAMPLE Suppose that the plan n = 20, c = 0, corresponding to a DQL of 1,0 % nonconforming items, is used.
For this plan, there is a 10 % risk of failing to contradict DQL when the actual quality level is 11,51 (LQR) times
worse than the DQL, i.e. the actual quality level is 11,51 % nonconforming items.
If, on the contrary, the actual quality level had been the DQL, i.e. if the actual quality level is 1,0
...
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