SIST ISO 2859-1:2003
(Main)Sampling procedures for inspection by attributes -- Part 1: Sampling schemes indexed by acceptance quality limit (AQL) for lot-by-lot inspection
Sampling procedures for inspection by attributes -- Part 1: Sampling schemes indexed by acceptance quality limit (AQL) for lot-by-lot inspection
1.1 This part of ISO 2859 specifies an acceptance sampling system for inspection by attributes. It is indexed in
terms of the acceptance quality limit (AQL).
Its purpose is to induce a supplier through the economic and psychological pressure of lot non-acceptance to maintain
a process average at least as good as the specified acceptance quality limit, while at the same time providing an upper
limit for the risk to the consumer of accepting the occasional poor lot.
Sampling schemes designated in this part of ISO 2859 are applicable, but not limited, to inspection of
¾ end items,
¾ components and raw materials,
¾ operations,
¾ materials in process,
¾ supplies in storage,
¾ maintenance operations,
¾ data or records, and
¾ administrative procedures.
1.2 These schemes are intended primarily to be used for a continuing series of lots, that is, a series long enough to
allow the switching rules (9.3) to be applied. These rules provide:
a) a protection to the consumer (by means of a switch to tightened inspection or discontinuation of sampling
inspection) should a deterioration in quality be detected;
b) an incentive (at the discretion of the responsible authority) to reduce inspection costs (by means of a switch to
reduced inspection) should consistently good quality be achieved.
Sampling plans in this part of ISO 2859 may also be used for the inspection of lots in isolation but, in this case the user
is strongly advised to consult the operating characteristic curves to find a plan that will yield the desired protection (see
12.6). In that case, the user is also referred to the sampling plans indexed by limiting quality (LQ) given in ISO 2859-2.
Règles d'échantillonnage pour les contrôles par attributs -- Partie 1: Procédures d'échantillonnage pour les contrôles lot par lot, indexés d'après le niveau de qualité acceptable (NQA)
Les procédures d'échantillonnage contenues dans la présente partie de l'ISO 2859 sont applicables, mais d'une manière non limitative, aux contrôles de différents domaines tels que: -produits Unis -composants ou madères premières -opérations -matériels en cours de fabrication -fournitures en stock -opérations d'entretien -informations ou enregistrements -procédures administratives. Ces procédures sont principalement destinées au contrôle de séries continues de lots, c'est-à-dire de séries suffisamment importantes pour permettre l'application des règles de modification du contrôle. Ces règles ont pour but: a) d'assurer la protection du client en cas de détection d'une détérioration de la qualité (par le passage à un contrôle renforcé ou l'interruption du contrôle); b) de constituer une incitation à réduire les coûts de contrôle (à la discrétion de l'autorité responsable) si la qualité se maintient continuellement bonne (par passage à un contrôle réduit). Les plans créchantillonnage de la présente partie de l'ISO 2859 peuvent aussi être utilisés pour le contrôle de lots isolés mais, dans ce cas, l'utilisateur doit avoir soin de consulter les courbes d'efficacité afin de trouver un plan qui lui donnera la protection désirée. Dans ce cas, l'utilisateur est également renvoyé aux plans d'échantillonnage indexés d'après la qualité limite (QL) spécifiés dans l'ISO 2859-2.
Postopki vzorčenja pri kontroli po opisnih (atributivnih) spremenljivkah – 1. del : Pravila vzorčenja razvrščena po prevzemni meji kakovosti (AQL) za kontrolo zaporednih partij (lotov)
General Information
Relations
Overview
ISO 2859-1:1999 specifies an acceptance sampling system for inspection by attributes, indexed by the Acceptance Quality Limit (AQL) for lot-by-lot inspection. Its purpose is to provide a standardized framework that pressures suppliers (economically and psychologically) to maintain process quality at or above a specified AQL while bounding consumer risk of accepting poor lots. The standard supports inspection of end items, components, in‑process materials, stored supplies, maintenance operations, records and administrative procedures.
Key topics and requirements
- AQL-based sampling schemes: Plans are indexed by AQL to determine sample sizes and acceptance numbers for lot acceptance decisions.
- Inspection modes: Defines normal, tightened and reduced inspection with formal switching rules to move between modes based on lot history.
- Sampling plan types: Includes single, double and multiple sampling schemes (master tables for normal/tightened/reduced inspection).
- Risk and performance tables: Tables and curves for producer’s risk, consumer’s risk quality, average outgoing quality limits (AOQL) and operating characteristic (OC) curves to assess plan performance.
- Sample size code letters and extensive tabulated plans: Code letters map lot sizes to sample sizes; auxiliary and fractional acceptance number plans are included for smoother progression between acceptance numbers.
- Optional features: Fractional acceptance number plans, skip‑lot sampling as an alternative to reduced inspection, and guidance for non‑constant sampling plans (informative Annex A).
- Use context: Primarily intended for a continuing series of lots (so switching rules can be applied), but tables and OC curves are provided for isolated-lot use with caution.
Practical applications
- Incoming inspection and supplier control: standardized lot acceptance criteria for purchased parts and materials.
- Production and in‑process quality control: sampling instead of 100% inspection when attributes (conforming/nonconforming) are measured.
- Storage, maintenance and administrative audits: periodic lot checks using attribute sampling.
- Quality contracts and procurement specifications: a common, internationally recognized method to define inspection obligations and acceptance criteria.
- Statistical quality practitioners use OC curves and risk tables to select plans that meet organizational tolerance for consumer/producer risk.
Who should use it
- Quality engineers, QA/QC managers and inspection teams
- Procurement and supplier quality professionals
- Regulatory bodies and auditors specifying acceptance criteria
- Statisticians designing sampling schemes for manufacturing or service processes
Related standards
- ISO 2859-0: Introduction and illustrative examples (recommended companion)
- ISO 2859-3: Skip‑lot sampling procedures (alternative to reduced inspection)
- ISO 3534 series: Vocabulary and symbols for statistics and quality control
Keywords: ISO 2859-1, AQL, acceptance sampling, lot-by-lot inspection, sampling plans, OC curves, producer’s risk, consumer’s risk, single sampling, double sampling, multiple sampling.
Standards Content (Sample)
SLOVENSKI STANDARD
01-junij-2003
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3UDYLODY]RUþHQMDUD]YUãþHQDSRSUHY]HPQLPHMLNDNRYRVWL $4/ ]DNRQWUROR
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Sampling procedures for inspection by attributes -- Part 1: Sampling schemes indexed by
acceptance quality limit (AQL) for lot-by-lot inspection
Règles d'échantillonnage pour les contrôles par attributs -- Partie 1: Procédures
d'échantillonnage pour les contrôles lot par lot, indexés d'après le niveau de qualité
acceptable (NQA)
Ta slovenski standard je istoveten z: ISO 2859-1:1999
ICS:
03.120.30 8SRUDEDVWDWLVWLþQLKPHWRG Application of statistical
methods
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
INTERNATIONAL ISO
STANDARD 2859-1
Second edition
1999-11-15
Sampling procedures for inspection by
attributes —
Part 1:
Sampling schemes indexed by acceptance
quality limit (AQL) for lot-by-lot inspection
Règles d'échantillonnage pour les contrôles par attributs —
Partie 1: Procédures d'échantillonnage pour les contrôles lot par lot,
indexés d'après le niveau de qualité acceptable (NQA)
A
Reference number
Contents
1 Scope .1
2 Normative references .2
3 Terms, definitions and symbols.2
4 Expression of nonconformity.7
5 Acceptance quality limit (AQL).8
6 Submission of product for sampling.8
7 Acceptance and non-acceptance.9
8 Drawing of samples.9
9 Normal, tightened and reduced inspection.10
10 Sampling plans .13
11 Determination of acceptability .14
12 Further information .14
13 Fractional acceptance number plans for single sampling (optional) .16
Tables
1 Sample size code letters .19
2-A Single sampling plans for normal inspection (Master table).20
2-B Single sampling plans for tightened inspection (Master table) .21
2-C Single sampling plans for reduced inspection (Master table).22
3-A Double sampling plans for normal inspection (Master table) .23
3-B Double sampling plans for tightened inspection (Master table).24
3-C Double sampling plans for reduced inspection (Master table) .25
4-A Multiple sampling plans for normal inspection (Master table).26
4-B Multiple sampling plans for tightened inspection (Master table).29
© ISO 1999
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic
or mechanical, including photocopying and microfilm, without permission in writing from the publisher.
International Organization for Standardization
Case postale 56 • CH-1211 Genève 20 • Switzerland
Internet iso@iso.ch
Printed in Switzerland
ii
© ISO
4-C Multiple sampling plans for reduced inspection (Master table). 32
5-A Producer's risk for normal inspection . 35
5-B Producer's risk for tightened inspection. 36
5-C Producer's risk for reduced inspection . 37
6-A Consumer's risk quality for normal inspection . 38
6-B Consumer's risk quality for tightened inspection . 39
6-C Consumer's risk quality for reduced inspection . 40
7-A Consumer's risk quality for normal inspection . 41
7-B Consumer's risk quality for tightened inspection . 42
7-C Consumer's risk quality for reduced inspection . 43
8-A Average outgoing quality limits for normal inspection (Single sampling plans). 44
8-B Average outgoing quality limits for tightened inspection (Single sampling plans) . 45
9 Average sample size curves for single, double and multiple sampling (normal, tightened and reduced
inspection). 46
10-A Tables for sample size code letter A (Individual plans). 48
10-B Tables for sample size code letter B (Individual plans). 50
10-C Tables for sample size code letter C (Individual plans). 52
10-D Tables for sample size code letter D (Individual plans). 54
10-E Tables for sample size code letter E (Individual plans) . 56
10-F Tables for sample size code letter F (Individual plans). 58
10-G Tables for sample size code letter G (Individual plans). 60
10-H Tables for sample size code letter H (Individual plans). 62
10-J Tables for sample size code letter J (Individual plans) . 64
10-K Tables for sample size code letter K (Individual plans). 66
10-L Tables for sample size code letter L (Individual plans). 68
10-M Tables for sample size code letter M (Individual plans) . 70
10-N Tables for sample size code letter N (Individual plans). 72
10-P Tables for sample size code letter P (Individual plans) . 74
10-Q Tables for sample size code letter Q (Individual plans). 76
10-R Tables for sample size code letter R (Individual plans). 78
10-S Tables for sample size code letter S (Individual plans) . 80
iii
© ISO
11-A Single sampling plans for normal inspection (Auxiliary master table) .81
11-B Single sampling plans for tightened inspection (Auxiliary master table).82
11-C Single sampling plans for reduced inspection (Auxiliary master table) .83
12 Scheme OC curves (Normalized) .84
Annex A (informative) Example for non-constant sampling plan .85
Bibliography.87
iv
© ISO
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO
member bodies). The work of preparing International Standards is normally carried out through ISO technical
committees. Each member body interested in a subject for which a technical committee has been established has
the right to be represented on that committee. International organizations, governmental and non-governmental, in
liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical
Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 3.
Draft International Standards adopted by the technical committees are circulated to the member bodies for voting.
Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote.
International Standard ISO 2859-1 was prepared by Technical Committee ISO/TC 69, Applications of statistical
methods, Subcommittee SC 5, Acceptance sampling.
This second edition of ISO 2859-1 cancels and replaces the first edition (ISO 2859-1:1989) of which it constitutes a
technical revision.
Significant changes in this edition include:
a new procedure for switching from normal to reduced inspection;
a reference to skip-lot sampling as an alternative to reduced inspection;
the term "limiting quality" has been changed to "consumer's risk quality" in the heading of Tables 6-A, 6-B, 6-C,
7-A, 7-B and 7-C;
a new table has been added giving producer's risk as the probability of rejection of lots with percent
nonconforming equal to the AQL;
optional fractional acceptance number plans have been added; the purpose of these plans is to provide a
consistent progression from the plans for acceptance number zero to the acceptance number 1 plans. The
fractional acceptance number plans are found in Tables 11-A, 11-B and 11-C, where they take the place of the
arrows in the corresponding positions in tables 2-A, 2-B and 2-C;
reduced plans have been changed to eliminate the gap between the acceptance and rejection numbers;
some changes have been made to the double sampling plans to provide a smaller average sample size;
multiple sampling plans have been changed to five stages rather than seven. The change has not increased
the average sample size. Some of the new plans have a smaller average sample size than their counterparts in
the previous edition;
scheme operating characteristic curves have been added as Table 12.
ISO 2859 consists of the following parts, under the general title Sampling procedures for inspection by attributes:
Part 0: Introduction to the ISO 2859 attribute sampling system
Part 1: Sampling schemes indexed by acceptance quality limit (AQL) for lot-by-lot inspection
Part 2: Sampling plans indexed by limiting quality (LQ) for isolated lot inspection
v
© ISO
Part 3: Skip-lot sampling procedures
It is highly recommended that this part of ISO 2859 be used together with ISO 2859-0, which contains illustrative
examples.
Annex A of this part of ISO 2859 is for information only.
vi
INTERNATIONAL STANDARD © ISO ISO 2859-1:1999(E)
Sampling procedures for inspection by attributes —
Part 1:
Sampling schemes indexed by acceptance quality limit (AQL) for
lot-by-lot inspection
1 Scope
1.1 This part of ISO 2859 specifies an acceptance sampling system for inspection by attributes. It is indexed in
terms of the acceptance quality limit (AQL).
Its purpose is to induce a supplier through the economic and psychological pressure of lot non-acceptance to maintain
a process average at least as good as the specified acceptance quality limit, while at the same time providing an upper
limit for the risk to the consumer of accepting the occasional poor lot.
Sampling schemes designated in this part of ISO 2859 are applicable, but not limited, to inspection of
end items,
components and raw materials,
operations,
materials in process,
supplies in storage,
maintenance operations,
data or records, and
administrative procedures.
1.2 These schemes are intended primarily to be used for a continuing series of lots, that is, a series long enough to
allow the switching rules (9.3) to be applied. These rules provide:
a) a protection to the consumer (by means of a switch to tightened inspection or discontinuation of sampling
inspection) should a deterioration in quality be detected;
b) an incentive (at the discretion of the responsible authority) to reduce inspection costs (by means of a switch to
reduced inspection) should consistently good quality be achieved.
Sampling plans in this part of ISO 2859 may also be used for the inspection of lots in isolation but, in this case the user
is strongly advised to consult the operating characteristic curves to find a plan that will yield the desired protection (see
12.6). In that case, the user is also referred to the sampling plans indexed by limiting quality (LQ) given in ISO 2859-2.
© ISO
2 Normative references
The following normative documents contain provisions which, through reference in this text, constitute provisions of
this part of ISO 2859. For dated references, subsequent amendments to, or revisions of, any of these publications
do not apply. However, parties to agreements based on this part of ISO 2859 are encouraged to investigate the
possibility of applying the most recent editions of the normative documents indicated below. For undated
references, the latest edition of the normative document referred to applies. Members of ISO and IEC maintain
registers of currently valid International Standards.
ISO 2859-3:1991, Sampling procedures for inspection by attributes — Part 3: Skip-lot sampling procedures.
ISO 3534-1:1993, Statistics — Vocabulary and symbols — Part 1: Probability and general statistical terms.
ISO 3534-2:1993, Statistics — Vocabulary and symbols — Part 2: Statistical quality control.
3 Terms, definitions and symbols
3.1 Terms and definitions
For the purposes of this part of ISO 2859, the terms and definitions given in ISO 3534-1 and ISO 3534-2 and the
following apply.
NOTE For ease of reference, the definitions of some of these terms are quoted from ISO 3534-1 and ISO 3534-2, while
others are redefined or newly defined.
3.1.1
inspection
activity such as measuring, examining, testing or gauging one or more characteristics of a product or service, and
comparing the results with specified requirements in order to establish whether conformity is achieved for each
characteristic
3.1.2
original inspection
first inspection of a lot according to the provisions of this part of ISO 2859
NOTE This is to be distinguished from the inspection of a lot which has been resubmitted after previous non-acceptance.
3.1.3
inspection by attributes
inspection whereby either the item is classified simply as conforming or nonconforming with respect to a specified
requirement or set of specified requirements, or the number of nonconformities in the item is counted
NOTE Inspection by attributes includes inspection for conformity of items as well as inspection for number of
nonconformities per hundred items.
3.1.4
item
that which can be individually described and considered
EXAMPLES
a physical item;
a defined quantity of material;
a service, an activity or a process;
an organization or a person; or
some combination thereof.
© ISO
3.1.5
nonconformity
non-fulfilment of a specified requirement
NOTE 1 In some situations specified requirements coincide with customer usage requirements (see defect, 3.1.6). In other
situations they may not coincide, being either more or less stringent, or the exact relationship between the two is not fully
known or understood.
NOTE 2 Nonconformity will generally be classified according to its degree of seriousness such as:
Class A: those nonconformities of a type considered to be of the highest concern; in acceptance sampling such types of
nonconformities will be assigned a very small acceptance quality limit value;
Class B: those nonconformities of a type considered to have the next lower degree of concern; therefore, these can be
assigned a larger acceptance quality limit value than those in class A and smaller than in class C, if a third class exists,
etc.
NOTE 3 Adding characteristics and classes of nonconformities will generally affect the overall probability of acceptance of
the product.
NOTE 4 The number of classes, the assignment into a class, and the choice of acceptance quality limit for each class,
should be appropriate to the quality requirements of the specific situation.
3.1.6
defect
non-fulfilment of an intended usage requirement
NOTE 1 The term "defect" is appropriate for use when a quality characteristic of a product or service is evaluated in terms of
usage (as contrasted to conformance to specifications).
NOTE 2 Since the term "defect" now has definite meaning within the law, it should not be used as a general term.
3.1.7
nonconforming item
item with one or more nonconformities
NOTE Nonconforming items will generally be classified by their degree of seriousness such as:
Class A: an item which contains one or more nonconformities of class A and may also contain nonconformities of class B
and/or class C, etc.;
Class B: an item which contains one or more nonconformities of class B and may also contain nonconformities of class C,
etc. but contains no nonconformity of class A.
3.1.8
percent nonconforming
áin a sampleñ one hundred times the number of nonconforming items in the sample divided by the sample size, viz:
d
·100
n
where
d is the number of nonconforming items in the sample;
n is the sample size
3.1.9
percent nonconforming
áin a population or lotñ one hundred times the number of nonconforming items in the population or lot divided by the
population or lot size, viz:
© ISO
D
100p = 100
N
where
p is the proportion of nonconforming items;
D is the number of nonconforming items in the population or lot;
N is the population or lot size
NOTE 1 In this part of ISO 2859 the terms percent nonconforming (3.1.8 and 3.1.9) or nonconformities per 100 items
(3.1.10 and 3.1.11) are mainly used in place of the theoretical terms "proportion of nonconforming items" and "nonconformities
per item" because the former terms are the most widely used.
NOTE 2 This definition differs from that found in ISO 3534-2.
3.1.10
nonconformities per 100 items
áin a sampleñ one hundred times the number of nonconformities in the sample divided by the sample size, viz:
d
n
where
d is the number of nonconformities in the sample;
n is the sample size
3.1.11
nonconformities per 100 items
áin a population or lotñ one hundred times the number of nonconformities in the population or lot divided by the
population or lot size, viz:
D
100 = 100
p
N
where
p is the number of nonconformities per item;
D is the number of nonconformities in the population or lot;
N is the population or lot size
NOTE An item may contain one or more nonconformities.
3.1.12
responsible authority
concept used to maintain the neutrality of this part of ISO 2859 (primarily for specification purposes), irrespective of
whether it is being invoked or applied by the first, second or third party
NOTE 1 The responsible authority may be:
a) the quality department within a supplier's organization (first party);
b) the purchaser or procurement organization (second party);
c) an independent verification or certification authority (third party);
© ISO
d) any of a), b) or c), differing according to function (see Note 2) as described in a written agreement between two of the
parties, for example a document between supplier and purchaser.
NOTE 2 The duties and functions of a responsible authority are outlined in this part of ISO 2859 (see 5.2, 6.2, 7.2, 7.3, 7.5,
7.6, 9.1, 9.3.3, 9.4, 10.1, 10.3, 13.1).
3.1.13
lot
definite amount of some product, material or service, collected together
NOTE An inspection lot may consist of several batches or parts of batches.
3.1.14
lot size
number of items in a lot
3.1.15
sample
set of one or more items taken from a lot and intended to provide information on the lot
3.1.16
sample size
number of items in the sample
3.1.17
sampling plan
combination of sample size(s) to be used and associated lot acceptability criteria
NOTE 1 A single sampling plan is a combination of sample size and acceptance and rejection numbers. A double sampling
plan is a combination of two sample sizes and acceptance and rejection numbers for the first sample and for the combined
sample.
NOTE 2 A sampling plan does not contain the rules on how to draw the sample.
NOTE 3 For the purposes of this part of ISO 2859, a distinction should be made between the terms sampling plan (3.1.17),
sampling scheme (3.1.18) and sampling system (3.1.19).
3.1.18
sampling scheme
combination of sampling plans with rules for changing from one plan to another
NOTE See 9.3.
3.1.19
sampling system
collection of sampling plans, or of sampling schemes, each with its own rules for changing plans, together with
sampling procedures including criteria by which appropriate plans or schemes may be chosen
NOTE This part of ISO 2859 is a sampling system indexed by lot-size ranges, inspection levels and AQLs. A sampling
system for LQ plans is given in ISO 2859-2.
3.1.20
normal inspection
use of a sampling plan (3.1.17) with an acceptance criterion that has been devised to secure the producer a high
probability of acceptance when the process average (3.1.25) of the lot is better than the acceptance quality limit
(3.1.26)
NOTE Normal inspection is used when there is no reason to suspect that the process average (3.1.25) differs from an
acceptable level.
© ISO
3.1.21
tightened inspection
use of a sampling plan (3.1.17) with an acceptance criterion that is tighter than that for the corresponding plan for
normal inspection (3.1.20)
NOTE Tightened inspection is invoked when the inspection results of a predetermined number of consecutive lots indicate
that the process average (3.1.25) might be poorer than the AQL (3.1.26).
3.1.22
reduced inspection
use of a sampling plan (3.1.17) with a sample size (3.1.16) that is smaller than that for the corresponding plan for
normal inspection (3.1.20) and with an acceptance criterion that is comparable to that for the corresponding plan
for normal inspection
NOTE 1 The discriminatory ability under reduced inspection is less than under normal inspection.
NOTE 2 Reduced inspection may be invoked when the inspection results of a predetermined number of consecutive lots
indicate that the process average (3.1.25) is better than the AQL (3.1.26).
3.1.23
switching score
indicator that is used under normal inspection to determine whether the current inspection results are sufficient to
allow for a switch to reduced inspection
NOTE See 9.3.3.
3.1.24
acceptance score
indicator that is used for fractional acceptance number plans to determine lot acceptability
NOTE See 13.2.1.2.
3.1.25
process average
process level averaged over a defined time period or quantity of production
[ISO 3534-2:1993, 3.1.2]
NOTE In this part of ISO 2859 the process average is the quality level (percent nonconforming or number of
nonconformities per hundred items) during a period when the process is in a state of statistical control.
3.1.26
acceptance quality limit
AQL
quality level that is the worst tolerable process average when a continuing series of lots is submitted for acceptance
sampling
NOTE 1 This concept only applies when a sampling scheme with rules for switching and for discontinuation, such as in
ISO 2859-1 or ISO 3951, is used.
NOTE 2 Although individual lots with quality as bad as the acceptance quality limit may be accepted with fairly high
probability, the designation of an acceptance quality limit does not suggest that this is a desirable quality level. Sampling
schemes found in International Standards such as this part of ISO 2859, with their rules for switching and for discontinuation of
sampling inspection, are designed to encourage suppliers to have process averages consistently better than the AQL.
Otherwise, there is a high risk that the inspection severity will be switched to tightened inspection under which the criteria for lot
acceptance become more demanding. Once on tightened inspection, unless action is taken to improve the process, it is very
likely that the rule requiring discontinuation of sampling inspection pending such improvement will be invoked.
3.1.27
consumer's risk quality
CRQ
lot or process quality level that in the sampling plan corresponds to a specified consumer's risk
© ISO
NOTE Consumer's risk is usually 10 %.
3.1.28
limiting quality
LQ
when a lot is considered in isolation, a quality level which for the purposes of sampling inspection is limited to a low
probability of acceptance
3.2 Symbols and abbreviations
The symbols and abbreviations used in this part of ISO 2859-1 are as follows:
Ac acceptance number
AQL acceptance quality limit (in percent nonconforming items or in nonconformities per hundred items)
AOQ average outgoing quality (in percent nonconforming items or in nonconformities per hundred items)
AOQL average outgoing quality limit (in percent nonconforming items or in nonconformities per hundred
items)
CRQ consumer's risk quality (in percent nonconforming items or in nonconformities per hundred items)
d number of nonconforming items (or nonconformities) found in a sample from a lot
D number of nonconforming items in a lot
LQ limiting quality (in percent nonconforming items or in nonconformities per hundred items)
N lot size
n sample size
p process average
p quality level for which the probability of acceptance is x, where x is a fraction
x
P probability of acceptance (in percent)
a
Re rejection number
NOTE The symbol n may be accompanied by a subscript. Numerical subscripts 1 to 5 denote the first to the fifth sample,
th
respectively. In general, n is the size of the i sample in double or multiple sampling.
i
4 Expression of nonconformity
4.1 General
The extent of nonconformity shall be expressed either in terms of percent nonconforming (see 3.1.8 and 3.1.9) or in
terms of nonconformities per 100 items (see 3.1.10 and 3.1.11). Tables 7, 8 and 10 are based on the assumption that
nonconformities occur randomly and with statistical independence. If it is known that one nonconformity in an item
could be caused by a condition also likely to cause others, the items shall be considered just as conforming or not and
multiple nonconformities ignored.
4.2 Classification of nonconformities
Since most acceptance sampling involves evaluation of more than one quality characteristic, and since they may differ
in importance in terms of quality and/or economic effects, it is often desirable to classify the types of nonconformities
according to agreed classes as defined in 3.1.5. The number of classes, the assignment of nonconformities into
© ISO
classes, and the choice of AQL for each class should be appropriate to the quality requirements of the specific
situation.
5 Acceptance quality limit (AQL)
5.1 Use and application
The AQL, together with the sample size code letter (see 10.2), is used for indexing the sampling plans and schemes
provided in this part of ISO 2859.
When a specific value of the AQL is designated for a certain nonconformity or group of nonconformities, it indicates that
the sampling scheme will accept the great majority of the lots submitted, provided the quality level (percent
nonconforming or nonconformities per 100 items) in these lots is no greater than the designated value of AQL. The
sampling plans provided are so arranged that the probability of acceptance at the designated AQL value depends upon
the sample size for a given AQL, being generally higher for large samples than for small ones.
The AQL is a parameter of the sampling scheme and should not be confused with the process average that describes
the operating level of the manufacturing process. It is expected that the process average will be better than the AQL to
avoid excessive rejections under this system.
CAUTION: The designation of an AQL shall not imply that the supplier has the right knowingly to supply any
nonconforming item.
5.2 Specifying AQLs
The AQL to be used shall be designated in the contract or by (or in accordance with the prescription laid down by) the
responsible authority. Different AQLs may be designated for groups of nonconformities considered collectively or for
individual nonconformities as defined in 3.1.5. The classification into groups should be appropriate to the quality
requirements of the specific situation. An AQL for a group of nonconformities may be designated in addition to AQLs for
individual nonconformities, or subgroups, within that group. When the quality level is expressed as percent of
nonconforming items (3.1.8 and 3.1.9), AQL values shall not exceed 10 % nonconforming. When the quality level is
expressed as number of nonconformities per 100 items (3.1.10 and 3.1.11), AQL values up to 1 000 nonconformities
per 100 items may be used.
5.3 Preferred AQLs
The series of values of AQLs given in the tables are known as the preferred series of AQLs. If, for any product, an AQL
is designated other than one of these values, these tables are not applicable.
6 Submission of product for sampling
6.1 Formation of lots
The product shall be assembled into identifiable lots, sub-lots, or in such other manner as may be laid down (see 6.2).
Each lot shall, as far as is practicable, consist of items of a single type, grade, class, size and composition,
manufactured under uniform conditions at essentially the same time.
6.2 Presentation of lots
The formation of the lots, the lot size and the manner in which each lot shall be presented and identified by the supplier
shall be designated or approved by, or according to, the responsible authority. As necessary, the supplier shall provide
adequate and suitable storage space for each lot, equipment needed for proper identification and presentation, and
personnel for all handling of product required for drawing of samples.
© ISO
7 Acceptance and non-acceptance
7.1 Acceptability of lots
Acceptability of a lot shall be determined by the use of a sampling plan or plans.
The term "non-acceptance" is used in this context for "rejection" when it refers to the result of following the procedure.
Forms of the term "reject" are retained when they refer to actions the consumer may take, as in "rejection number."
7.2 Disposition of non-acceptable lots
The responsible authority shall decide how lots that are not accepted will be disposed of. Such lots may be scrapped,
sorted (with or without nonconforming items being replaced), reworked, re-evaluated against more specific usability
criteria, or held for additional information, etc.
7.3 Nonconforming items
If a lot has been accepted, the right is reserved to not accept any item found nonconforming during inspection, whether
that item formed part of a sample or not. Items found nonconforming may be reworked or replaced by conforming
items, and resubmitted for inspection with the approval of, and in the manner specified by, the responsible authority.
7.4 Classes of nonconformities or nonconforming items
Specific assignment of nonconformities or nonconforming items to two or more classes requires using a set of
sampling plans. In general, the set of sampling plans have a common sample size, but different acceptance numbers
for each class having a different AQL, such as in Tables 2, 3 and 4.
7.5 Special reservation for critical classes of nonconformities
Some types of nonconformities may have critical importance. This subclause specifies the special provisions for such
types of designated non-conformities. At the discretion of the responsible authority, every item in the lot may be
required to be inspected for such designated classes of nonconformities. The right is reserved to inspect every item
submitted for such designated nonconformities and to not accept the lot immediately if a nonconformity of this class is
found. The right is also reserved to sample, for specified classes of nonconformities, every lot submitted by the supplier
and to not accept any lot if a sample drawn from it is found to contain one or more of these nonconformities.
7.6 Resubmitted lots
All parties shall be immediately notified if a lot is found not acceptable. Such lots shall not be resubmitted until all items
are re-examined or retested and the supplier is satisfied that all nonconforming items have been removed or replaced
by conforming items, or all nonconformities have been corrected. The responsible authority shall determine whether
normal or tightened inspection shall be used on re-inspection and whether re-inspection shall include all types or
classes of nonconformities or only the particular types or classes of nonconformities which caused initial non-
acceptance.
8 Drawing of samples
8.1 Sample selection
The items selected for the sample shall be drawn from the lot by simple random sampling (see 2.1.5 in
ISO 3534-2:1993). However, when the lot consists of sub-lots or strata, identified by some rational criterion, stratified
sampling shall be used in such a way that the size of the subsample from each sublot or stratum is proportional to the
size of that sublot or stratum (for further details see 2.25 in ISO 2859-0:1995).
8.2 Time for drawing the samples
Samples may be drawn after the lot has been produced, or during production of the lot. In either case, the samples
shall be selected according to 8.1.
© ISO
8.3 Double or multiple sampling
When double or multiple sampling is to be used, each subsequent sample shall be selected from the remainder of the
same lot.
9 Normal, tightened and reduced inspection
9.1 Start of inspection
Normal inspection shall be carried out at the start of inspection, unless otherwise directed by the responsible authority.
9.2 Continuation of inspection
Normal, tightened or reduced inspection shall continue unchanged on successive lots, except where the switching
procedures (see 9.3) require the severity of the inspection to be changed. The switching procedures shall be applied to
each class of nonconformities or nonconforming items independently.
9.3 Switching rules and procedures (see Figure 1)
9.3.1 Normal to tightened
When normal inspection is being carried out, tightened inspection shall be implemented as soon as two out of five (or
fewer than five) consecutive lots have been non-acceptable on original inspection (that is, ignoring resubmitted lots or
batches for this procedure).
9.3.2 Tightened to normal
When tightened inspection is being carried out, normal inspection shall be re-instated when five consecutive lots have
been considered acceptable on original inspection.
9.3.3 Normal to reduced
9.3.3.1 General
When normal inspection is being carried out, reduced inspection shall be implemented provided that all of the following
conditions are satisfied:
a) the current value of the switching score (see 9.3.3.2) is at least 30; and
b) production is at a steady rate; and
c) reduced inspection is considered desirable by the responsible authority.
© ISO
© ISO
9.3.3.2 Switching score
The calculation of the switching score shall be initiated at the start of normal inspection unless otherwise specified by
the responsible authority.
The switching score shall be set at zero at the start and updated following the inspection of each subsequent lot on
original normal inspection.
a) Single sampling plans:
1) when the acceptance number is 2 or more, add 3 to the switching score if the lot would have been
accepted if the AQL had been one step tighter; otherwise reset the switching score to zero;
2) when the acceptance number is 0 or 1, add 2 to the switching score if the lot is accepted; otherwise reset
the switching score to zero.
b) Double and multiple sampling plans:
1) when a double sampling plan is used, add 3 to the switching score if the lot is accepted after the first
sample; otherwise reset the switching score to zero;
2) when a multiple sampling plan is used, add 3 to the switching score if the lot is accepted by the third
sample; otherwise reset the switching score to zero.
NOTE The application of the switching score is illustrated in annex A.
9.3.4 Reduced to normal
When reduced inspection is being carried out, normal inspection shall be re-instated if any of the following occur on
original inspection:
a) a lot is not accepted; or
b) production becomes irregular or delayed; or
c) other conditions warrant that normal inspection shall be re-instated.
9.4 Discontinuation of inspection
If the cumulative number of lots not accepted in a sequence of consecutive lots on original tightened inspection
reaches 5, the acceptance procedures of this part of ISO 2859 shall not be resumed until action has been taken by the
supplier to improve the quality of the submitted product or service, and the responsible authority has agreed that this
action is likely to be effective. Tightened inspection shall then be used as if 9.3.1 had been invoked.
9.5 Skip-lot sampling
The lot-by-lot inspection in this part of ISO 2859 may be replaced by skip-lot sampling when the requirements of
ISO 2859-3 are fulfilled.
NOTE There are limitations to the use of the skip-lot procedures of ISO 2859-3 in place of the reduced-inspection
procedures of this part of ISO 2859. Some of the AQLs and inspection levels are not applicable.
© ISO
10 Sampling plans
10.1 Inspection level
The inspection level designates the relative amount of inspection. Three inspection levels, I, II and III, are given in
Table 1 for general use. Unless otherwise specified, level II shall be used. Level I may be used when less
discrimination is needed or level III when greater discrimination is required. Four additional special levels, S-1, S-2, S-3
and S-4 are also given in Table 1 and may be used where relatively small sample sizes are necessary and larger
sampling risks can be tolerated.
The inspection level required for any particular application shall be specified by the responsible authority. This allows
the authority to require greater discrimination for some purposes and less for others.
At each inspection level, the switching rules shall operate to require normal, tightened and reduced inspection, as
specified in clause 9. The choice of inspection level is quite separate from these three severities of inspection. Thus,
the inspection level that has been specified shall be kept unchanged when switching between normal, tightened and
reduced inspection.
In the designation of inspection levels S-1 to S-4, care shall be exercised to avoid AQLs inconsistent with these
inspection levels. For instance, the code letters under S-1 go no further than D, equivalent to a single sample size of 8,
but it is of no use to specify S-1 if the AQL is 0,1 %, for which the minimum sample size is 125.
The amount of information about the quality of a lot gained from examining samples drawn from the lot depends upon
the absolute size of the samples, not upon the relative size of the sample to the lot size, provided the sample is small
relative to the lot that is examined. In spite of this, there are three reasons for varying the sample size with the lot size:
a) when the loss due to a wrong decision is high, it is more important to make the correct decision;
b) with a large lot, a sample size can be afforded that would be uneconomic for a small lot;
c) truly random sampling is relatively more difficult if the sample is too small a proportion of the lot.
10.2 Sample size code letters
Sample sizes are designated by sample size code letters. Table 1 shall be used to find the applicable code letter for the
particular lot size and the prescribed inspection level.
NOTE For economy of space in the tables or to avoid unnecessary repetition in the text, the abbreviated term "code letter"
is sometimes used.
10.3 Obtaining a sampling plan
The AQL and the sample size code letter shall be used to obtain the sampling plan from Tables 2, 3, 4 or 11. For a
specified AQL and a given lot size, the same combination of AQL and sample size code letter shall be used to obtain
the sampling plan from the table for normal, tightened and reduced inspection.
When no sampling plan is available for a given combination of AQL and sample size code letter, the tables direct the
user to a different letter. The sample size to be used is given by the new sample size code letter, not by the original
letter. If this procedure leads to different sample sizes f
...
INTERNATIONAL ISO
STANDARD 2859-1
Second edition
1999-11-15
Sampling procedures for inspection by
attributes —
Part 1:
Sampling schemes indexed by acceptance
quality limit (AQL) for lot-by-lot inspection
Règles d'échantillonnage pour les contrôles par attributs —
Partie 1: Procédures d'échantillonnage pour les contrôles lot par lot,
indexés d'après le niveau de qualité acceptable (NQA)
A
Reference number
Contents
1 Scope .1
2 Normative references .2
3 Terms, definitions and symbols.2
4 Expression of nonconformity.7
5 Acceptance quality limit (AQL).8
6 Submission of product for sampling.8
7 Acceptance and non-acceptance.9
8 Drawing of samples.9
9 Normal, tightened and reduced inspection.10
10 Sampling plans .13
11 Determination of acceptability .14
12 Further information .14
13 Fractional acceptance number plans for single sampling (optional) .16
Tables
1 Sample size code letters .19
2-A Single sampling plans for normal inspection (Master table).20
2-B Single sampling plans for tightened inspection (Master table) .21
2-C Single sampling plans for reduced inspection (Master table).22
3-A Double sampling plans for normal inspection (Master table) .23
3-B Double sampling plans for tightened inspection (Master table).24
3-C Double sampling plans for reduced inspection (Master table) .25
4-A Multiple sampling plans for normal inspection (Master table).26
4-B Multiple sampling plans for tightened inspection (Master table).29
© ISO 1999
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic
or mechanical, including photocopying and microfilm, without permission in writing from the publisher.
International Organization for Standardization
Case postale 56 • CH-1211 Genève 20 • Switzerland
Internet iso@iso.ch
Printed in Switzerland
ii
© ISO
4-C Multiple sampling plans for reduced inspection (Master table). 32
5-A Producer's risk for normal inspection . 35
5-B Producer's risk for tightened inspection. 36
5-C Producer's risk for reduced inspection . 37
6-A Consumer's risk quality for normal inspection . 38
6-B Consumer's risk quality for tightened inspection . 39
6-C Consumer's risk quality for reduced inspection . 40
7-A Consumer's risk quality for normal inspection . 41
7-B Consumer's risk quality for tightened inspection . 42
7-C Consumer's risk quality for reduced inspection . 43
8-A Average outgoing quality limits for normal inspection (Single sampling plans). 44
8-B Average outgoing quality limits for tightened inspection (Single sampling plans) . 45
9 Average sample size curves for single, double and multiple sampling (normal, tightened and reduced
inspection). 46
10-A Tables for sample size code letter A (Individual plans). 48
10-B Tables for sample size code letter B (Individual plans). 50
10-C Tables for sample size code letter C (Individual plans). 52
10-D Tables for sample size code letter D (Individual plans). 54
10-E Tables for sample size code letter E (Individual plans) . 56
10-F Tables for sample size code letter F (Individual plans). 58
10-G Tables for sample size code letter G (Individual plans). 60
10-H Tables for sample size code letter H (Individual plans). 62
10-J Tables for sample size code letter J (Individual plans) . 64
10-K Tables for sample size code letter K (Individual plans). 66
10-L Tables for sample size code letter L (Individual plans). 68
10-M Tables for sample size code letter M (Individual plans) . 70
10-N Tables for sample size code letter N (Individual plans). 72
10-P Tables for sample size code letter P (Individual plans) . 74
10-Q Tables for sample size code letter Q (Individual plans). 76
10-R Tables for sample size code letter R (Individual plans). 78
10-S Tables for sample size code letter S (Individual plans) . 80
iii
© ISO
11-A Single sampling plans for normal inspection (Auxiliary master table) .81
11-B Single sampling plans for tightened inspection (Auxiliary master table).82
11-C Single sampling plans for reduced inspection (Auxiliary master table) .83
12 Scheme OC curves (Normalized) .84
Annex A (informative) Example for non-constant sampling plan .85
Bibliography.87
iv
© ISO
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO
member bodies). The work of preparing International Standards is normally carried out through ISO technical
committees. Each member body interested in a subject for which a technical committee has been established has
the right to be represented on that committee. International organizations, governmental and non-governmental, in
liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical
Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 3.
Draft International Standards adopted by the technical committees are circulated to the member bodies for voting.
Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote.
International Standard ISO 2859-1 was prepared by Technical Committee ISO/TC 69, Applications of statistical
methods, Subcommittee SC 5, Acceptance sampling.
This second edition of ISO 2859-1 cancels and replaces the first edition (ISO 2859-1:1989) of which it constitutes a
technical revision.
Significant changes in this edition include:
a new procedure for switching from normal to reduced inspection;
a reference to skip-lot sampling as an alternative to reduced inspection;
the term "limiting quality" has been changed to "consumer's risk quality" in the heading of Tables 6-A, 6-B, 6-C,
7-A, 7-B and 7-C;
a new table has been added giving producer's risk as the probability of rejection of lots with percent
nonconforming equal to the AQL;
optional fractional acceptance number plans have been added; the purpose of these plans is to provide a
consistent progression from the plans for acceptance number zero to the acceptance number 1 plans. The
fractional acceptance number plans are found in Tables 11-A, 11-B and 11-C, where they take the place of the
arrows in the corresponding positions in tables 2-A, 2-B and 2-C;
reduced plans have been changed to eliminate the gap between the acceptance and rejection numbers;
some changes have been made to the double sampling plans to provide a smaller average sample size;
multiple sampling plans have been changed to five stages rather than seven. The change has not increased
the average sample size. Some of the new plans have a smaller average sample size than their counterparts in
the previous edition;
scheme operating characteristic curves have been added as Table 12.
ISO 2859 consists of the following parts, under the general title Sampling procedures for inspection by attributes:
Part 0: Introduction to the ISO 2859 attribute sampling system
Part 1: Sampling schemes indexed by acceptance quality limit (AQL) for lot-by-lot inspection
Part 2: Sampling plans indexed by limiting quality (LQ) for isolated lot inspection
v
© ISO
Part 3: Skip-lot sampling procedures
It is highly recommended that this part of ISO 2859 be used together with ISO 2859-0, which contains illustrative
examples.
Annex A of this part of ISO 2859 is for information only.
vi
INTERNATIONAL STANDARD © ISO ISO 2859-1:1999(E)
Sampling procedures for inspection by attributes —
Part 1:
Sampling schemes indexed by acceptance quality limit (AQL) for
lot-by-lot inspection
1 Scope
1.1 This part of ISO 2859 specifies an acceptance sampling system for inspection by attributes. It is indexed in
terms of the acceptance quality limit (AQL).
Its purpose is to induce a supplier through the economic and psychological pressure of lot non-acceptance to maintain
a process average at least as good as the specified acceptance quality limit, while at the same time providing an upper
limit for the risk to the consumer of accepting the occasional poor lot.
Sampling schemes designated in this part of ISO 2859 are applicable, but not limited, to inspection of
end items,
components and raw materials,
operations,
materials in process,
supplies in storage,
maintenance operations,
data or records, and
administrative procedures.
1.2 These schemes are intended primarily to be used for a continuing series of lots, that is, a series long enough to
allow the switching rules (9.3) to be applied. These rules provide:
a) a protection to the consumer (by means of a switch to tightened inspection or discontinuation of sampling
inspection) should a deterioration in quality be detected;
b) an incentive (at the discretion of the responsible authority) to reduce inspection costs (by means of a switch to
reduced inspection) should consistently good quality be achieved.
Sampling plans in this part of ISO 2859 may also be used for the inspection of lots in isolation but, in this case the user
is strongly advised to consult the operating characteristic curves to find a plan that will yield the desired protection (see
12.6). In that case, the user is also referred to the sampling plans indexed by limiting quality (LQ) given in ISO 2859-2.
© ISO
2 Normative references
The following normative documents contain provisions which, through reference in this text, constitute provisions of
this part of ISO 2859. For dated references, subsequent amendments to, or revisions of, any of these publications
do not apply. However, parties to agreements based on this part of ISO 2859 are encouraged to investigate the
possibility of applying the most recent editions of the normative documents indicated below. For undated
references, the latest edition of the normative document referred to applies. Members of ISO and IEC maintain
registers of currently valid International Standards.
ISO 2859-3:1991, Sampling procedures for inspection by attributes — Part 3: Skip-lot sampling procedures.
ISO 3534-1:1993, Statistics — Vocabulary and symbols — Part 1: Probability and general statistical terms.
ISO 3534-2:1993, Statistics — Vocabulary and symbols — Part 2: Statistical quality control.
3 Terms, definitions and symbols
3.1 Terms and definitions
For the purposes of this part of ISO 2859, the terms and definitions given in ISO 3534-1 and ISO 3534-2 and the
following apply.
NOTE For ease of reference, the definitions of some of these terms are quoted from ISO 3534-1 and ISO 3534-2, while
others are redefined or newly defined.
3.1.1
inspection
activity such as measuring, examining, testing or gauging one or more characteristics of a product or service, and
comparing the results with specified requirements in order to establish whether conformity is achieved for each
characteristic
3.1.2
original inspection
first inspection of a lot according to the provisions of this part of ISO 2859
NOTE This is to be distinguished from the inspection of a lot which has been resubmitted after previous non-acceptance.
3.1.3
inspection by attributes
inspection whereby either the item is classified simply as conforming or nonconforming with respect to a specified
requirement or set of specified requirements, or the number of nonconformities in the item is counted
NOTE Inspection by attributes includes inspection for conformity of items as well as inspection for number of
nonconformities per hundred items.
3.1.4
item
that which can be individually described and considered
EXAMPLES
a physical item;
a defined quantity of material;
a service, an activity or a process;
an organization or a person; or
some combination thereof.
© ISO
3.1.5
nonconformity
non-fulfilment of a specified requirement
NOTE 1 In some situations specified requirements coincide with customer usage requirements (see defect, 3.1.6). In other
situations they may not coincide, being either more or less stringent, or the exact relationship between the two is not fully
known or understood.
NOTE 2 Nonconformity will generally be classified according to its degree of seriousness such as:
Class A: those nonconformities of a type considered to be of the highest concern; in acceptance sampling such types of
nonconformities will be assigned a very small acceptance quality limit value;
Class B: those nonconformities of a type considered to have the next lower degree of concern; therefore, these can be
assigned a larger acceptance quality limit value than those in class A and smaller than in class C, if a third class exists,
etc.
NOTE 3 Adding characteristics and classes of nonconformities will generally affect the overall probability of acceptance of
the product.
NOTE 4 The number of classes, the assignment into a class, and the choice of acceptance quality limit for each class,
should be appropriate to the quality requirements of the specific situation.
3.1.6
defect
non-fulfilment of an intended usage requirement
NOTE 1 The term "defect" is appropriate for use when a quality characteristic of a product or service is evaluated in terms of
usage (as contrasted to conformance to specifications).
NOTE 2 Since the term "defect" now has definite meaning within the law, it should not be used as a general term.
3.1.7
nonconforming item
item with one or more nonconformities
NOTE Nonconforming items will generally be classified by their degree of seriousness such as:
Class A: an item which contains one or more nonconformities of class A and may also contain nonconformities of class B
and/or class C, etc.;
Class B: an item which contains one or more nonconformities of class B and may also contain nonconformities of class C,
etc. but contains no nonconformity of class A.
3.1.8
percent nonconforming
áin a sampleñ one hundred times the number of nonconforming items in the sample divided by the sample size, viz:
d
·100
n
where
d is the number of nonconforming items in the sample;
n is the sample size
3.1.9
percent nonconforming
áin a population or lotñ one hundred times the number of nonconforming items in the population or lot divided by the
population or lot size, viz:
© ISO
D
100p = 100
N
where
p is the proportion of nonconforming items;
D is the number of nonconforming items in the population or lot;
N is the population or lot size
NOTE 1 In this part of ISO 2859 the terms percent nonconforming (3.1.8 and 3.1.9) or nonconformities per 100 items
(3.1.10 and 3.1.11) are mainly used in place of the theoretical terms "proportion of nonconforming items" and "nonconformities
per item" because the former terms are the most widely used.
NOTE 2 This definition differs from that found in ISO 3534-2.
3.1.10
nonconformities per 100 items
áin a sampleñ one hundred times the number of nonconformities in the sample divided by the sample size, viz:
d
n
where
d is the number of nonconformities in the sample;
n is the sample size
3.1.11
nonconformities per 100 items
áin a population or lotñ one hundred times the number of nonconformities in the population or lot divided by the
population or lot size, viz:
D
100 = 100
p
N
where
p is the number of nonconformities per item;
D is the number of nonconformities in the population or lot;
N is the population or lot size
NOTE An item may contain one or more nonconformities.
3.1.12
responsible authority
concept used to maintain the neutrality of this part of ISO 2859 (primarily for specification purposes), irrespective of
whether it is being invoked or applied by the first, second or third party
NOTE 1 The responsible authority may be:
a) the quality department within a supplier's organization (first party);
b) the purchaser or procurement organization (second party);
c) an independent verification or certification authority (third party);
© ISO
d) any of a), b) or c), differing according to function (see Note 2) as described in a written agreement between two of the
parties, for example a document between supplier and purchaser.
NOTE 2 The duties and functions of a responsible authority are outlined in this part of ISO 2859 (see 5.2, 6.2, 7.2, 7.3, 7.5,
7.6, 9.1, 9.3.3, 9.4, 10.1, 10.3, 13.1).
3.1.13
lot
definite amount of some product, material or service, collected together
NOTE An inspection lot may consist of several batches or parts of batches.
3.1.14
lot size
number of items in a lot
3.1.15
sample
set of one or more items taken from a lot and intended to provide information on the lot
3.1.16
sample size
number of items in the sample
3.1.17
sampling plan
combination of sample size(s) to be used and associated lot acceptability criteria
NOTE 1 A single sampling plan is a combination of sample size and acceptance and rejection numbers. A double sampling
plan is a combination of two sample sizes and acceptance and rejection numbers for the first sample and for the combined
sample.
NOTE 2 A sampling plan does not contain the rules on how to draw the sample.
NOTE 3 For the purposes of this part of ISO 2859, a distinction should be made between the terms sampling plan (3.1.17),
sampling scheme (3.1.18) and sampling system (3.1.19).
3.1.18
sampling scheme
combination of sampling plans with rules for changing from one plan to another
NOTE See 9.3.
3.1.19
sampling system
collection of sampling plans, or of sampling schemes, each with its own rules for changing plans, together with
sampling procedures including criteria by which appropriate plans or schemes may be chosen
NOTE This part of ISO 2859 is a sampling system indexed by lot-size ranges, inspection levels and AQLs. A sampling
system for LQ plans is given in ISO 2859-2.
3.1.20
normal inspection
use of a sampling plan (3.1.17) with an acceptance criterion that has been devised to secure the producer a high
probability of acceptance when the process average (3.1.25) of the lot is better than the acceptance quality limit
(3.1.26)
NOTE Normal inspection is used when there is no reason to suspect that the process average (3.1.25) differs from an
acceptable level.
© ISO
3.1.21
tightened inspection
use of a sampling plan (3.1.17) with an acceptance criterion that is tighter than that for the corresponding plan for
normal inspection (3.1.20)
NOTE Tightened inspection is invoked when the inspection results of a predetermined number of consecutive lots indicate
that the process average (3.1.25) might be poorer than the AQL (3.1.26).
3.1.22
reduced inspection
use of a sampling plan (3.1.17) with a sample size (3.1.16) that is smaller than that for the corresponding plan for
normal inspection (3.1.20) and with an acceptance criterion that is comparable to that for the corresponding plan
for normal inspection
NOTE 1 The discriminatory ability under reduced inspection is less than under normal inspection.
NOTE 2 Reduced inspection may be invoked when the inspection results of a predetermined number of consecutive lots
indicate that the process average (3.1.25) is better than the AQL (3.1.26).
3.1.23
switching score
indicator that is used under normal inspection to determine whether the current inspection results are sufficient to
allow for a switch to reduced inspection
NOTE See 9.3.3.
3.1.24
acceptance score
indicator that is used for fractional acceptance number plans to determine lot acceptability
NOTE See 13.2.1.2.
3.1.25
process average
process level averaged over a defined time period or quantity of production
[ISO 3534-2:1993, 3.1.2]
NOTE In this part of ISO 2859 the process average is the quality level (percent nonconforming or number of
nonconformities per hundred items) during a period when the process is in a state of statistical control.
3.1.26
acceptance quality limit
AQL
quality level that is the worst tolerable process average when a continuing series of lots is submitted for acceptance
sampling
NOTE 1 This concept only applies when a sampling scheme with rules for switching and for discontinuation, such as in
ISO 2859-1 or ISO 3951, is used.
NOTE 2 Although individual lots with quality as bad as the acceptance quality limit may be accepted with fairly high
probability, the designation of an acceptance quality limit does not suggest that this is a desirable quality level. Sampling
schemes found in International Standards such as this part of ISO 2859, with their rules for switching and for discontinuation of
sampling inspection, are designed to encourage suppliers to have process averages consistently better than the AQL.
Otherwise, there is a high risk that the inspection severity will be switched to tightened inspection under which the criteria for lot
acceptance become more demanding. Once on tightened inspection, unless action is taken to improve the process, it is very
likely that the rule requiring discontinuation of sampling inspection pending such improvement will be invoked.
3.1.27
consumer's risk quality
CRQ
lot or process quality level that in the sampling plan corresponds to a specified consumer's risk
© ISO
NOTE Consumer's risk is usually 10 %.
3.1.28
limiting quality
LQ
when a lot is considered in isolation, a quality level which for the purposes of sampling inspection is limited to a low
probability of acceptance
3.2 Symbols and abbreviations
The symbols and abbreviations used in this part of ISO 2859-1 are as follows:
Ac acceptance number
AQL acceptance quality limit (in percent nonconforming items or in nonconformities per hundred items)
AOQ average outgoing quality (in percent nonconforming items or in nonconformities per hundred items)
AOQL average outgoing quality limit (in percent nonconforming items or in nonconformities per hundred
items)
CRQ consumer's risk quality (in percent nonconforming items or in nonconformities per hundred items)
d number of nonconforming items (or nonconformities) found in a sample from a lot
D number of nonconforming items in a lot
LQ limiting quality (in percent nonconforming items or in nonconformities per hundred items)
N lot size
n sample size
p process average
p quality level for which the probability of acceptance is x, where x is a fraction
x
P probability of acceptance (in percent)
a
Re rejection number
NOTE The symbol n may be accompanied by a subscript. Numerical subscripts 1 to 5 denote the first to the fifth sample,
th
respectively. In general, n is the size of the i sample in double or multiple sampling.
i
4 Expression of nonconformity
4.1 General
The extent of nonconformity shall be expressed either in terms of percent nonconforming (see 3.1.8 and 3.1.9) or in
terms of nonconformities per 100 items (see 3.1.10 and 3.1.11). Tables 7, 8 and 10 are based on the assumption that
nonconformities occur randomly and with statistical independence. If it is known that one nonconformity in an item
could be caused by a condition also likely to cause others, the items shall be considered just as conforming or not and
multiple nonconformities ignored.
4.2 Classification of nonconformities
Since most acceptance sampling involves evaluation of more than one quality characteristic, and since they may differ
in importance in terms of quality and/or economic effects, it is often desirable to classify the types of nonconformities
according to agreed classes as defined in 3.1.5. The number of classes, the assignment of nonconformities into
© ISO
classes, and the choice of AQL for each class should be appropriate to the quality requirements of the specific
situation.
5 Acceptance quality limit (AQL)
5.1 Use and application
The AQL, together with the sample size code letter (see 10.2), is used for indexing the sampling plans and schemes
provided in this part of ISO 2859.
When a specific value of the AQL is designated for a certain nonconformity or group of nonconformities, it indicates that
the sampling scheme will accept the great majority of the lots submitted, provided the quality level (percent
nonconforming or nonconformities per 100 items) in these lots is no greater than the designated value of AQL. The
sampling plans provided are so arranged that the probability of acceptance at the designated AQL value depends upon
the sample size for a given AQL, being generally higher for large samples than for small ones.
The AQL is a parameter of the sampling scheme and should not be confused with the process average that describes
the operating level of the manufacturing process. It is expected that the process average will be better than the AQL to
avoid excessive rejections under this system.
CAUTION: The designation of an AQL shall not imply that the supplier has the right knowingly to supply any
nonconforming item.
5.2 Specifying AQLs
The AQL to be used shall be designated in the contract or by (or in accordance with the prescription laid down by) the
responsible authority. Different AQLs may be designated for groups of nonconformities considered collectively or for
individual nonconformities as defined in 3.1.5. The classification into groups should be appropriate to the quality
requirements of the specific situation. An AQL for a group of nonconformities may be designated in addition to AQLs for
individual nonconformities, or subgroups, within that group. When the quality level is expressed as percent of
nonconforming items (3.1.8 and 3.1.9), AQL values shall not exceed 10 % nonconforming. When the quality level is
expressed as number of nonconformities per 100 items (3.1.10 and 3.1.11), AQL values up to 1 000 nonconformities
per 100 items may be used.
5.3 Preferred AQLs
The series of values of AQLs given in the tables are known as the preferred series of AQLs. If, for any product, an AQL
is designated other than one of these values, these tables are not applicable.
6 Submission of product for sampling
6.1 Formation of lots
The product shall be assembled into identifiable lots, sub-lots, or in such other manner as may be laid down (see 6.2).
Each lot shall, as far as is practicable, consist of items of a single type, grade, class, size and composition,
manufactured under uniform conditions at essentially the same time.
6.2 Presentation of lots
The formation of the lots, the lot size and the manner in which each lot shall be presented and identified by the supplier
shall be designated or approved by, or according to, the responsible authority. As necessary, the supplier shall provide
adequate and suitable storage space for each lot, equipment needed for proper identification and presentation, and
personnel for all handling of product required for drawing of samples.
© ISO
7 Acceptance and non-acceptance
7.1 Acceptability of lots
Acceptability of a lot shall be determined by the use of a sampling plan or plans.
The term "non-acceptance" is used in this context for "rejection" when it refers to the result of following the procedure.
Forms of the term "reject" are retained when they refer to actions the consumer may take, as in "rejection number."
7.2 Disposition of non-acceptable lots
The responsible authority shall decide how lots that are not accepted will be disposed of. Such lots may be scrapped,
sorted (with or without nonconforming items being replaced), reworked, re-evaluated against more specific usability
criteria, or held for additional information, etc.
7.3 Nonconforming items
If a lot has been accepted, the right is reserved to not accept any item found nonconforming during inspection, whether
that item formed part of a sample or not. Items found nonconforming may be reworked or replaced by conforming
items, and resubmitted for inspection with the approval of, and in the manner specified by, the responsible authority.
7.4 Classes of nonconformities or nonconforming items
Specific assignment of nonconformities or nonconforming items to two or more classes requires using a set of
sampling plans. In general, the set of sampling plans have a common sample size, but different acceptance numbers
for each class having a different AQL, such as in Tables 2, 3 and 4.
7.5 Special reservation for critical classes of nonconformities
Some types of nonconformities may have critical importance. This subclause specifies the special provisions for such
types of designated non-conformities. At the discretion of the responsible authority, every item in the lot may be
required to be inspected for such designated classes of nonconformities. The right is reserved to inspect every item
submitted for such designated nonconformities and to not accept the lot immediately if a nonconformity of this class is
found. The right is also reserved to sample, for specified classes of nonconformities, every lot submitted by the supplier
and to not accept any lot if a sample drawn from it is found to contain one or more of these nonconformities.
7.6 Resubmitted lots
All parties shall be immediately notified if a lot is found not acceptable. Such lots shall not be resubmitted until all items
are re-examined or retested and the supplier is satisfied that all nonconforming items have been removed or replaced
by conforming items, or all nonconformities have been corrected. The responsible authority shall determine whether
normal or tightened inspection shall be used on re-inspection and whether re-inspection shall include all types or
classes of nonconformities or only the particular types or classes of nonconformities which caused initial non-
acceptance.
8 Drawing of samples
8.1 Sample selection
The items selected for the sample shall be drawn from the lot by simple random sampling (see 2.1.5 in
ISO 3534-2:1993). However, when the lot consists of sub-lots or strata, identified by some rational criterion, stratified
sampling shall be used in such a way that the size of the subsample from each sublot or stratum is proportional to the
size of that sublot or stratum (for further details see 2.25 in ISO 2859-0:1995).
8.2 Time for drawing the samples
Samples may be drawn after the lot has been produced, or during production of the lot. In either case, the samples
shall be selected according to 8.1.
© ISO
8.3 Double or multiple sampling
When double or multiple sampling is to be used, each subsequent sample shall be selected from the remainder of the
same lot.
9 Normal, tightened and reduced inspection
9.1 Start of inspection
Normal inspection shall be carried out at the start of inspection, unless otherwise directed by the responsible authority.
9.2 Continuation of inspection
Normal, tightened or reduced inspection shall continue unchanged on successive lots, except where the switching
procedures (see 9.3) require the severity of the inspection to be changed. The switching procedures shall be applied to
each class of nonconformities or nonconforming items independently.
9.3 Switching rules and procedures (see Figure 1)
9.3.1 Normal to tightened
When normal inspection is being carried out, tightened inspection shall be implemented as soon as two out of five (or
fewer than five) consecutive lots have been non-acceptable on original inspection (that is, ignoring resubmitted lots or
batches for this procedure).
9.3.2 Tightened to normal
When tightened inspection is being carried out, normal inspection shall be re-instated when five consecutive lots have
been considered acceptable on original inspection.
9.3.3 Normal to reduced
9.3.3.1 General
When normal inspection is being carried out, reduced inspection shall be implemented provided that all of the following
conditions are satisfied:
a) the current value of the switching score (see 9.3.3.2) is at least 30; and
b) production is at a steady rate; and
c) reduced inspection is considered desirable by the responsible authority.
© ISO
© ISO
9.3.3.2 Switching score
The calculation of the switching score shall be initiated at the start of normal inspection unless otherwise specified by
the responsible authority.
The switching score shall be set at zero at the start and updated following the inspection of each subsequent lot on
original normal inspection.
a) Single sampling plans:
1) when the acceptance number is 2 or more, add 3 to the switching score if the lot would have been
accepted if the AQL had been one step tighter; otherwise reset the switching score to zero;
2) when the acceptance number is 0 or 1, add 2 to the switching score if the lot is accepted; otherwise reset
the switching score to zero.
b) Double and multiple sampling plans:
1) when a double sampling plan is used, add 3 to the switching score if the lot is accepted after the first
sample; otherwise reset the switching score to zero;
2) when a multiple sampling plan is used, add 3 to the switching score if the lot is accepted by the third
sample; otherwise reset the switching score to zero.
NOTE The application of the switching score is illustrated in annex A.
9.3.4 Reduced to normal
When reduced inspection is being carried out, normal inspection shall be re-instated if any of the following occur on
original inspection:
a) a lot is not accepted; or
b) production becomes irregular or delayed; or
c) other conditions warrant that normal inspection shall be re-instated.
9.4 Discontinuation of inspection
If the cumulative number of lots not accepted in a sequence of consecutive lots on original tightened inspection
reaches 5, the acceptance procedures of this part of ISO 2859 shall not be resumed until action has been taken by the
supplier to improve the quality of the submitted product or service, and the responsible authority has agreed that this
action is likely to be effective. Tightened inspection shall then be used as if 9.3.1 had been invoked.
9.5 Skip-lot sampling
The lot-by-lot inspection in this part of ISO 2859 may be replaced by skip-lot sampling when the requirements of
ISO 2859-3 are fulfilled.
NOTE There are limitations to the use of the skip-lot procedures of ISO 2859-3 in place of the reduced-inspection
procedures of this part of ISO 2859. Some of the AQLs and inspection levels are not applicable.
© ISO
10 Sampling plans
10.1 Inspection level
The inspection level designates the relative amount of inspection. Three inspection levels, I, II and III, are given in
Table 1 for general use. Unless otherwise specified, level II shall be used. Level I may be used when less
discrimination is needed or level III when greater discrimination is required. Four additional special levels, S-1, S-2, S-3
and S-4 are also given in Table 1 and may be used where relatively small sample sizes are necessary and larger
sampling risks can be tolerated.
The inspection level required for any particular application shall be specified by the responsible authority. This allows
the authority to require greater discrimination for some purposes and less for others.
At each inspection level, the switching rules shall operate to require normal, tightened and reduced inspection, as
specified in clause 9. The choice of inspection level is quite separate from these three severities of inspection. Thus,
the inspection level that has been specified shall be kept unchanged when switching between normal, tightened and
reduced inspection.
In the designation of inspection levels S-1 to S-4, care shall be exercised to avoid AQLs inconsistent with these
inspection levels. For instance, the code letters under S-1 go no further than D, equivalent to a single sample size of 8,
but it is of no use to specify S-1 if the AQL is 0,1 %, for which the minimum sample size is 125.
The amount of information about the quality of a lot gained from examining samples drawn from the lot depends upon
the absolute size of the samples, not upon the relative size of the sample to the lot size, provided the sample is small
relative to the lot that is examined. In spite of this, there are three reasons for varying the sample size with the lot size:
a) when the loss due to a wrong decision is high, it is more important to make the correct decision;
b) with a large lot, a sample size can be afforded that would be uneconomic for a small lot;
c) truly random sampling is relatively more difficult if the sample is too small a proportion of the lot.
10.2 Sample size code letters
Sample sizes are designated by sample size code letters. Table 1 shall be used to find the applicable code letter for the
particular lot size and the prescribed inspection level.
NOTE For economy of space in the tables or to avoid unnecessary repetition in the text, the abbreviated term "code letter"
is sometimes used.
10.3 Obtaining a sampling plan
The AQL and the sample size code letter shall be used to obtain the sampling plan from Tables 2, 3, 4 or 11. For a
specified AQL and a given lot size, the same combination of AQL and sample size code letter shall be used to obtain
the sampling plan from the table for normal, tightened and reduced inspection.
When no sampling plan is available for a given combination of AQL and sample size code letter, the tables direct the
user to a different letter. The sample size to be used is given by the new sample size code letter, not by the original
letter. If this procedure leads to different sample sizes for different classes of nonconformities or nonconforming items,
the sample size code letter corresponding to the largest sample size derived may be used for all classes of
nonconformities or nonconforming items, when designated or approved by the responsible authority. As an alternative
to a single sampling plan with an acceptance number of 0, the plan with an acceptance number of 1 with its
correspondingly larger sample size for a designated AQL (where available) may be used, when designated or
approved by the responsible authority. As another alternative, the optional fractional acceptance number plans
described in clause 13 may be used when approved by the responsible authority.
© ISO
10.4 Types of sampling plans
Three types of sampling plans, single, double and multiple, are given in Tables 2, 3 and 4, respectively. When several
types of plans are available for a given AQL and sample size code letter, any one may be used. A decision as to the
type of plan, either single, double or multiple, when available for a given AQL and sample size code letter, shall usually
be based upon the comparison between the administrative difficulty and the average sample sizes of the available
plans. For the sampling plans given in this part of ISO 2859, the average sample size of multiple plans is less than for
double, and both
...
NORME ISO
INTERNATIONALE 2859-1
Deuxième édition
1999-11-15
Règles d'échantillonnage pour les contrôles
par attributs —
Partie 1:
Procédures d'échantillonnage pour les
contrôles lot par lot, indexés d'après le niveau
de qualité acceptable (NQA)
Sampling procedures for inspection by attributes —
Part 1: Sampling schemes indexed by acceptance quality limit (AQL) for
lot-by-lot inspection
A
Numéro de référence
Sommaire
1 Domaine d’application .1
2 Références normatives .2
3 Termes, définitions et symboles .2
4 Expression de la non-conformité.7
5 Niveau de qualité acceptable (NQA) .8
6 Présentation du produit pour échantillonnage.8
7 Acceptation et rejet.9
8 Prélèvement des échantillons .10
9 Contrôles normal, renforcé et réduit .10
10 Plans d'échantillonnage.13
11 Détermination de l'acceptabilité.14
12 Renseignements complémentaires .15
13 Plans à critère d'acceptation décimal en échantillonnage simple (optionnel).16
Tableaux
1 Lettres-code d'effectif d'échantillon .19
2-A Plans d'échantillonnage simple en contrôle normal (Tableau général) .20
2-B Plans d'échantillonnage simple en contrôle renforcé (Tableau général).21
2-C Plans d'échantillonnage simple en contrôle réduit (Tableau général) .22
3-A Plans d'échantillonnage double en contrôle normal (Tableau général).23
3-B Plans d'échantillonnage double en contrôle renforcé (Tableau général) .24
3-C Plans d'échantillonnage double en contrôle réduit (Tableau général).25
4-A Plans d'échantillonnage multiple en contrôle normal (Tableau général).26
4-B Plans d'échantillonnage multiple en contrôle renforcé (Tableau général) .29
© ISO 1999
Droits de reproduction réservés. Sauf prescription différente, aucune partie de cette publication ne peut être reproduite ni utilisée sous quelque
forme que ce soit et par aucun procédé, électronique ou mécanique, y compris la photocopie et les microfilms, sans l'accord écrit de l'éditeur.
Organisation internationale de normalisation
Case postale 56 • CH-1211 Genève 20 • Suisse
Internet iso@iso.ch
Imprimé en Suisse
ii
© ISO
4-C Plans d'échantillonnage multiple en contrôle réduit (Tableau général).32
5-A Risque du fournisseur en contrôle normal . 35
5-B Risque du fournisseur en contrôle renforcé. 36
5-C Risque du fournisseur en contrôle réduit . 37
6-A Qualité du risque client en contrôle normal. 38
6-B Qualité du risque client en contrôle renforcé . 39
6-C Qualité du risque client en contrôle réduit. 40
7-A Qualité du risque client en contrôle normal. 41
7-B Qualité du risque client en contrôle renforcé . 42
7-C Qualité du risque client en contrôle réduit. 43
8-A Limite de la qualité moyenne après contrôle en contrôle normal (Plans d'échantillonnage simple) . 44
8-B Limite de la qualité moyenne après contrôle en contrôle renforcé (Plans d'échantillonnage simple). 45
9 Courbes de l'effectif moyen d'échantillon pour l'échantillonnage simple, l'échantillonnage double
et l'échantillonnage multiple (Contrôle normal, contrôle renforcé et contrôle réduit) . 46
10-A Tableaux pour la lettre-code d'effectif d'échantillon A (Plans individuels) . 48
10-B Tableaux pour la lettre-code d'effectif d'échantillon B (Plans individuels) . 50
10-C Tableaux pour la lettre-code d'effectif d'échantillon C (Plans individuels) . 52
10-D Tableaux pour la lettre-code d'effectif d'échantillon D (Plans individuels) . 54
10-E Tableaux pour la lettre-code d'effectif d'échantillon E (Plans individuels).56
10-F Tableaux pour la lettre-code d'effectif d'échantillon F (Plans individuels) .58
10-G Tableaux pour la lettre-code d'effectif d'échantillon G (Plans individuels). 60
10-H Tableaux pour la lettre-code d'effectif d'échantillon H (Plans individuels) . 62
10-J Tableaux pour la lettre-code d'effectif d'échantillon J (Plans individuels) .64
10-K Tableaux pour la lettre-code d'effectif d'échantillon K (Plans individuels) .66
10-L Tableaux pour la lettre-code d'effectif d'échantillon L (Plans individuels) .68
10-M Tableaux pour la lettre-code d'effectif d'échantillon M (Plans individuels) . 70
10-N Tableaux pour la lettre-code d'effectif d'échantillon N (Plans individuels) . 72
10-P Tableaux pour la lettre-code d'effectif d'échantillon P (Plans individuels).74
10-Q Tableaux pour la lettre-code d'effectif d'échantillon Q (Plans individuels). 76
10-R Tableaux pour la lettre-code d'effectif d'échantillon R (Plans individuels) .78
10-S Tableaux pour la lettre-code d'effectif d'échantillon S (Plans individuels).80
iii
© ISO
11-A Plans d'échantillonnage simple en contrôle normal (Tableau général auxiliaire).81
11-B Plans d'échantillonnage simple en contrôle renforcé (Tableau général auxiliaire) .82
11-C Plans d'échantillonnage simple en contrôle réduit (Tableau général auxiliaire).83
12 Courbes d'efficacité (OC) normalisées.84
Annexe A (informative) Exemple dans le cas d'un plan d'échantillonnage non constant.86
Bibliographie.87
iv
© ISO
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 (CEI) en ce qui concerne la normalisation électrotechnique.
Les Normes internationales sont rédigées conformément aux règles données dans les Directives ISO/CEI, Partie 3.
Les projets de Normes internationales adoptés par les comités techniques sont soumis aux comités membres pour
vote. Leur publication comme Normes internationales requiert l'approbation de 75 % au moins des comités
membres votants.
La Norme internationale ISO 2859-1 a été élaborée par le comité technique ISO/TC 69, Application des méthodes
statistiques, sous-comité SC 5, Échantillonnage en vue d'acceptation.
Cette deuxième édition de l'ISO 2859-1 annule et remplace la première édition (ISO 2859-1:1989), dont elle
constitue une révision technique.
La présente édition contient des modifications significatives, à savoir:
une nouvelle méthode de modification du contrôle normal au contrôle réduit;
une référence à l'échantillonnage successif partiel comme alternative au contrôle réduit;
le terme «qualité limite» a été remplacé par «qualité du risque client» dans le titre des Tableaux 6-A, 6-B, 6-C,
7-A, 7-B et 7-C;
un nouveau tableau a été ajouté qui donne le risque fournisseur comme probabilité de rejet des lots avec
pourcentage d'individus non conformes égal au NQA;
des plans optionnels à critère d'acceptation décimal ont été ajoutés; l'objectif de ces plans est de fournir une
progression continue des plans à critère d'acceptation zéro aux plans à critère d'acceptation 1. Les plans à
critère d'acceptation décimal sont présentés dans les Tableaux 11-A, 11-B et 11-C, dans lesquelles ils
remplacent les flèches aux endroits correspondants des Tableaux 2-A, 2-B et 2-C;
des plans réduits ont été modifiés pour éliminer l'intervalle entre les critères d'acceptation et de rejet;
des modifications ont été apportées aux plans d'échantillonnage doubles pour fournir un effectif moyen
d'échantillon inférieur;
des plans d'échantillonnage multiples ont été modifiés et comportent maintenant cinq étapes au lieu de sept.
Cette modification n'augmente pas l'effectif moyen d'échantillon. Certains des nouveaux plans ont un effectif
d'échantillon inférieur à ceux de l'édition précédente;
des courbes d'efficacité ont été introduites (voir Tableau 12).
v
© ISO
L'ISO 2859 comprend les parties suivantes, présentées sous le titre général Règles d'échantillonnage pour les
contrôles par attributs:
Partie 0: Introduction au système d'échantillonnage par attributs de l'ISO 2859
Partie 1: Procédures d'échantillonnage pour les contrôles lot par lot, indexés d'après le niveau de qualité
acceptable (NQA)
Partie 2: Plans d'échantillonnage pour les contrôles de lots isolés, indexés d'après la qualité limite (QL)
Partie 3: Procédures d'échantillonnage successif partiel
Il est fortement recommandé d'utiliser la présente partie de l'ISO 2859 conjointement avec l'ISO 2859-0 qui contient
des exemples explicatifs.
L'annexe A de la présente partie de l'ISO 2859 est donnée uniquement à titre d'information.
vi
NORME INTERNATIONALE © ISO ISO 2859-1:1999(F)
Règles d'échantillonnage pour les contrôles par attributs —
Partie 1:
Procédures d'échantillonnage pour les contrôles lot par lot, indexés
d'après le niveau de qualité acceptable (NQA)
1 Domaine d’application
1.1 La présente partie de l'ISO 2859 spécifie un système d'échantillonnage pour acceptation pour les contrôles par
attributs. Elle est indexée d'après le niveau de qualité acceptable (NQA).
Son but est, par les moyens de pression économiques et psychologiques relevant de la non-acceptation de lots, de
contraindre un fournisseur à maintenir la qualité moyenne de la fabrication à un niveau au moins égal au niveau de
qualité acceptable spécifié, tout en limitant le risque pour le client d'accepter occasionnellement un lot défectueux.
Les procédures d'échantillonnage contenues dans la présente partie de l'ISO 2859 sont applicables, mais d'une
manière non limitative, aux contrôles de différents domaines tels que:
produits finis;
composants ou matières premières;
opérations;
matériels en cours de fabrication;
fournitures en stock;
opérations d'entretien;
informations ou enregistrements;
procédures administratives.
1.2 Ces procédures sont principalement destinées au contrôle de séries continues de lots, c'est-à-dire de séries
suffisamment importantes pour permettre l'application des règles de modification du contrôle (9.3). Ces règles ont
pour but:
a) d'assurer la protection du client en cas de détection d'une détérioration de la qualité (par le passage à un
contrôle renforcé ou l'interruption du contrôle);
b) de constituer une incitation à réduire les coûts de contrôle (à la discrétion de l'autorité responsable) si la qualité
se maintient continuellement bonne (par passage à un contrôle réduit).
Les plans d'échantillonnage de la présente partie de l'ISO 2859 peuvent aussi être utilisés pour le contrôle de lots
isolés mais, dans ce cas, l'utilisateur doit avoir soin de consulter les courbes d'efficacité afin de trouver un plan qui
lui donnera la protection désirée (voir 12.6). Dans ce cas, l'utilisateur est également renvoyé aux plans
d'échantillonnage indexés d'après la qualité limite (QL) spécifiés dans l'ISO 2859-2.
© ISO
2 Références normatives
Les documents normatifs suivants contiennent des dispositions qui, par suite de la référence qui y est faite,
constituent des dispositions valables pour la présente partie de l'ISO 2859. Pour les références datées, les
amendements ultérieurs ou les révisions de ces publications ne s’appliquent pas. Toutefois, les parties prenantes
aux accords fondés sur la présente partie de l'ISO 2859 sont invitées à rechercher la possibilité d'appliquer les
éditions les plus récentes des documents normatifs indiqués ci-après. Pour les références non datées, la dernière
édition du document normatif en référence s’applique. Les membres de l'ISO et de la CEI possèdent le registre des
Normes internationales en vigueur.
ISO 2859-3:1991, Règles d'échantillonnage pour les contrôles par attributs — Partie 3: Procédures
d'échantillonnage successif partiel.
ISO 3534-1:1993, Statistique — Vocabulaire et symboles — Partie 1: Probabilité et termes statistiques généraux.
ISO 3534-2:1993, Statistique — Vocabulaire et symboles — Partie 2: Maîtrise statistique de la qualité.
3 Termes, définitions et symboles
3.1 Termes et définitions
Pour les besoins de la présente partie de l'ISO 2859, les termes et définitions donnés dans l'ISO 3534-1 et
l'ISO 3534-2, ainsi que les termes et définitions suivants s'appliquent.
NOTE Afin d'en faciliter l'application, les définitions de certains de ces termes sont tirées de l'ISO 3534-1 et de
l'ISO 3534-2, alors que d'autres termes sont redéfinis ou nouvellement définis.
3.1.1
contrôle
actions telles que mesurer, examiner, essayer, passer au calibre une ou plusieurs caractéristiques d'un produit ou
service, et comparer les résultats obtenus aux exigences spécifiques afin de déterminer si la conformité de chacune
des caractéristiques est atteinte
3.1.2
contrôle en première présentation
premier contrôle d'un lot conformément aux dispositions de la présente partie de l'ISO 2859
NOTE À ne pas confondre avec le contrôle d'un lot qui est à nouveau présenté au contrôle après avoir été non accepté.
3.1.3
contrôle par attributs
contrôle par lequel un individu est simplement classé conforme ou non conforme, ceci par rapport à une exigence
spécifiée ou à un ensemble d'exigences spécifiées, ou bien par lequel le nombre de non-conformités dans l'individu
est compté
NOTE Le contrôle par attributs comprend le contrôle de conformité des individus ainsi que le contrôle du nombre de non-
conformités par cent individus.
3.1.4
individu
ce qui peut être décrit et considéré individuellement
EXEMPLES
une entité physique;
une quantité définie de matière;
un service, une activité ou un processus;
un organisme ou une personne; ou
une combinaison de ces éléments.
© ISO
3.1.5
non-conformité
non-satisfaction aux exigences spécifiées
NOTE 1 Dans certaines situations, les exigences spécifiées coïncident avec les conditions d'utilisation requises par un client
(voir défaut, 3.1.6). Dans d'autres situations, il n'y a pas coïncidence, soit que les exigences sont plus ou moins strictes, soit
que la relation exacte avec les conditions d'utilisation est peu connue ou mal comprise.
NOTE 2 La non-conformité peut être en général classée de la façon suivante, en fonction de son degré de gravité:
Classe A: Type de non-conformités considéré comme ayant les plus graves incidences. Dans un contrôle de réception
par échantillonnage, ce type de non-conformités se verra affecter une valeur du niveau de qualité acceptable très faible;
Classe B: Type de non-conformités ayant une incidence moins importante et pour lesquelles pourra être fixée une valeur
du niveau de qualité acceptable supérieure à celles de la classe A et inférieure à celles de la classe C, si une troisième
catégorie existe, et ainsi de suite.
NOTE 3 L'ajout de caractères et de classes de non-conformités affecte généralement la probabilité globale d'acceptation du
produit.
NOTE 4 Il convient d'adapter le nombre de classes, l'affectation d'une non-conformité dans une classe donnée ainsi que le
choix du niveau de qualité acceptable pour chaque classe aux exigences de qualité de la situation particulière considérée.
3.1.6
défaut
non-satisfaction aux exigences de l'utilisation prévue
NOTE 1 Le terme «défaut» est d'usage approprié quand une caractéristique de qualité d'un produit ou d'un service est
évaluée en fonction de l'utilisation attendue (par opposition avec la conformité à des spécifications).
NOTE 2 Le terme «défaut» ayant une signification bien précise du point de vue légal, il convient de ne pas l'employer
comme un terme général.
3.1.7
individu non conforme
individu avec une ou plusieurs non-conformités
NOTE Les individus non conformes sont généralement classés de la façon suivante, en fonction de leur degré de gravité:
Classe A: individu qui contient une ou plusieurs non-conformités de classe A et qui peut aussi contenir des non-
conformités de classe B et/ou C, et ainsi de suite;
Classe B: individu qui contient une ou plusieurs non-conformités de classe B et qui peut aussi contenir des non-
conformités de classe C, et ainsi de suite, mais ne contient pas de non-conformités de classe A.
3.1.8
pourcentage de non conformes
ádans un échantillonñ cent fois le nombre d'individus non conformes de l'échantillon divisé par l'effectif de
l'échantillon, soit:
d
·100
n
où
d est le nombre d'individus non conformes de l'échantillon;
n est l'effectif d'échantillon.
3.1.9
pourcentage de non conformes
ádans une population ou dans un lotñ cent fois le nombre d'individus non conformes de la population ou du lot divisé
par l'effectif de la population ou du lot, soit:
D
100 p = 100
N
© ISO
où
p est la proportion d'individus non conformes;
D est le nombre d'individus non conformes de la population ou du lot;
N est l'effectif de la population ou du lot.
NOTE 1 Dans la présente partie de l'ISO 2859, les termes pourcentage de non conformes (3.1.8 et 3.1.9) et nombre de
non-conformités par cent individus (3.1.10 et 3.1.11) sont principalement employés à la place des termes théoriques
«proportion d'individus non conformes» et «nombre de non-conformités par individu», car les deux termes précités sont les
plus largement répandus.
NOTE 2 Cette définition est différente de celle donnée dans l'ISO 3534-2.
3.1.10
nombre de non-conformités par 100 individus
ádans un échantillonñ cent fois le nombre de non-conformités de l'échantillon divisé par l'effectif d'échantillon, soit:
d
n
où
d est le nombre de non-conformités trouvées dans l'échantillon;
n est l'effectif d'échantillon.
3.1.11
nombre de non-conformités par 100 individus
ádans une population ou dans un lotñ cent fois le nombre de non-conformités de la population ou du lot divisé par
l'effectif de la population ou du lot, soit:
D
100 p = 100
N
où
p est le nombre de non-conformités par individu;
D est le nombre de non-conformités de la population ou du lot;
N est l'effectif de la population ou du lot.
NOTE Un individu peut contenir une ou plusieurs non-conformités.
3.1.12
autorité responsable
concept utilisé pour garantir la neutralité de la présente partie de l'ISO 2859 (essentiellement en matière de
spécification), qu'elle soit invoquée ou appliquée par les parties ou par les tiers
NOTE 1 L'autorité responsable peut être:
a) le service qualité de la société du fournisseur (première partie);
b) le client ou le service des approvisionnements (seconde partie);
c) un organisme indépendant de vérification et de certification (tierce partie);
d) n'importe lequel parmi a), b) et c), distinctement selon la fonction considérée (voir Note 2), en conformité à un accord écrit
entre les deux parties, par exemple un document entre le fournisseur et le client.
NOTE 2 Les tâches et fonctions de l'autorité responsable sont indiquées dans la présente partie de l'ISO 2859 (voir 5.2, 6.2,
7.2, 7.3, 7.5, 7.6, 9.1, 9.3.3, 9.4, 10.1, 10.3 et 13.1).
© ISO
3.1.13
lot
quantité définie d'un produit, d'une matière ou d'un service réunis
NOTE Un lot pour contrôle peut être constitué de plusieurs lots de production ou de parties de lots de production.
3.1.14
effectif du lot
nombre d'individus dans un lot
3.1.15
échantillon
ensemble d'un ou de plusieurs individus prélevés dans un lot et destinés à fournir des informations sur ce lot
3.1.16
effectif d'échantillon
nombre d'individus constituant un échantillon
3.1.17
plan d'échantillonnage
combinaison de l'effectif ou des effectifs d'échantillon soumis au contrôle et des critères d'acceptabilité du lot
correspondants
NOTE 1 Un plan d'échantillonnage simple est la combinaison d'un effectif d'échantillon et de critères d'acceptation et de
rejet. Un plan d'échantillonnage double est la combinaison de deux effectifs d'échantillon et de critères d'acceptation et de rejet
pour le premier échantillon et pour l'échantillon combiné.
NOTE 2 Un plan d'échantillonnage ne contient pas de règles indiquant la manière dont sont constitués les échantillons.
NOTE 3 Pour les besoins de la présente partie de l'ISO 2859, il est utile de faire la distinction entre les termes plan
d'échantillonnage (3.1.17), procédure d'échantillonnage (3.1.18) et système d'échantillonnage (3.1.19).
3.1.18
procédure d'échantillonnage
combinaison de plans d'échantillonnage assortis de règles indiquant comment passer d'un plan d'échantillonnage à
un autre
NOTE Voir 9.3.
3.1.19
système d'échantillonnage
ensemble de plans ou de procédures d'échantillonnage assorti(e)s de leurs propres règles de changement de plan,
et de procédures d'échantillonnage comprenant les critères qui permettent d'opter pour les plans ou procédures
approprié(e)s
NOTE La présente partie de l'ISO 2859 présente un système d'échantillonnage indexé suivant les classes d'effectifs de lot,
des niveaux de contrôle et des NQA. Un système de plans indexés d'après la qualité limite (QL) est présenté dans
l'ISO 2859-2.
3.1.20
contrôle normal
utilisation d'un plan d'échantillonnage (3.1.17) avec un critère d'acceptation qui a été conçu pour garantir au
fournisseur une grande probabilité d'acceptation si la moyenne de processus (3.1.25) du lot est supérieure au
niveau de qualité acceptable (3.1.26)
NOTE Le contrôle normal est utilisé lorsqu'il n'y a pas de raison de penser que la moyenne de processus (3.1.25) diffère du
niveau acceptable.
3.1.21
contrôle renforcé
utilisation d'un plan d'échantillonnage (3.1.17) avec un critère d'acceptation plus sévère que celui du plan
correspondant en contrôle normal (3.1.20)
NOTE Le contrôle renforcé est demandé lorsque les résultats de contrôle d'un nombre prédéterminé de lots consécutifs
indiquent que la moyenne de processus (3.1.25) pourrait être inférieure au NQA (3.1.26).
© ISO
3.1.22
contrôle réduit
utilisation d'un plan d'échantillonnage (3.1.17) avec un effectif d'échantillon (3.1.16) plus faible que celui du plan
correspondant en contrôle normal (3.1.20) et un critère d'acceptation comparable à celui du plan correspondant
en contrôle normal
NOTE 1 La capacité discriminatoire est inférieure sous contrôle réduit par rapport au contrôle normal.
NOTE 2 Le contrôle réduit peut être demandé lorsque les résultats de contrôle d'un nombre prédéterminé de lots consécutifs
indique que la moyenne de processus (3.1.25) est supérieure au NQA (3.1.26).
3.1.23
score de passage
indicateur utilisé en contrôle normal pour déterminer si les résultats obtenus pendant le contrôle en cours sont
suffisamment satisfaisants pour permettre le passage au contrôle réduit
NOTE Voir 9.3.3.
3.1.24
score d'acceptation
indicateur utilisé pour des plans à critère d'acceptation décimal pour déterminer l'acceptabilité du lot
NOTE Voir 13.2.1.2.
3.1.25
moyenne d'un processus
moyenne du niveau du processus sur une période de temps définie ou sur une quantité de production définie
[ISO 3534-2, 3.1.2]
NOTE Dans la présente partie de l'ISO 2859, la moyenne d'un processus est le niveau de qualité (pourcentage d'individus
non conformes ou nombre de non-conformités par cent individus) pendant une période où le processus est en état de maîtrise
statistique.
3.1.26
niveau de qualité acceptable
NQA
sur une série continue de lots, niveau de qualité qui, pour le contrôle par échantillonnage, constitue la limite pour
une moyenne de processus satisfaisante
NOTE 1 Ce concept ne s'applique que dans le cas où une procédure d'échantillonnage comportant des règles de passage
et de suspension de contrôle, telles que définies dans l'ISO 2859-1 et l'ISO 3951, est utilisée.
NOTE 2 Bien que des lots individuels d'aussi mauvaise qualité que la limite d'acceptation de qualité puissent être acceptés
avec une assez forte probabilité, la désignation d'une limite d'acceptation de qualité ne suggère pas que ce soit un niveau de
qualité souhaitable. Les procédures d'échantillonnage définies dans des Normes internationales telles que la présente partie
de l'ISO 2859, avec leurs règles de passage et de suspension de contrôle d'échantillonnage, sont destinées à encourager les
fournisseurs à obtenir des moyennes de processus nettement meilleures que la NQA. Faute de quoi, il y a un grand risque que
la sévérité du contrôle devienne renforcée, auquel cas les critères d'acceptation des lots deviennent plus exigeants. Une fois
en contrôle renforcé, et à moins que des actions soient entreprises pour améliorer le processus, il est très probable que la
règle de suspension du contrôle soit invoquée dans l'attente de cette amélioration.
3.1.27
qualité du risque client
QRC
niveau de qualité du lot ou du processus qui, dans un plan d'échantillonnage, correspond à un risque client spécifié
NOTE Le risque client est généralement de 10 %.
3.1.28
qualité limite
QL
pour un lot considéré isolément, niveau de qualité qui, pour le contrôle par échantillonnage, correspond à une
probabilité d'acceptation relativement faible
© ISO
3.2 Symboles et abréviations
Les symboles et abréviations utilisés dans la présente partie de l'ISO 2859 sont les suivants:
Ac critère d'acceptation
d nombre d'individus non conformes (ou de non-conformités) trouvé(e)s dans un échantillon tiré d'un lot
D nombre d'individus non conformes dans un lot
LQMAC limite de qualité moyenne après contrôle (en pourcentage d'individus non conformes ou en nombre de
non-conformités par cent individus)
n effectif d'échantillon
N effectif du lot
NQA niveau de qualité acceptable (en pourcentage d'individus non conformes ou en nombre de non-
conformités par cent individus)
p moyenne de processus
p niveau de qualité pour lequel la probabilité d'acceptation est x, et où x est une décimale
x
P probabilité d'acceptation (en pourcentage)
a
QL qualité limite (en pourcentage d'individus non conformes ou en nombre de non-conformités par cent
individus)
QMAC qualité moyenne après contrôle (en pourcentage d'individus non conformes ou en nombre de non-
conformités par cent individus)
QRC qualité du risque client (en pourcentage d'individus non conformes ou en nombre de non-conformités par
cent individus)
Re critère de rejet
NOTE Le symbole n peut être affecté d'un indice. Les indices 1 à 5 désignent respectivement les échantillons 1 à 5.
ème
Généralement, n est l'effectif du i échantillon, en échantillonnage double et multiple.
i
4 Expression de la non-conformité
4.1 Généralités
Le degré de non-conformité du produit doit être exprimé soit en pourcentage d'individus non conformes (voir 3.1.8
et 3.1.9), soit en nombre de non-conformités par 100 individus (voir 3.1.10 et 3.1.11). Les Tableaux 7, 8 et 10 sont
basées sur l'hypothèse que les non-conformités apparaissent de façon aléatoire et statistiquement indépendante. Si
l'on sait qu'une non-conformité dans un individu est causée par une condition également susceptible d'être la cause
d'autres non-conformités, les individus doivent être considérés comme étant conformes ou non et les non-
conformités multiples ignorées.
4.2 Classification des non-conformités
Étant donné que la plupart des échantillonnages pour acceptation entraînent l'évaluation de plus d'une
caractéristique de qualité et qu'ils peuvent différer de façon importante en termes de qualité et/ou de conséquences
économiques, il est souvent souhaitable de classer les types de non-conformités suivant les classes acceptées et
définies en 3.1.5. Il convient d'adapter le nombre de classes, l'affectation de non-conformités dans des classes
© ISO
données ainsi que le choix du NQA pour chaque classe aux exigences de qualité de la situation particulière
considérée.
5 Niveau de qualité acceptable (NQA)
5.1 Utilisation et application
Le NQA est utilisé en même temps que la lettre-code d'effectif d'échantillon (voir 10.2) pour repérer les plans
d'échantillonnage et les procédures d'échantillonnage décrits dans la présente partie de l'ISO 2859.
Fixer pour une non-conformité, ou un groupe de non-conformités données, une valeur déterminée du NQA revient à
indiquer que la procédure par échantillonnage conduira à accepter la grande majorité des lots soumis au contrôle, à
condition que le niveau de qualité du pourcentage d'individus non conformes (ou du nombre de non-conformités par
100 individus) dans ces lots ne dépasse pas la valeur fixée pour le NQA. Les plans d'échantillonnage contenus
dans la présente partie de l'ISO 2859 ont été établis de telle façon que la probabilité d'acceptation pour un NQA
déterminé dépende de l'effectif de l'échantillon, cette probabilité étant généralement plus élevée, pour un NQA
donné, pour les échantillons d'effectif élevé que pour les échantillons de faible effectif.
Le NQA est un paramètre de la procédure d'échantillonnage, à ne pas confondre avec la moyenne d'un processus
qui définit le niveau opératoire d'un processus de fabrication. Il faut normalement que la moyenne de processus soit
supérieure au NQA afin d'éviter, lors du contrôle, le rejet d'un nombre excessif de lots.
ATTENTION: La fixation d'un NQA n'implique pas, pour le fournisseur, le droit de livrer sciemment des
individus non conformes.
5.2 Spécifications des NQA
Le NQA à utiliser doit être spécifié dans les contrats ou par l'autorité responsable (ou conformément aux exigences
établies par cette dernière). Différents NQA peuvent être fixés pour des groupes de non-conformités considérées
collectivement, ou pour chaque non-conformité particulière définie en 3.1.5. La classification en groupes doit
correspondre aux exigences de qualité de la situation considérée. On peut fixer un NQA pour un groupe de non-
conformités en plus des NQA pour des non-conformités ou sous-groupes compris dans ce groupe. Lorsque le
niveau de qualité est exprimé en pourcentage d'individus non conformes (3.1.8 et 3.1.9), les valeurs du NQA ne
doivent pas dépasser 10 % de non conformes. Lorsque le niveau de qualité est exprimé en nombre de non-
conformités par 100 individus (3.1.10 et 3.1.11), les valeurs du NQA jusqu'à 1 000 non-conformités par 100
individus peuvent être utilisées.
5.3 NQA recommandés
Les séries de valeurs des NQA données dans les tableaux sont dites «séries de valeurs recommandées» du NQA.
Si pour un produit quelconque, on spécifie une valeur du NQA autre qu'une de ces valeurs, les tableaux ne sont
pas applicables.
6 Présentation du produit pour échantillonnage
6.1 Constitution des lots
Le produit doit être rassemblé en lots ou sous-lots identifiables, ou de toute autre manière qui pourrait être prescrite
(voir 6.2). Chaque lot doit, autant que possible, être constitué d'individus d'un seul type et d'une seule classe, taille
et composition, fabriqués dans les mêmes conditions et essentiellement dans la même période de temps.
© ISO
6.2 Présentation des lots
La constitution des lots, leur effectif et la façon dont chaque lot doit être présenté et identifié par le fournisseur
doivent être spécifiés ou approuvés par, ou selon, l'autorité responsable. Si cela est nécessaire, le fournisseur doit
prévoir un espace suffisant et approprié pour le stockage de chaque lot, les moyens nécessaires à l'identification et
à la présentation correcte des lots et le personnel pour toutes les manutentions du produit requises lors du
prélèvement des échantillons.
7 Acceptation et rejet
7.1 Acceptabilité des lots
L'acceptabilité d'un lot doit être déterminée au moyen d'un ou de plusieurs plans d'échantillonnage.
Le terme «non-acceptation» est utilisé à la place de «rejet» quand il qualifie le résultat de la procédure. Le mot
«rejet» et ses dérivés servent à qualifier les mesures qui peuvent être prises par le client, telles que celles
impliquées par «critère de rejet».
7.2 Enlèvement des lots non acceptables
C'est l'autorité responsable qui décide du sort des lots non acceptés. Ces lots peuvent être mis au rebut, triés (avec
ou sans remplacement des individus non conformes), remaniés, réévalués selon des critères d'utilisation plus
spécifiques, mis de côté pour informations complémentaires, etc.
7.3 Individus non conformes
Si un lot est accepté, réserve expresse est faite du droit de ne pas accepter tout individu non conforme trouvé
pendant le contrôle, que cet individu fasse partie ou non d'un échantillon. Les individus trouvés non conformes
peuvent être retouchés ou remplacés par des individus conformes, puis soumis à un nouveau contrôle avec
l'agrément et suivant les exigences de l'autorité responsable.
7.4 Classes de non-conformités ou d'individus non conformes
L'affectation de non-conformités ou d'individus non conformes à deux classes ou plus nécessite d'utiliser un
ensemble de plans d'échantillonnage. En général, les plans d'échantillonnage ont un effectif d'échantillons commun
mais des critères d'acceptation différents pour chacune des classes de NQA différent (voir Tableaux 2, 3 et 4).
7.5 Réserve spéciale concernant les classes critiques de non-conformités
Certains types de non-conformités peuvent avoir une importance critique. Le présent paragraphe spécifie les
dispositions particulières pour de tels types de non-conformités particulières. À la discrétion de l'autorité
responsable, il peut être décidé de contrôler chaque individu du lot en ce qui concerne ces classes de non-
conformités particulières. Réserve est faite du droit de contrôler chaque individu présenté en ce qui concerne ces
non-conformités particulières et de ne pas accepter tout de suite le lot lorsqu'une non-conformité de ce type est
trouvée. Réserve est également faite du droit d'échantillonnage, pour des classes de non-conformités spécifiées, de
chaque lot présenté par le fournisseur et du droit de ne pas accepter le lot si l'échantillon prélevé contient une ou
plusieurs de ces non-conformités.
7.6 Lots soumis à un nouveau contrôle
Toutes les parties doivent être immédiatement averties quand un lot n'est pas accepté. De tels lots ne doivent pas
être représentés au contrôle que lorsque tous les individus auront été examinés ou réessayés et lorsque le
fournisseur aura vérifié que tous les individus non conformes ont été éliminés ou remplacés par des individus
conformes ou l'ensemble des non-conformités corrigées. L'autorité responsable doit décider si le nouveau contrôle
doit être effectué en contrôle normal ou en contrôle renforcé; elle doit décider également si le nouveau contrôle doit
s'appliquer à tous les types ou à toutes les classes de non-conformités ou seulement aux types ou classes
particuliers (particulières) de non-conformités ayant provoqué la non-acceptation initiale.
© ISO
8 Prélèvement des échantillons
8.1 Choix de l'échantillon
Les individus choisis pour l'échantillon doivent être prélevés du lot par échantillonnage simple aléatoire (voir 2.1.5
de l'ISO 3534-2:1993). Cependant, lorsque le lot est composé de sous-lots ou strates de lots identifiés suivant un
certain critère rationnel, l'échantillonnage stratifié doit être utilisé de sorte que l'effectif du sous-échantillon de
chacun des sous-lots ou strates de lots soit proportionnel à l'effectif de ce sous-lot ou strate de lots (pour plus de
détails, voir 2.25 de l'ISO 2859-0:1995).
8.2 Moment du prélèvement
Les échantillons peuvent être prélevés soit après production du lot, soit pendant la production du lot. Dans les deux
cas, les échantillons doivent être prélevés conformément à 8.1.
8.3 Échantillonnage double ou multiple
Dans le cas d'un échantillonnage double ou multiple, chaque échantillon suivant doit être prélevé dans le restant du
même lot.
9 Contrôles normal, renforcé et réduit
9.1 Début du contrôle
Le contrôle normal doit être adopté au début du contrôle, sauf stipulation contraire de l'autorité responsable.
9.2 Poursuite du contrôle
Le contrôle normal, renforcé ou réduit doit se poursuivre tel quel sur les lots successifs, sauf si les règles fixées en
9.3 requièrent une modification de la sévérité du contrôle. Ces règles doivent être appliquées de façon
indépendante pour chaque classe de non-conformités ou d'individus non conformes.
9.3 Règles de modification du contrôle (voir Figure 1)
9.3.1 Passage du contrôle normal au contrôle renforcé
Si l'on se trouve en contrôle normal, le contrôle renforcé doit être instauré dès que deux lots sur cinq (ou sur moins
de cinq lots) consécutifs, contrôlés en première présentation, ne sont pas acceptés (on ne tient pas compte dans ce
chiffre des lots présentés une seconde fois au contrôle).
9.3.2 Passage du contrôle renforcé au contrôle normal
Si l'on se trouve en contrôle renforcé, le contrôle normal doit être rétabli dès que cinq lots consécutifs ont été
acceptés en première présentation.
© ISO
© ISO
9.3.3 Passage du contrôle normal au contrôle réduit
9.3.3.1 Généralités
Si l'on se trouve en contrôle normal, le contrôle réduit doit être instauré lorsque toutes les éventualités suivantes se
produisent en première présentation des lots:
a) la valeur du score de passage (voir 9.3.3.2) pour le contrôle en cours est au moins à 30, et
b) la production est régulière, et
c) l'autorité responsable estime souhaitable de passer au contrôle réduit.
9.3.3.2 Score de passage
Le calcul du score de passage doit commencer au démarrage du contrôle normal, sauf spécification contraire de
l'autorité responsable.
Le score de passage doit être mis à zéro au démarrage et mis à jour au fur et à mesure de la progression du
contrôle de chaque lot successivement soumis au contrôle normal en première présentation.
a) Plans d'échantillonnage simple:
1) lorsque le critère d'acceptation est supérieur ou égal à 2, ajouter 3 au score de passage si le lot avait été
accepté avec un NQA supérieur; sinon, remettre le score de passage à zéro;
2) lorsque le critère d'acceptation est 0 ou 1, ajouter 2 au score de passage si le lot est accepté; sinon,
remettre le score de passage à zéro.
b) Plans d'échantillonnage double et multiple:
1) dans le cas d'un plan d'échantillonnage double, ajouter 3 au score de passage si le lot est accepté après
le premier échantillon; sinon, remettre le score de passage à zéro;
2) dans le cas d'un plan d'échantillonnage multiple, ajouter 3 au score de passage si le lot est accepté au
troisième échantillon; sinon, remettre le score de passage à zéro.
NOTE L'application du score de passage est illustrée dans l'annexe A.
9.3.4 Passage du contrôle réduit au contrôle normal
Si l'on se trouve en contrôle réduit, le contrôle normal doit être rétabli lorsque l'une quelconque des éventualités
suivantes se produit en première présentation des lots:
a) un lot n'est pas accepté, ou
b) la production devient irrégulière ou se ralentit, ou
c) d'autres conditions justifient que le contrôle normal soit rétabli.
9.4 Suspension du contrôle
Si le nombre cumulé de lots non acceptés dans une séquence de lots consécutifs soumis en première présentation
au contrôle renforcé est de 5, les procédures d'acceptation de la présente partie de l'ISO 2859 ne doivent pas être
rétablies tant que des mesures destinées à améliorer la qualité du produit ou service présenté au contrôle n'ont pas
été prises par le fournisseur, et tant que l'autorité responsable n'a pas reconnu les probabilités de réussite de cette
action. Le contrôle renforcé doit alors être appliqué comme si 9.3.1 avait été invoqué.
© ISO
9.5 Procédure d'échantillonnage successif partiel
Le contrôle lot par lot dans la présente partie de l'ISO 2859 peut être remplacé par l'échantillonnage successif
partiel si les exigences de l'ISO 2859-3 sont satisfaites.
NOTE L'utilisation des procédures d'échantillonnage successif partiel de l'ISO 2859-3 à la place des procédures de contrôle
réduit de la présente partie de l'ISO 2859 comporte des limites. Certains NQA et certains niveaux de contrôle ne sont pas
applicables.
10 Plans d'échantillonnage
10.1 Niveau de contrôle
Le niveau de contrôle représente la proportion de contrôle. Pour les usages généraux, trois niveaux de con
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Frequently Asked Questions
SIST ISO 2859-1:2003 is a standard published by the Slovenian Institute for Standardization (SIST). Its full title is "Sampling procedures for inspection by attributes -- Part 1: Sampling schemes indexed by acceptance quality limit (AQL) for lot-by-lot inspection". This standard covers: 1.1 This part of ISO 2859 specifies an acceptance sampling system for inspection by attributes. It is indexed in terms of the acceptance quality limit (AQL). Its purpose is to induce a supplier through the economic and psychological pressure of lot non-acceptance to maintain a process average at least as good as the specified acceptance quality limit, while at the same time providing an upper limit for the risk to the consumer of accepting the occasional poor lot. Sampling schemes designated in this part of ISO 2859 are applicable, but not limited, to inspection of ¾ end items, ¾ components and raw materials, ¾ operations, ¾ materials in process, ¾ supplies in storage, ¾ maintenance operations, ¾ data or records, and ¾ administrative procedures. 1.2 These schemes are intended primarily to be used for a continuing series of lots, that is, a series long enough to allow the switching rules (9.3) to be applied. These rules provide: a) a protection to the consumer (by means of a switch to tightened inspection or discontinuation of sampling inspection) should a deterioration in quality be detected; b) an incentive (at the discretion of the responsible authority) to reduce inspection costs (by means of a switch to reduced inspection) should consistently good quality be achieved. Sampling plans in this part of ISO 2859 may also be used for the inspection of lots in isolation but, in this case the user is strongly advised to consult the operating characteristic curves to find a plan that will yield the desired protection (see 12.6). In that case, the user is also referred to the sampling plans indexed by limiting quality (LQ) given in ISO 2859-2.
1.1 This part of ISO 2859 specifies an acceptance sampling system for inspection by attributes. It is indexed in terms of the acceptance quality limit (AQL). Its purpose is to induce a supplier through the economic and psychological pressure of lot non-acceptance to maintain a process average at least as good as the specified acceptance quality limit, while at the same time providing an upper limit for the risk to the consumer of accepting the occasional poor lot. Sampling schemes designated in this part of ISO 2859 are applicable, but not limited, to inspection of ¾ end items, ¾ components and raw materials, ¾ operations, ¾ materials in process, ¾ supplies in storage, ¾ maintenance operations, ¾ data or records, and ¾ administrative procedures. 1.2 These schemes are intended primarily to be used for a continuing series of lots, that is, a series long enough to allow the switching rules (9.3) to be applied. These rules provide: a) a protection to the consumer (by means of a switch to tightened inspection or discontinuation of sampling inspection) should a deterioration in quality be detected; b) an incentive (at the discretion of the responsible authority) to reduce inspection costs (by means of a switch to reduced inspection) should consistently good quality be achieved. Sampling plans in this part of ISO 2859 may also be used for the inspection of lots in isolation but, in this case the user is strongly advised to consult the operating characteristic curves to find a plan that will yield the desired protection (see 12.6). In that case, the user is also referred to the sampling plans indexed by limiting quality (LQ) given in ISO 2859-2.
SIST ISO 2859-1:2003 is classified under the following ICS (International Classification for Standards) categories: 03.120.30 - Application of statistical methods. The ICS classification helps identify the subject area and facilitates finding related standards.
SIST ISO 2859-1:2003 has the following relationships with other standards: It is inter standard links to SIST ISO 2859-1:2003/Amd 1:2020, SIST ISO 2859-1:2003/C1:2003, ISO 2859-1:1989/Cor 1:1993, ISO 2859-1:1989, SIST ISO 2859-1:1996/C1:1996, SIST ISO 2859-1:1996; is excused to SIST ISO 2859-1:2003/Amd 1:2020, ISO 2859-1:1999/Cor 1:2001, SIST ISO 2859-1:2003/C1:2003. Understanding these relationships helps ensure you are using the most current and applicable version of the standard.
SIST ISO 2859-1:2003 is associated with the following European legislation: EU Directives/Regulations: 2007-01-5312. When a standard is cited in the Official Journal of the European Union, products manufactured in conformity with it benefit from a presumption of conformity with the essential requirements of the corresponding EU directive or regulation.
You can purchase SIST ISO 2859-1:2003 directly from iTeh Standards. The document is available in PDF format and is delivered instantly after payment. Add the standard to your cart and complete the secure checkout process. iTeh Standards is an authorized distributor of SIST standards.
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