INTERNATIONAL ISO

STANDARD 2859-2

Second edition
2020-02

Sampling procedures for inspection by

attributes —
Part 2:
Sampling plans indexed by limiting
quality (LQ) for isolated lot inspection
Règles d'échantillonnage pour les contrôles par attributs —
Partie 2: Plans d'échantillonnage pour les contrôles de lots isolés,
indexés d'après la qualité limite (QL)

Reference number
ISO 2859-2:2020(E)

© ISO 2020
ISO 2859-2:2020(E)


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 ISO 2859-2:2020(E)


Contents Page

Foreword......................................................................................................................................................................................................................................... iv
1 Scope.................................................................................................................................................................................................................................. 1
2 Normative references....................................................................................................................................................................................... 1
3 Terms and definitions, and symbols and abbreviated terms.................................................................................. 2
3.1 Terms and definitions........................................................................................................................................................................ 2
3.2 Symbols and abbreviated terms............................................................................................................................................... 3
4 Choice of sampling plan................................................................................................................................................................................. 3
4.1 General............................................................................................................................................................................................................ 3
4.2 Choice of limiting quality (LQ)................................................................................................................................................... 5
4.3 Obtaining a sampling plan............................................................................................................................................................. 6
5 Acceptance and non-acceptance........................................................................................................................................................... 7
5.1 Drawing of samples.............................................................................................................................................................................. 7
5.2 Acceptance of lots.................................................................................................................................................................................. 7
5.3 Disposition of non-accepted lots.............................................................................................................................................. 7
5.4 Accepted lots with one or more nonconforming units or nonconformities....................................... 7
5.5 Resubmitted lots..................................................................................................................................................................................... 7
6 Sampling for nonconformities................................................................................................................................................................ 7
6.1 Sampling for nonconformities for lots with correlation of the nonconformities........................... 7
6.2 Sampling for nonconformities for lots without correlation of the nonconformities................... 8
6.3 General advice on sampling for nonconformities...................................................................................................... 8
7 Examples........................................................................................................................................................................................................................ 8
7.1 Example of sampling for nonconforming items.......................................................................................................... 8
7.2 Example of sampling for nonconformities for lots with correlation......................................................... 8
7.3 Example of sampling for nonconformities for lots without correlation................................................. 9
8 Additional information about the tables..................................................................................................................................... 9
8.1 Tables 8 to 15 ........................................................................................................................................................................................... 9
8.2 Tables 16 and 17 ................................................................................................................................................................................... 9
Annex A (informative) Statistical properties of single sampling plans..........................................................................37
Annex B (informative) Calculation of the statistical indices......................................................................................................40
Annex C (informative) Information on technical background of confidence intervals.................................45
Bibliography.............................................................................................................................................................................................................................. 46

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ISO 2859-2:2020(E)


Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www​.iso​.org/​directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www​.iso​.org/​patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to
the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see
www​.iso​.org/​iso/​foreword​.html.
This document was prepared by Technical Committee ISO/TC  69, Application of statistical methods,
Subcommittee SC 5, Acceptance sampling.
This second edition cancels and replaces the first edition (ISO 2859-2:1985), which has been technically
revised.
The main changes compared to the previous edition are as follows:
— inclusion of a sampling plan for the number of nonconformities per item in the lot;
— extension of the range of preferred LQ values from the original range "0,5 0,8 1,25 2 3,15 5 8
12,5 20 31,5 to the new one "0,05 0,008 0,125 0,2 0,315 0,5 0,8 1,25 2 3,15 5 8 12,5
20 31,5 50 80 125 200 315 500 800 1 250 2 000 3 150";
— tables of shortest length confidence intervals for lot proportion nonconforming under confidence
levels 0,95 and 0.99;
— new technical annexes: Annex A on "Statistical properties of single sampling plans", Annex B on
"Calculation of the statistical indices" and Annex C on "Information on technical background of
confidence intervals".
A list of all parts in the ISO 2859 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www​.iso​.org/​members​.html.

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INTERNATIONAL STANDARD ISO 2859-2:2020(E)

Sampling procedures for inspection by attributes —

Part 2:
Sampling plans indexed by limiting quality (LQ) for
isolated lot inspection

1 Scope
This document specifies an acceptance sampling system for inspection by attributes indexed by limiting
quality (LQ). The sampling system is used for lots in isolation (isolated sequences of lots, an isolated
lot, a unique lot or a short series of lots), where switching rules, such as those of ISO 2859-1, are not
applicable. Inspection levels, as provided by ISO 2859-1 to control the relative amount of inspection, are
not provided in this document. In many industrial situations, in which switching rules might be used,
they are not applied for a number of reasons, not all of which might be valid:
a) production is intermittent (not continuous);
b) production is from several different sources in varying quantities, i.e. “job lots”;
c) lots are isolated;
d) lots are resubmitted after inspection.
The sampling plans in this document are indexed by a series of specified values of limiting quality (LQ),
where the consumer’s risk (the probability of acceptance at the LQ) is usually below 0,10 (10 %), except
in some instances.
This document is intended both for inspection for nonconforming items and for inspection for
nonconformities per 100 items.
It is intended to be used when the supplier and the consumer both regard the lot to be in isolation. That
is, the lot is unique in that it is the only one of its type produced. It can also be used when there is a
series of lots too short for switching rules to be applied.

2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO  2859-1, Sampling procedures for inspection by attributes — Part 1: Sampling schemes indexed by
acceptance quality limit (AQL) for lot-by-lot inspection
ISO 3534-1, Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in
probability
ISO 3534-2, Statistics — Vocabulary and symbols — Part 2: Applied statistics

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