SIST ISO 28592:2018
Double sampling plans by attributes with minimal sample sizes, indexed by producer's risk quality (PRQ) and consumer's risk quality (CRQ)
Double sampling plans by attributes with minimal sample sizes, indexed by producer's risk quality (PRQ) and consumer's risk quality (CRQ)
This International Standard provides double sampling plans by attributes for the acceptance inspection of lots of discrete items. The plans are indexed by the producer's risk quality (PRQ) and the consumer's
risk quality (CRQ) where the nominal producer's and consumer's risks are respectively either (5 %,
5 %), (5 %, 10 %) or (10 %, 10 %). Plans are provided for inspection for percent nonconforming and for
inspection for nonconformities per 100 items. The lot is accepted if there are no nonconforming items
(nonconformities) in the first random sample, and rejected if it contains two or more nonconforming
items (nonconformities). If precisely one nonconforming item is found in the first sample, a second
random sample is drawn; the lot is then accepted if the second sample contains no nonconforming items
(nonconformities) and rejected otherwise.
The objective of this International Standard is to provide procedures that enable lot disposition to be
determined quickly and economically if quality is particularly good or bad. For intermediate quality,
a second sample is drawn in order to be able to discriminate more reliably between acceptable and
unacceptable lots. The two sample sizes are chosen to minimize the maximum expected sample size
with respect to incoming quality subject to the nominal risks not being exceeded.
Similarly, the plans may be used to test the hypothesis that a lot or process quality level is equal to the
PRQ (i.e. acceptable) against the alternative hypothesis that the quality level is equal to the CRQ (i.e.
unacceptable).
The plans are preferable to single sampling plans where the cost of inspection is high, where the delay
and uncertainty caused by the possible requirement for second samples is inconsequential and where a
relatively large ratio of the consumer's risk quality to the producer's risk quality can be tolerated.
The plans are suitable for isolated lots or for short series of lots, where the sum of the two sample sizes
is no larger than about 10 % of the size of the lot. The plans are also suitable for continuing series of lots
when lots that fail to satisfy the acceptance criteria are 100 % inspected and all nonconforming items
replaced by conforming items; however, for continuing series of lots, consideration should also be given
to using double sampling plans from ISO 2859-1.
The statistical theory underlying the plans, tables and figures is provided in Annex A.
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)
Dvojni načrti vzorčenja za opisne spremenljivke z najmanjšimi velikostmi vzorcev, razvrščeni po stopnji kakovosti, ki ustreza določenemu tveganju proizvajalca in odjemalca
Ta mednarodni standard zagotavlja dvojne načrte vzorčenja za opisne spremenljivke za pregled sprejemljivosti serij diskretnih elementov. Načrti so razvrščeni po stopnji kakovosti, ki ustreza določenemu tveganju proizvajalca in odjemalca, pri čemer tveganja nominalnega proizvajalca in odjemalca znašajo (5 %, 5 %), (5 %, 10 %) ali (10 %, 10 %). Načrti se zagotovijo za inšpekcijski pregled za popolno neskladnost in za inšpekcijski pregled za neskladnosti na 100 elementov. Serija je sprejeta, če ni neskladnih elementov (neskladnosti) v prvem naključnem vzorcu, in zavrnjena, če vsebuje dva ali več neskladnih elementov (neskladnosti). Če se v prvem vzorcu odkrije natanko en neskladen element, se izbere drug naključen vzorec; serija je sprejeta, če drugi vzorec ne vsebuje neskladnih elementov (neskladnosti), sicer pa je zavrnjena.
Cilj tega mednarodnega standarda je določiti postopke, ki omogočajo hitro in ekonomično določitev odstranitve serije, če je kakovost zlasti dobra ali slaba. Za vmesno kakovost se izbere drug vzorec, da se omogoči zanesljivejše razlikovanje med sprejemljivimi in nesprejemljivimi serijami. Dve velikosti vzorcev se izbereta, da se zmanjša največja pričakovana velikost vzorca
ob upoštevanju vhodne kakovosti, ki je predmet nominalnega tveganja, ki se ne preseže.
Podobno se lahko načrti uporabijo za preskušanje hipoteze, da je stopnja kakovosti serije ali procesa enaka PRQ (tj. sprejemljiva), v primerjavi z alternativno hipotezo, da je stopnja kakovosti enaka CRQ (tj. nesprejemljiva).
Načrti imajo prednost pred enojnimi vzorčnimi načrti, kadar je strošek inšpekcijskega pregleda visok, kadar sta zamuda in negotovost, ki ju povzroči morebitna zahteva po jemanju drugega vzorca, nepomembni, ter kadar je možno dopustiti razmeroma velik delež stopnje kakovosti, ki ustreza določenemu tveganju odjemalca, glede na stopnjo kakovosti, ki ustreza določenemu tveganju proizvajalca. Načrti so primerni za izolirane serije ali za kratke sklope serij, kadar vsota dveh velikosti vzorcev ni večja od približno 10 % velikosti serije. Načrti so primerni tudi za trajne sklope serij, kadar so serije, ki ne izpolnjujejo meril sprejemljivosti, 100-odstotno pregledane, vsi neskladni elementi pa so nadomeščeni s skladnimi elementi; vendar bi bilo treba pri trajnih sklopih serij razmisliti tudi o uporabi dvojnih vzorčnih načrtov iz standarda ISO 2859-1.
Statistična teorija, na kateri temeljijo načrti, preglednice in vrednosti, je opisana v dodatku A.
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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 28592:2017(E)
©
ISO 2017
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ISO 28592:2017(E)
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ii © ISO 2017 – All rights reserved
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ISO 28592:2017(E)
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
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ISO 28592:2017(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 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.
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ISO 28592:2017(E)
A list of all documents in the new ISO 28590 - ISO 28599 series of International Standards can be found
on the ISO website.
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ISO 28592:2017(E)
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.
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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 for the acceptance inspection
of lots of discrete items. The plans are indexed by the producer's risk quality (PRQ) and the consumer's
risk quality (CRQ) where the nominal producer's and consumer's risks are respectively either (5 %,
5 %), (5 %, 10 %) or (10 %, 10 %). Plans are provided for inspection for percent nonconforming and for
inspection for nonconformities per 100 items. The lot is accepted if there are no nonconforming items
(nonconformities) in the first random sample, and rejected if it contains two or more nonconforming
items (nonconformities). If precisely one nonconforming item is found in the first sample, a second
random sample is drawn; the lot is then accepted if the second sample contains no nonconforming items
(nonconformities) and rejected otherwise.
The objective of this International Standard is to provide procedures that enable lot disposition to be
determined quickly and economically if quality is particularly good or bad. For intermediate quality,
a second sample is drawn in order to be able to discriminate more reliably between acceptable and
unacceptable lots. The two sample sizes are chosen to minimize the maximum expected sample size
with respect to incoming quality subject to the nominal risks not being exceeded.
Similarly, the plans may be used to test the hypothesis that a lot or process quality level is equal to the
PRQ (i.e. acceptable) against the alternative hypothesis that the quality level is equal to the CRQ (i.e.
unacceptable).
The plans are preferable to single sampling plans where the cost of inspection is high, where the delay
and uncertainty caused by the possible requirement for second samples is inconsequential and where a
relatively large ratio of the consumer's risk quality to the producer's risk quality can be tolerated.
The plans are suitable for isolated lots or for short series of lots, where the sum of the two sample sizes
is no larger than about 10 % of the size of the lot. The plans are also suitable for continuing series of lots
when lots that fail to satisfy the acceptance criteria are 100 % inspected and all nonconforming items
replaced by conforming items; however, for continuing series of lots, consideration should also be given
to using double sampling plans from ISO 2859-1.
The statistical theory underlying the plans, tables and figures is provided in Annex A.
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.
There are no normative references in this document.
3 Terms, definitions, abbreviations and symbols
3.1 Terms, definitions and abbreviations
The words “accept”, “accepted”, “acceptable”, etc., refer only to the use of the sampling plans contained
in this International Standard and do not imply an agreement to accept any product. Determination of
acceptability by the customer shall be as described in contractual documents.
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ISO 28592:2017(E)
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at http://www.iso.org/obp
— IEC Electropedia: available at http://www.electropedia.org/
3.1.1
consumer's risk
CR
〈acceptance sampling〉 probability of acceptance when the quality level (3.1.5) of the process has a value
stated by the acceptance sampling plan as unsatisfactory
[SOURCE: ISO 3534-2:2006; 4.6.2]
3.1.2
consumer's risk quality
CRQ
〈acceptance sampling〉 quality level (3.1.5) of a lot or process which, in the acceptance sampling plan,
corresponds to a specified consumer's risk (3.1.1)
[SOURCE: ISO 3534-2:2006; 4.6.9]
3.1.3
producer's risk
PR
〈acceptance sampling〉 probability of non-acceptance when the quality level (3.1.5) of the process has a
value stated by the plan as acceptable
[SOURCE: ISO 3534-2:2006; 4.6.4]
3.1.4
producer's risk quality
PRQ
〈acceptance sampling〉 quality level (3.1.5) of a lot or process which, in the acceptance sampling plan,
corresponds to a specified producer's risk (3.1.3)
[SOURCE: ISO 3534-2:2006; 4.6.10]
3.1.5
quality level
〈acceptance sampling〉 quality expressed as a rate of nonconforming units or rate of number of
nonconformities (3.1.9)
[SOURCE: ISO 3534-2:2006; 4.6.16]
Note 1 to entry: Rate (or fraction) can be expressed in the unit 1 or in percentage. Rate of nonconforming units
can be read as a numerical value or a percentage of nonconforming units. Rate of number of nonconformities can
be read as a number of nonconformities per unit or per 100 units.
3.1.6
average sample size
ASSI
〈acceptance sampling〉 average number of units in sample inspected per lot in reaching decisions to
accept or not to accept when using a given acceptance sampling plan
Note 1 to entry: ASSI is dependent on the actual quality level (3.1.5) of the submitted lots.
[SOURCE: ISO 3534-2:2006; 4.7.3]
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ISO 28592:2017(E)
3.1.7
average outgoing quality
AOQ
〈acceptance sampling〉 expected average quality level (3.1.5) of outgoing product for a given value of
incoming product quality
[SOURCE: ISO 3534-2:2006; 4.7.1]
3.1.8
average outgoing quality limit
AOQL
〈acceptance sampling〉 maximum AOQ (3.1.7) over all possible values of incoming product quality level
(3.1.5) for a given acceptance sampling plan and rectification of all non-accepted lots unless specified
otherwise
[SOURCE: ISO 3534-2:2006; 4.7.2]
3.1.9
nonconformity
non-fulfilment of a requirement
[SOURCE: ISO 9000:2015; 3.6.9; ISO 3534-2:2006; 3.1.11]
Note 1 to entry: See notes to defect (3.1.11).
3.1.10
nonconforming item
item with one or more nonconformities (3.1.9)
[SOURCE: ISO 3534-2:2006; 1.2.12]
3.1.11
defect
non-fulfilment of a requirement related to an intended or specified use
[SOURCE: ISO 3534-2:2006; 3.1.12]
Note 1 to entry: The distinction between the concepts defect and nonconformity (3.1.9) is important as it has legal
connotations, particularly those associated with product liability issues. Consequently, the term “defect” should
be used with extreme caution.
Note 2 to entry: The intended use by the customer can be affected by the nature of the information, such as
operating or maintenance instructions, provided by the customer.
3.2 Symbols
α producer's risk
β consumer's risk
m size of the second sample in a double sampling plan
n size of the first sample in a double sampling plan
4 Choosing and operating a sampling plan
4.1 Choosing a plan
The appropriate table from among Tables 1 to 6 shall be selected in accordance with whether inspection
is for nonconforming items or nonconformities and the values of the nominal producer's and consumer's
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ISO 28592:2017(E)
risks. The selected table shall be entered with the PRQ and CRQ to obtain the sample sizes n and m of
the double sampling plan.
When the table indicates by asterisks that no double sampling plan with the prescribed acceptance
and rejection numbers is available with the required properties, consideration should be given to
decreasing the PRQ or increasing the CRQ, or both.
4.2 Operating a plan for nonconforming items
4.2.1 Acceptance sampling
A random sample of size n shall be drawn and inspected, where n is the first sample size given by the
plan. If no nonconforming items are found in this first sample, the lot shall be accepted. If the number
of nonconforming items found in this first sample is greater than or equal to two, the lot shall not be
accepted.
If one nonconforming item is found in the first random sample, a second random sample of size m shall be
drawn and inspected, where m is the second sample size given by the plan. If no further nonconforming
items are found in this second sample, the lot shall be accepted. If one or more nonconforming items are
found in this second sample, the lot shall not be accepted.
4.2.2 Hypothesis testing
The double sampling plan may alternatively be used for hypothesis testing when it is required to test the
null hypothesis that the quality level is less than or equal to the PRQ against the alternative hypothesis
that the quality level is greater than or equal to the CRQ. A first random sample of size n shall be drawn
and inspected, where n is the first sample size given by the plan. If no nonconforming items are found in
this first sample, the null hypothesis shall be accepted. If the number of nonconforming items found in
this first sample is greater than or equal to two, the alternative hypothesis shall be accepted.
If one nonconforming item is found in the first random sample, a second random sample of size
m shall be drawn and inspected, where m is the second sample size given by the plan. If no further
nonconforming items are found in this second sample, the null hypothesis shall be accepted. If one
or more nonconforming items are found in this second sample, the alternative hypothesis shall be
accepted.
4.3 Operating a plan for nonconformities
4.3.1 Acceptance sampling
In order to determine the acceptability of a lot in a nonconformities-per-hundred-items inspection,
the procedure specified in 4.2.1 for nonconforming inspection shall be used, except that the term
“nonconforming items” shall be replaced by “nonconformities”.
4.3.2 Hypothesis testing
In order to carry out a hypothesis test in a nonconformities-per-hundred-items inspection, the procedure
specified in 4.2.2 for nonconforming inspection shall be used, except that the term “nonconforming
items” shall be replaced by “nonconformities”.
4.4 Notation
A notation used to describe such plans is (n, 0, 2; m, 1, 2). This indicates that the acceptance and rejection
numbers for the first sample of size n are 0 and 2, and that the acceptance and rejection numbers for the
first and second samples combined are 1 and 2, where the second sample is of size m.
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ISO 28592:2017(E)
5 Operating characteristics
The operating characteristic curves, shown in Figures 1 to 6, indicate the probability that a lot will be
accepted under the various sampling plans for a range of quality levels.
The curves are based on the assumption that the sum of the two sample sizes is no more than about
10 % of the lot size. If the sum of the two sample sizes exceeds 10 % of the lot size, then the probabilities
of accepting the lot are higher than those shown by the curves at all quality levels, so the producer's risk
is reduced and the consumer's risk is increased.
NOTE A formula for the operating characteristic curves is provided in A.1.3 for nonconforming items and in
A.2.3 for nonconformities.
6 Average sample sizes
6.1 Curtailed inspection
Under curtailed inspection, inspection is stopped as soon as the inspection results are sufficient
to establish whether or not the lot is acceptable or, in the case of hypothesis testing, as soon as it is
clear which hypothesis will be accepted. In the case of the double sampling plans in this International
Standard, inspection would cease as soon as two nonconforming items (nonconformities) were found
in the first sample or as soon as one nonconforming item (nonconformity) was found in the second
sample. The operating characteristic curves are unaffected by curtailment, but the average sample size
is reduced. The reduction is small at good quality levels but substantial at very poor quality levels. The
disadvantage of curtailment is that it results in less precise estimates of the lot or process quality level;
this matters more in the case of a continuing series of lots.
6.2 Average sample size (ASSI) for uncurtailed inspection
Average sample size curves for uncurtailed inspection for the double sampling plans of this
International Standard are shown in Figures 7 to 12. These curves show the average sample sizes that
may be expected to occur under the various sampling plans for a range of levels of process quality. For
all the plans, the ASSI
— begins at the value n for perfect quality (because only the whole of the first sample is inspected),
— rises to a maximum where the process quality level p is equal to 1/n, i.e. 100/n % nonconforming or
100/n nonconformities per 100 items,
— falls more gradually to the value n as the process quality level p worsens beyond 1/n (again because
ultimately only the whole of the first sample is inspected).
NOTE A formula for the average sample size for uncurtailed inspection is provided in A.1.4.1 for
nonconforming items and in A.2.4.1 for nonconformities. Formulae for the corresponding maximum ASSI are
given in A.1.5 and A.2.5.
The average sample sizes of the double sampling plans at the PRQ and CRQ for uncurtailed inspection
are given in Tables 7 to 12. Also given are the maximum average sample sizes.
EXAMPLE Suppose that it is required to carry out a test of whether the quality level in a large lot is no more
than 0,25 % nonconforming. It has been agreed that the probability of acceptance should be at least 95 % if the lot
has a quality level of 0,25 % nonconforming, but no more than 5 % if the quality is as bad as 5 % nonconforming.
Thus the PRQ is 0,25 % and the CRQ is 5 %, with producer's and consumer's risks both equal to 5 %.
Table 1 shows that the appropriate plan has an initial sample of size n = 66 and a second sample size, if
required, of m = 39. Table 7 shows for this sampling plan that the ASSI is 71,5 at the PRQ and 70,6 at the
CRQ, with a maximum of 80,5.
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ISO 28592:2017(E)
6.3 Average sample size (ASSI) for curtailed inspection
Average sample size curves for curtailed inspection for the double sampling plans of this International
Standard are shown in Figures 19 to 24. As in the case of uncurtailed inspection, for all the plans the
ASSI begins at the value n for perfect quality and rises to a maximum. For plans for nonconforming
items the ASSI then falls to the value 2 as quality worsens, because at least two nonconforming items
are required for non-acceptance; for plans for nonconformities the ASSI falls to the value 1 as quality
worsens because, at a quality level of an infinite number of nonconformities per 100 items, the first
item will be certain to have more than one nonconformity.
NOTE Formulae for the average sample sizes under curtailed inspection are provided in A.1.4.2 for
nonconforming items and in A.2.4.2 for nonconformities.
The average sample sizes
...
SLOVENSKI STANDARD
SIST ISO 28592:2018
01-julij-2018
1DGRPHãþD
SIST ISO 28801:2014
'YRMQLQDþUWLY]RUþHQMD]DRSLVQHVSUHPHQOMLYNH]QDMPDQMãLPLYHOLNRVWPLY]RUFHY
UD]YUãþHQLSRVWRSQMLNDNRYRVWLNLXVWUH]DGRORþHQHPXWYHJDQMXSURL]YDMDOFDLQ
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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)
Ta slovenski standard je istoveten z: ISO 28592:2017
ICS:
03.120.30 8SRUDEDVWDWLVWLþQLKPHWRG Application of statistical
methods
SIST ISO 28592:2018 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST ISO 28592:2018
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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 28592:2017(E)
©
ISO 2017
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SIST ISO 28592:2018
ISO 28592:2017(E)
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ii © ISO 2017 – All rights reserved
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SIST ISO 28592:2018
ISO 28592:2017(E)
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
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ISO 28592:2017(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 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.
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A list of all documents in the new ISO 28590 - ISO 28599 series of International Standards can be found
on the ISO website.
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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.
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SIST ISO 28592:2018
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 for the acceptance inspection
of lots of discrete items. The plans are indexed by the producer's risk quality (PRQ) and the consumer's
risk quality (CRQ) where the nominal producer's and consumer's risks are respectively either (5 %,
5 %), (5 %, 10 %) or (10 %, 10 %). Plans are provided for inspection for percent nonconforming and for
inspection for nonconformities per 100 items. The lot is accepted if there are no nonconforming items
(nonconformities) in the first random sample, and rejected if it contains two or more nonconforming
items (nonconformities). If precisely one nonconforming item is found in the first sample, a second
random sample is drawn; the lot is then accepted if the second sample contains no nonconforming items
(nonconformities) and rejected otherwise.
The objective of this International Standard is to provide procedures that enable lot disposition to be
determined quickly and economically if quality is particularly good or bad. For intermediate quality,
a second sample is drawn in order to be able to discriminate more reliably between acceptable and
unacceptable lots. The two sample sizes are chosen to minimize the maximum expected sample size
with respect to incoming quality subject to the nominal risks not being exceeded.
Similarly, the plans may be used to test the hypothesis that a lot or process quality level is equal to the
PRQ (i.e. acceptable) against the alternative hypothesis that the quality level is equal to the CRQ (i.e.
unacceptable).
The plans are preferable to single sampling plans where the cost of inspection is high, where the delay
and uncertainty caused by the possible requirement for second samples is inconsequential and where a
relatively large ratio of the consumer's risk quality to the producer's risk quality can be tolerated.
The plans are suitable for isolated lots or for short series of lots, where the sum of the two sample sizes
is no larger than about 10 % of the size of the lot. The plans are also suitable for continuing series of lots
when lots that fail to satisfy the acceptance criteria are 100 % inspected and all nonconforming items
replaced by conforming items; however, for continuing series of lots, consideration should also be given
to using double sampling plans from ISO 2859-1.
The statistical theory underlying the plans, tables and figures is provided in Annex A.
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.
There are no normative references in this document.
3 Terms, definitions, abbreviations and symbols
3.1 Terms, definitions and abbreviations
The words “accept”, “accepted”, “acceptable”, etc., refer only to the use of the sampling plans contained
in this International Standard and do not imply an agreement to accept any product. Determination of
acceptability by the customer shall be as described in contractual documents.
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For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at http://www.iso.org/obp
— IEC Electropedia: available at http://www.electropedia.org/
3.1.1
consumer's risk
CR
〈acceptance sampling〉 probability of acceptance when the quality level (3.1.5) of the process has a value
stated by the acceptance sampling plan as unsatisfactory
[SOURCE: ISO 3534-2:2006; 4.6.2]
3.1.2
consumer's risk quality
CRQ
〈acceptance sampling〉 quality level (3.1.5) of a lot or process which, in the acceptance sampling plan,
corresponds to a specified consumer's risk (3.1.1)
[SOURCE: ISO 3534-2:2006; 4.6.9]
3.1.3
producer's risk
PR
〈acceptance sampling〉 probability of non-acceptance when the quality level (3.1.5) of the process has a
value stated by the plan as acceptable
[SOURCE: ISO 3534-2:2006; 4.6.4]
3.1.4
producer's risk quality
PRQ
〈acceptance sampling〉 quality level (3.1.5) of a lot or process which, in the acceptance sampling plan,
corresponds to a specified producer's risk (3.1.3)
[SOURCE: ISO 3534-2:2006; 4.6.10]
3.1.5
quality level
〈acceptance sampling〉 quality expressed as a rate of nonconforming units or rate of number of
nonconformities (3.1.9)
[SOURCE: ISO 3534-2:2006; 4.6.16]
Note 1 to entry: Rate (or fraction) can be expressed in the unit 1 or in percentage. Rate of nonconforming units
can be read as a numerical value or a percentage of nonconforming units. Rate of number of nonconformities can
be read as a number of nonconformities per unit or per 100 units.
3.1.6
average sample size
ASSI
〈acceptance sampling〉 average number of units in sample inspected per lot in reaching decisions to
accept or not to accept when using a given acceptance sampling plan
Note 1 to entry: ASSI is dependent on the actual quality level (3.1.5) of the submitted lots.
[SOURCE: ISO 3534-2:2006; 4.7.3]
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3.1.7
average outgoing quality
AOQ
〈acceptance sampling〉 expected average quality level (3.1.5) of outgoing product for a given value of
incoming product quality
[SOURCE: ISO 3534-2:2006; 4.7.1]
3.1.8
average outgoing quality limit
AOQL
〈acceptance sampling〉 maximum AOQ (3.1.7) over all possible values of incoming product quality level
(3.1.5) for a given acceptance sampling plan and rectification of all non-accepted lots unless specified
otherwise
[SOURCE: ISO 3534-2:2006; 4.7.2]
3.1.9
nonconformity
non-fulfilment of a requirement
[SOURCE: ISO 9000:2015; 3.6.9; ISO 3534-2:2006; 3.1.11]
Note 1 to entry: See notes to defect (3.1.11).
3.1.10
nonconforming item
item with one or more nonconformities (3.1.9)
[SOURCE: ISO 3534-2:2006; 1.2.12]
3.1.11
defect
non-fulfilment of a requirement related to an intended or specified use
[SOURCE: ISO 3534-2:2006; 3.1.12]
Note 1 to entry: The distinction between the concepts defect and nonconformity (3.1.9) is important as it has legal
connotations, particularly those associated with product liability issues. Consequently, the term “defect” should
be used with extreme caution.
Note 2 to entry: The intended use by the customer can be affected by the nature of the information, such as
operating or maintenance instructions, provided by the customer.
3.2 Symbols
α producer's risk
β consumer's risk
m size of the second sample in a double sampling plan
n size of the first sample in a double sampling plan
4 Choosing and operating a sampling plan
4.1 Choosing a plan
The appropriate table from among Tables 1 to 6 shall be selected in accordance with whether inspection
is for nonconforming items or nonconformities and the values of the nominal producer's and consumer's
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risks. The selected table shall be entered with the PRQ and CRQ to obtain the sample sizes n and m of
the double sampling plan.
When the table indicates by asterisks that no double sampling plan with the prescribed acceptance
and rejection numbers is available with the required properties, consideration should be given to
decreasing the PRQ or increasing the CRQ, or both.
4.2 Operating a plan for nonconforming items
4.2.1 Acceptance sampling
A random sample of size n shall be drawn and inspected, where n is the first sample size given by the
plan. If no nonconforming items are found in this first sample, the lot shall be accepted. If the number
of nonconforming items found in this first sample is greater than or equal to two, the lot shall not be
accepted.
If one nonconforming item is found in the first random sample, a second random sample of size m shall be
drawn and inspected, where m is the second sample size given by the plan. If no further nonconforming
items are found in this second sample, the lot shall be accepted. If one or more nonconforming items are
found in this second sample, the lot shall not be accepted.
4.2.2 Hypothesis testing
The double sampling plan may alternatively be used for hypothesis testing when it is required to test the
null hypothesis that the quality level is less than or equal to the PRQ against the alternative hypothesis
that the quality level is greater than or equal to the CRQ. A first random sample of size n shall be drawn
and inspected, where n is the first sample size given by the plan. If no nonconforming items are found in
this first sample, the null hypothesis shall be accepted. If the number of nonconforming items found in
this first sample is greater than or equal to two, the alternative hypothesis shall be accepted.
If one nonconforming item is found in the first random sample, a second random sample of size
m shall be drawn and inspected, where m is the second sample size given by the plan. If no further
nonconforming items are found in this second sample, the null hypothesis shall be accepted. If one
or more nonconforming items are found in this second sample, the alternative hypothesis shall be
accepted.
4.3 Operating a plan for nonconformities
4.3.1 Acceptance sampling
In order to determine the acceptability of a lot in a nonconformities-per-hundred-items inspection,
the procedure specified in 4.2.1 for nonconforming inspection shall be used, except that the term
“nonconforming items” shall be replaced by “nonconformities”.
4.3.2 Hypothesis testing
In order to carry out a hypothesis test in a nonconformities-per-hundred-items inspection, the procedure
specified in 4.2.2 for nonconforming inspection shall be used, except that the term “nonconforming
items” shall be replaced by “nonconformities”.
4.4 Notation
A notation used to describe such plans is (n, 0, 2; m, 1, 2). This indicates that the acceptance and rejection
numbers for the first sample of size n are 0 and 2, and that the acceptance and rejection numbers for the
first and second samples combined are 1 and 2, where the second sample is of size m.
4 © ISO 2017 – All rights reserved
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5 Operating characteristics
The operating characteristic curves, shown in Figures 1 to 6, indicate the probability that a lot will be
accepted under the various sampling plans for a range of quality levels.
The curves are based on the assumption that the sum of the two sample sizes is no more than about
10 % of the lot size. If the sum of the two sample sizes exceeds 10 % of the lot size, then the probabilities
of accepting the lot are higher than those shown by the curves at all quality levels, so the producer's risk
is reduced and the consumer's risk is increased.
NOTE A formula for the operating characteristic curves is provided in A.1.3 for nonconforming items and in
A.2.3 for nonconformities.
6 Average sample sizes
6.1 Curtailed inspection
Under curtailed inspection, inspection is stopped as soon as the inspection results are sufficient
to establish whether or not the lot is acceptable or, in the case of hypothesis testing, as soon as it is
clear which hypothesis will be accepted. In the case of the double sampling plans in this International
Standard, inspection would cease as soon as two nonconforming items (nonconformities) were found
in the first sample or as soon as one nonconforming item (nonconformity) was found in the second
sample. The operating characteristic curves are unaffected by curtailment, but the average sample size
is reduced. The reduction is small at good quality levels but substantial at very poor quality levels. The
disadvantage of curtailment is that it results in less precise estimates of the lot or process quality level;
this matters more in the case of a continuing series of lots.
6.2 Average sample size (ASSI) for uncurtailed inspection
Average sample size curves for uncurtailed inspection for the double sampling plans of this
International Standard are shown in Figures 7 to 12. These curves show the average sample sizes that
may be expected to occur under the various sampling plans for a range of levels of process quality. For
all the plans, the ASSI
— begins at the value n for perfect quality (because only the whole of the first sample is inspected),
— rises to a maximum where the process quality level p is equal to 1/n, i.e. 100/n % nonconforming or
100/n nonconformities per 100 items,
— falls more gradually to the value n as the process quality level p worsens beyond 1/n (again because
ultimately only the whole of the first sample is inspected).
NOTE A formula for the average sample size for uncurtailed inspection is provided in A.1.4.1 for
nonconforming items and in A.2.4.1 for nonconformities. Formulae for the corresponding maximum ASSI are
given in A.1.5 and A.2.5.
The average sample sizes of the double sampling plans at the PRQ and CRQ for uncurtailed inspection
are given in Tables 7 to 12. Also given are the maximum average sample sizes.
EXAMPLE Suppose that it is required to carry out a test of whether the quality level in a large lot is no more
than 0,25 % nonconforming. It has been agreed that the probability of acceptance should be at least 95 % if the lot
has a quality level of 0,25 % nonconforming, but no more than 5 % if the quality is as bad as 5 % nonconforming.
Thus the PRQ is 0,25 % and the CRQ is 5 %, with producer's and consumer's risks both equal to 5 %.
Table 1 shows that the appropriate plan has an initial sam
...
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