SIST ISO 28592:2018

INTERNATIONAL ISO
STANDARD 28592
First edition
2017-10
Double sampling plans by attributes
with minimal sample sizes, indexed
by producer's risk quality (PRQ) and
consumer's risk quality (CRQ)
Plans d'échantillonnage double par attributs, avec taille d'échantillon
minimale, indexés par la qualité du risque du fournisseur (QRF) et la
qualité du risque du client (QRC)
Reference number
©
ISO 2017
© ISO 2017, Published in Switzerland
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form
or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior
written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of
the requester.
ISO copyright office
Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. +41 22 749 01 11
Fax +41 22 749 09 47
copyright@iso.org
www.iso.org
ii © ISO 2017 – All rights reserved

Contents Page
Foreword .iv
Introduction .vi
1 Scope . 1
2 Normative references . 1
3 Terms, definitions, abbreviations and symbols . 1
3.1 Terms, definitions and abbreviations . 1
3.2 Symbols . 3
4 Choosing and operating a sampling plan . 3
4.1 Choosing a plan. 3
4.2 Operating a plan for nonconforming items . 4
4.2.1 Acceptance sampling . 4
4.2.2 Hypothesis testing . 4
4.3 Operating a plan for nonconformities . 4
4.3.1 Acceptance sampling . 4
4.3.2 Hypothesis testing . 4
4.4 Notation . 4
5 Operating characteristics . 5
6 Average sample sizes . 5
6.1 Curtailed inspection . 5
6.2 Average sample size (ASSI) for uncurtailed inspection . 5
6.3 Average sample size (ASSI) for curtailed inspection . 6
7 Actual producer's and consumer's risks . 6
8 Average outgoing quality (AOQ) . 6
9 Examples . 6
9.1 Example of sampling plan for nonconforming items . 6
9.2 Example of sampling plan for nonconformities . 7
10 Tables and figures . 7
Annex A (informative) Statistical theory underlying the plans, tables and figures .71
Bibliography .79
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 on 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 the following
URL: www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 5, Acceptance sampling.
This first edition of ISO 28592 cancels and replaces ISO 28801:2011, of which it constitutes a minor
revision to change the reference number from 28801 to 28592.
With the view to achieve a more consistent portfolio, TC 69/SC 5 has simultaneously renumbered the
following standards, by means of minor revisions:
Old reference New reference Title
ISO 2859-10:2006 ISO 28590:2017 Sampling procedures for inspection by attributes — Introduction
to the ISO 2859 series of standards for sampling for inspection by
attributes
ISO 8422:2006 ISO 28591:2017 Sequential sampling plans for inspection by attributes
ISO 28801:2011 ISO 28592:2017 Double sampling plans by attributes with minimal sample sizes,
indexed by producer's risk quality (PRQ) and consumer's risk
quality (CRQ)
ISO 18414:2006 ISO 28593:2017 Acceptance sampling procedures by attributes — Accept-zero sampling
system based on credit principle for controlling outgoing quality
ISO 21247:2005 ISO 28594:2017 Combined accept-zero sampling systems and process control pro-
cedures for product acceptance
ISO 14560:2004 ISO 28597:2017 Acceptance sampling procedures by attributes — Specified quality
levels in nonconforming items per million
ISO 13448-1:2005 ISO 28598-1:2017 Acceptance sampling procedures based on the allocation of priorities
principle (APP) — Part 1: Guidelines for the APP approach
ISO 13448-2:2004 ISO 28598-2:2017 Acceptance sampling procedures based on the allocation of prior-
ities principle (APP) — Part 2: Coordinated single sampling plans
for acceptance sampling by attributes
Cross references between the above listed documents have been corrected in the minor revisions.
iv © ISO 2017 – All rights reserved

A list of all documents in the new ISO 28590 - ISO 28599 series of International Standards can be found
on the ISO website.
Introduction
ISO 2859-1 provides double sampling plans for sampling by attributes. Those plans are indexed by
acceptance quality limit (AQL) and are thus designed for a continuing series of lots. For each preferred
range of lot sizes, i.e. for each sample size code letter, the first and second sample sizes of the double
sampling plans in ISO 2859-1 are constant and equal across AQLs, while the acceptance numbers
increase with the AQL.
As production processes and quality levels have improved during the latter half of the twentieth
century, there has been a shift of interest towards sampling plans with smaller acceptance and rejection
numbers than most of the plans in ISO 2859-1.
Moreover, in some industries, in an effort to focus on customers' more specific requirements, there has
also been a trend towards shorter production runs. Sometimes these production runs are too short for
the switching rules of AQL-indexed plans (such as those of ISO 2859-1) to operate effectively.
In order to address an evolving market need, this International Standard has been developed to provide
double sampling plans by attributes indexed by producer's risk quality (PRQ) and consumer's risk
quality (CRQ) and having the smallest possible acceptance and rejection numbers. No constraint has
been placed on the relative sizes of the first and second sample sizes; instead, the first and second
sample sizes have been derived to minimize the expected total amount of sampling subject to the
nominal producer's risk, α, and consumer's risk, β, not being exceeded. The combinations (α, β) of
nominal risks provided in this International Standard are (5 %, 5 %), (5 %, 10 %) and (10 %, 10 %).
Thus, the double sampling plans provided in this International Standard are of the following kind. In
the case of sampling for nonconforming items, a lot is acceptable if no nonconforming items are found in
the first random sample, and not acceptable if the sample contains two or more nonconforming items. If
the first random sample contains precisely one nonconforming item, a second, smaller random sample
is taken; if no nonconforming items are found in the second sample, then the lot is acceptable, otherwise
it is not acceptable. For each pair of nominal producer's and consumer's risk, up to 17 preferred nominal
values of CRQ and up to 17 preferred nominal values of PRQ are provided.
Similar plans are provided for nonconformities.
The double sampling sample sizes are minimal among sampling plans for acceptance inspection of
isolated lots or for short series of lots. However, because the ISO 28592 plans do not rely on the protection
of switching rules, the sample sizes are necessarily larger than those used for lot-by-lot inspection, such
as those of ISO 2859-1, for similar producer's and consumer's quality levels, where these exist. This
is illustrated by the following two examples, both for nonconforming items with nominal maximum
producer's and consumer's risks or 5 % and 10 % respectively.
EXAMPLE 1
Realized Realized Producer's Consumer's
Sample
Source producer's consumer's risk quali- risk quality
sizes
risk risk ty (PRQ) (CRQ)
ISO 2859-1, code letter E, AQL = 1 % 5 % 10 % 0,394 % 20,6 % 8,8
ISO 28592, Tables 2 and 14 0,266 % 9,639 % 0,4 % 20 % 12,9
EXAMPLE 2
Realized Realized Producer's Consumer's
Sample
Source producer's consumer's risk quali- risk quality
sizes
risk risk ty (PRQ) (CRQ)
ISO 2859-1, code letter F, AQL = 0,65 % 5 % 10 % 0,256 % 10,9 % 13,13
ISO 28592, Tables 2 and 14 0,435 % 9,920 % 0,25 % 10 % 26,16
A compensating feature of the ISO 28592 plans is that many of the realized producer's risks are much
smaller than their nominal values.
vi © ISO 2017 – All rights reserved

INTERNATIONAL STANDARD ISO 28592:2017(E)
Double sampling plans by attributes with minimal sample
sizes, indexed by producer's risk quality (PRQ) and
consumer's risk quality (CRQ)
1 Scope
This International Standard provides double sampling plans by attributes
...

INTERNATIONAL ISO
STANDARD 28592
First edition
2017-10
Double sampling plans by attributes
with minimal sample sizes, indexed
by producer's risk quality (PRQ) and
consumer's risk quality (CRQ)
Plans d'échantillonnage double par attributs, avec taille d'échantillon
minimale, indexés par la qualité du risque du fournisseur (QRF) et la
qualité du risque du client (QRC)
Reference number
©
ISO 2017
© ISO 2017, Published in Switzerland
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form
or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior
written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of
the requester.
ISO copyright office
Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. +41 22 749 01 11
Fax +41 22 749 09 47
copyright@iso.org
www.iso.org
ii © ISO 2017 – All rights reserved

Contents Page
Foreword .iv
Introduction .vi
1 Scope . 1
2 Normative references . 1
3 Terms, definitions, abbreviations and symbols . 1
3.1 Terms, definitions and abbreviations . 1
3.2 Symbols . 3
4 Choosing and operating a sampling plan . 3
4.1 Choosing a plan. 3
4.2 Operating a plan for nonconforming items . 4
4.2.1 Acceptance sampling . 4
4.2.2 Hypothesis testing . 4
4.3 Operating a plan for nonconformities . 4
4.3.1 Acceptance sampling . 4
4.3.2 Hypothesis testing . 4
4.4 Notation . 4
5 Operating characteristics . 5
6 Average sample sizes . 5
6.1 Curtailed inspection . 5
6.2 Average sample size (ASSI) for uncurtailed inspection . 5
6.3 Average sample size (ASSI) for curtailed inspection . 6
7 Actual producer's and consumer's risks . 6
8 Average outgoing quality (AOQ) . 6
9 Examples . 6
9.1 Example of sampling plan for nonconforming items . 6
9.2 Example of sampling plan for nonconformities . 7
10 Tables and figures . 7
Annex A (informative) Statistical theory underlying the plans, tables and figures .71
Bibliography .79
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 on 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 the following
URL: www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 5, Acceptance sampling.
This first edition of ISO 28592 cancels and replaces ISO 28801:2011, of which it constitutes a minor
revision to change the reference number from 28801 to 28592.
With the view to achieve a more consistent portfolio, TC 69/SC 5 has simultaneously renumbered the
following standards, by means of minor revisions:
Old reference New reference Title
ISO 2859-10:2006 ISO 28590:2017 Sampling procedures for inspection by attributes — Introduction
to the ISO 2859 series of standards for sampling for inspection by
attributes
ISO 8422:2006 ISO 28591:2017 Sequential sampling plans for inspection by attributes
ISO 28801:2011 ISO 28592:2017 Double sampling plans by attributes with minimal sample sizes,
indexed by producer's risk quality (PRQ) and consumer's risk
quality (CRQ)
ISO 18414:2006 ISO 28593:2017 Acceptance sampling procedures by attributes — Accept-zero sampling
system based on credit principle for controlling outgoing quality
ISO 21247:2005 ISO 28594:2017 Combined accept-zero sampling systems and process control pro-
cedures for product acceptance
ISO 14560:2004 ISO 28597:2017 Acceptance sampling procedures by attributes — Specified quality
levels in nonconforming items per million
ISO 13448-1:2005 ISO 28598-1:2017 Acceptance sampling procedures based on the allocation of priorities
principle (APP) — Part 1: Guidelines for the APP approach
ISO 13448-2:2004 ISO 28598-2:2017 Acceptance sampling procedures based on the allocation of prior-
ities principle (APP) — Part 2: Coordinated single sampling plans
for acceptance sampling by attributes
Cross references between the above listed documents have been corrected in the minor revisions.
iv © ISO 2017 – All rights reserved

A list of all documents in the new ISO 28590 - ISO 28599 series of International Standards can be found
on the ISO website.
Introduction
ISO 2859-1 provides double sampling plans for sampling by attributes. Those plans are indexed by
acceptance quality limit (AQL) and are thus designed for a continuing series of lots. For each preferred
range of lot sizes, i.e. for each sample size code letter, the first and second sample sizes of the double
sampling plans in ISO 2859-1 are constant and equal across AQLs, while the acceptance numbers
increase with the AQL.
As production processes and quality levels have improved during the latter half of the twentieth
century, there has been a shift of interest towards sampling plans with smaller acceptance and rejection
numbers than most of the plans in ISO 2859-1.
Moreover, in some industries, in an effort to focus on customers' more specific requirements, there has
also been a trend towards shorter production runs. Sometimes these production runs are too short for
the switching rules of AQL-indexed plans (such as those of ISO 2859-1) to operate effectively.
In order to address an evolving market need, this International Standard has been developed to provide
double sampling plans by attributes indexed by producer's risk quality (PRQ) and consumer's risk
quality (CRQ) and having the smallest possible acceptance and rejection numbers. No constraint has
been placed on the relative sizes of the first and second sample sizes; instead, the first and second
sample sizes have been derived to minimize the expected total amount of sampling subject to the
nominal producer's risk, α, and consumer's risk, β, not being exceeded. The combinations (α, β) of
nominal risks provided in this International Standard are (5 %, 5 %), (5 %, 10 %) and (10 %, 10 %).
Thus, the double sampling plans provided in this International Standard are of the following kind. In
the case of sampling for nonconforming items, a lot is acceptable if no nonconforming items are found in
the first random sample, and not acceptable if the sample contains two or more nonconforming items. If
the first random sample contains precisely one nonconforming item, a second, smaller random sample
is taken; if no nonconforming items are found in the second sample, then the lot is acceptable, otherwise
it is not acceptable. For each pair of nominal producer's and consumer's risk, up to 17 preferred nominal
values of CRQ and up to 17 preferred nominal values of PRQ are provided.
Similar plans are provided for nonconformities.
The double sampling sample sizes are minimal among sampling plans for acceptance inspection of
isolated lots or for short series of lots. However, because the ISO 28592 plans do not rely on the protection
of switching rules, the sample sizes are necessarily larger than those used for lot-by-lot inspection, such
as those of ISO 2859-1, for similar producer's and consumer's quality levels, where these exist. This
is illustrated by the following two examples, both for nonconforming items with nominal maximum
producer's and consumer's risks or 5 % and 10 % respectively.
EXAMPLE 1
Realized Realized Producer's Consumer's
Sample
Source producer's consumer's risk quali- risk quality
sizes
risk risk ty (PRQ) (CRQ)
ISO 2859-1, code letter E, AQL = 1 % 5 % 10 % 0,394 % 20,6 % 8,8
ISO 28592, Tables 2 and 14 0,266 % 9,639 % 0,4 % 20 % 12,9
EXAMPLE 2
Realized Realized Producer's Consumer's
Sample
Source producer's consumer's risk quali- risk quality
sizes
risk risk ty (PRQ) (CRQ)
ISO 2859-1, code letter F, AQL = 0,65 % 5 % 10 % 0,256 % 10,9 % 13,13
ISO 28592, Tables 2 and 14 0,435 % 9,920 % 0,25 % 10 % 26,16
A compensating feature of the ISO 28592 plans is that many of the realized producer's risks are much
smaller than their nominal values.
vi © ISO 2017 – All rights reserved

INTERNATIONAL STANDARD ISO 28592:2017(E)
Double sampling plans by attributes with minimal sample
sizes, indexed by producer's risk quality (PRQ) and
consumer's risk quality (CRQ)
1 Scope
This International Standard provides double sampling plans by attributes
...