SIST ISO 28591:2018
Sequential sampling plans for inspection by attributes
Sequential sampling plans for inspection by attributes
This International Standard specifies sequential sampling plans and procedures for inspection by
attributes of discrete items.
The plans are indexed in terms of the producer's risk point and the consumer's risk point. Therefore,
they can be used not only for the purposes of acceptance sampling, but for a more general purpose of
the verification of simple statistical hypotheses for proportions.
The purpose of this International Standard is to provide procedures for sequential assessment of
inspection results that may be used to induce the supplier, through the economic and psychological
pressure of non-acceptance of lots of inferior quality, to supply lots of a quality having a high probability
of acceptance. At the same time, the consumer is protected by a prescribed upper limit to the probability
of accepting lots of poor quality.
This International Standard provides sampling plans that are applicable, but not limited, to inspection
in different fields, such as:
— end items,
— components and raw materials,
— operations,
— materials in process,
— supplies in storage,
— maintenance operations,
— data or records, and
— administrative procedures.
This International Standard contains sampling plans for inspection by attributes of discrete items.
The sampling plans may be used when the extent of nonconformity is expressed either in terms of
proportion (or percent) nonconforming items or in terms of nonconformities per item (per 100 items).
The sampling plans are based on the assumption that nonconformities occur randomly and with
statistical independence. There may be good reasons to suspect that one nonconformity in an item
could be caused by a condition also likely to cause others. If so, it would be better to consider the items
just as conforming or not, and ignore multiple nonconformities.
The sampling plans from this International Standard should primarily be used for the analysis of
samples taken from processes. For example, they may be used for the acceptance sampling of lots taken
from a process that is under statistical control. However, they may also be used for the acceptance
sampling of an isolated lot when its size is large, and the expected fraction nonconforming is small
(significantly smaller than 10 %).
In the case of the acceptance sampling of continuing series of lots, the system of sequential sampling
plans indexed by acceptance quality limit (AQL) for lot-by-lot inspection published in ISO 2859-5 should
be applied.
Plans d'échantillonnage progressif pour le contrôle par attributs
L'ISO 28591 :2017 sp�cifie des plans et des r�gles d'�chantillonnage progressif pour le contr�le par attributs d'individus discrets.
Les plans sont index�s en termes de point du risque fournisseur et de point du risque client. Par cons�quent, ils peuvent �tre utilis�s pour l'�chantillonnage pour acceptation mais �galement � des fins plus g�n�rales de v�rification d'hypoth�ses statistiques simples concernant des proportions.
L'ISO 28591 :2017 fournit des r�gles, bas�es sur la d�termination progressive des r�sultats de contr�le, pouvant �tre utilis�es pour inciter le fournisseur, par des pressions �conomiques et psychologiques li�es � la non-acceptation de lots de qualit� inf�rieure, � fournir des lots de qualit� ayant une forte probabilit� d'acceptation. En m�me temps, le client est prot�g� par une limite sup�rieure impos�e de la probabilit� d'accepter des lots de faible qualit�.
L'ISO 28591 :2017 fournit des plans d'�chantillonnage, d'une mani�re non limitative, notamment aux contr�les ci-apr�s:
? produits finis;
? composants et mati�res premi�res;
? op�rations;
? mat�riaux en cours de fabrication;
? fournitures en stock;
? op�rations d'entretien;
? informations ou enregistrements;
? proc�dures administratives.
Sekvenčni načrti vzorčenja za kontrolo po opisnih spremenljivkah
Ta mednarodni standard določa sekvenčne načrte vzorčenja in postopke za kontrolo po opisnih spremenljivkah diskretnih elementov.
Načrti so indeksirani glede na tveganje proizvajalca in tveganje odjemalca. Zaradi tega jih je poleg vzorčenja pri sprejemu mogoče uporabljati tudi za bolj splošne namene preverjanja preprostih statističnih hipotez glede deležev.
Namen tega mednarodnega standarda je zagotoviti postopke za sekvenčno ocenjevanje rezultatov kontrole, ki jih je mogoče uporabiti za spodbujanje dobavitelja k dobavi kakovostnih serij z visoko verjetnostjo sprejemljivosti z uporabo ekonomskih in psiholoških pritiskov zaradi nesprejemljivosti serij slabše kakovosti. Istočasno je odjemalec zaščiten zaradi predpisane zgornje meje verjetnosti
za sprejem serij slabe kvalitete.
Ta mednarodni standard zagotavlja načrte vzorčenja, ki jih je med drugim mogoče uporabiti za kontrole na različnih področjih, na primer:
– končni izdelki,
– komponente in surovine,
– postopki,
– materiali v procesu,
– zaloge v skladišču,
– vzdrževalna dela,
– podatki ali evidence in
– administrativni postopki.
Ta mednarodni standard vsebuje načrte vzorčenja za kontrolo po opisnih spremenljivkah diskretnih elementov. Načrte vzorčenja je mogoče uporabiti, če je obseg neskladnosti izražen v deležu (ali odstotkih) neskladnih primerkov ali v številu neskladnosti na element (na 100 elementov). Načrti vzorčenja temeljijo na predpostavki, da se neskladnosti pojavljajo naključno in statistično neodvisno. Morda obstajajo dobri razlogi za sum, da je posamezno neskladnost v elementu povzročila okoliščina, ki lahko verjetno povzroči tudi druge. V takšnem primeru je bolje presojati elemente samo glede tega, ali so skladni ali ne, in ignorirati večkratne neskladnosti.
Načrti vzorčenja iz tega mednarodnega standarda so primarno namenjeni uporabi za analizo vzorcev, odvzetih iz procesov. Mogoče jih je na primer uporabiti za vzorčenje pri sprejemu serij, odvzetih iz procesa, za katerega se izvaja statistični nadzor. Vendar pa jih je mogoče uporabiti tudi za vzorčenje pri sprejemu izolirane serije, če gre za serijo velike velikosti in je pričakovan delež neskladnosti majhen (bistveno manjši od 10 %).
V primeru vzorčenja pri sprejemu trajnih sklopov serij je treba uporabiti sistem sekvenčnih načrtov vzorčenja, ki so indeksirani po sprejemljivi ravni kakovosti (AQL) za kontrolo posameznih serij, objavljeni v standardu ISO 2859-5.
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INTERNATIONAL ISO
STANDARD 28591
First edition
2017-10
Sequential sampling plans for
inspection by attributes
Plans d'échantillonnage progressif pour le contrôle par attributs
Reference number
ISO 28591:2017(E)
©
ISO 2017
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ISO 28591:2017(E)
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© ISO 2017, Published in Switzerland
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ii © ISO 2017 – All rights reserved
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ISO 28591:2017(E)
Contents Page
Foreword .iv
Introduction .vi
1 Scope . 1
2 Normative references . 2
3 Terms and definitions . 2
4 Symbols and abbreviated terms . 6
5 Principles of sequential sampling plans for inspection by attributes .7
6 Selection of a sampling plan . 7
6.1 Producer’s risk point and consumer’s risk point . 7
6.2 Preferred values of Q and Q .
PR CR 8
6.3 Pre-operation preparations . 8
6.3.1 Obtaining the parameters h , h and g .8
A R
6.3.2 Obtaining the curtailment values . 8
7 Operation of a sequential sampling plan . 8
7.1 Specification of the plan . 8
7.2 Drawing a sample item . 8
7.3 Count and cumulative count . 8
7.3.1 Count . 8
7.3.2 Cumulative count . 8
7.4 Choice between numerical and graphical methods . 8
7.5 Numerical method . 9
7.5.1 Preparation of the acceptability table . 9
7.5.2 Making decisions . 9
7.6 Graphical method .10
7.6.1 Preparation of the acceptability chart .10
7.6.2 Making decisions .11
8 Numerical example .12
9 Tables .12
Annex A (informative) Statistical properties of the sequential sampling plan
for inspection by attributes.30
Bibliography .39
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ISO 28591:2017(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 28591 cancels and replaces ISO 8422:2006, of which it constitutes a minor
revision to change the reference number from 8422 to 28591.
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 28591:2017(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 28591:2017(E)
Introduction
In contemporary production processes, quality is often expected to reach such high levels that the
−6
number of nonconforming items is reported in parts per million (10 ). Under such circumstances,
popular acceptance sampling plans, such as those presented in ISO 2859-1, require prohibitively large
sample sizes. To overcome this problem, users apply acceptance sampling plans with higher probabilities
of wrong decisions or, in extreme situations, abandon the use of acceptance sampling procedures
altogether. However, in many situations there is still a need to accept products of high quality using
standardized statistical methods. In such cases, there is a need to apply statistical procedures that
require the smallest possible sample sizes. Sequential sampling plans are the only statistical procedures
that satisfy that need as, among all possible sampling plans having similar statistical properties, the
sequential sampling plan has the smallest average sample size.
The principal advantage of sequential sampling plans is the reduction in the average sample size. The
average sample size is the weighted average of all the sample sizes that may occur under a sampling
plan for a given lot or process quality level. Like double and multiple sampling plans, the use of
sequential sampling plans leads to a smaller average sample size than single sampling plans having
the equivalent operating characteristic. However, the average savings are even greater when using a
sequential sampling plan than when a double or multiple sampling plan is used. For lots of very good
quality, the maximum savings for sequential sampling plans may reach 85 %, as compared to 37 % for
double sampling plans and 75 % for multiple sampling plans. On the other hand, when using a double,
multiple or sequential sampling plan, the actual number of items inspected for a particular lot may
exceed the sample size, n , of the corresponding single sampling plan. For double and multiple sampling
0
plans, there is an upper limit of 1,25 n to the actual number of items to be inspected. For classical
0
sequential sampling plans, there is no such limit, and the actual number of inspected items may exceed
the corresponding single sample size, n , or be even as large as the lot size, N. For the sequential sampling
0
plans in this International Standard, a curtailment rule has been introduced involving an upper limit n
t
on the actual number of items to be inspected.
Other factors that should be taken into account include:
a) Simplicity
The rules of a sequential sampling plan are more easily misunderstood by inspectors than the simple
rules for a single sampling plan.
b) Variability in the amount of inspection
As the actual number of items inspected for a particular lot is not known in advance, the use of
sequential sampling plans brings about various organisational difficulties. For example, scheduling of
inspection operations may be difficult.
c) Ease of drawing sample items
If drawing sample items at different times is expensive, the reduction in the average sample size by
sequential sampling plans may be cancelled out by the increased sampling cost.
d) Duration of test
If the test of a single item is of long duration and a number of items can be tested simultaneously,
sequential sampling plans are much more time-consuming than the corresponding single sampling plans.
e) Variability of quality within the lot
If the lot consists of two or more sublots from different sources and if there is likely to be a substantial
difference between the qualities of the sublots, drawing of a representative sample under a sequential
sampling plan is far more awkward than under the corresponding single sampling plan.
The advantages and disadvantages of double and multiple sampling plans always lie between those of
single and sequential sampling plans. The balance between the advantage of a smaller average sample
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ISO 28591:2017(E)
size and the above disadvantages leads to the conclusion that sequential sampling plans are suitable
only when inspection of individual items is costly in comparison with inspection overheads.
The choice between single, double, multiple and sequential sampling plans shall be made before the
inspection of a lot is started. During inspection of a lot, it is not permitted to switch from one type
to another, because the operating characteristics of the plan may be drastically changed if the actual
inspection results influence the choice of acceptability criteria.
Although use of sequential sampling plans is on average much more economical than the use of
corresponding single sampling plans, acceptance or non-acceptance may occur at a very late stage
due to the cumulative count of nonconforming items (or nonconformities) remaining between the
acceptance number and the rejection number for a long time. When using the graphical method, this
corresponds to the random progress of the step curve remaining in the indecision zone. Such a situation
is most likely to occur when the lot or process quality level (in terms of percent nonconforming or in
nonconformities per 100 items) is close to (100g), where g is the parameter giving the slope of the
acceptance and rejection lines.
To improve upon this situation, the sample size curtailment value is set before the inspection of a
lot is begins. If the cumulative sample size reaches the curtailment value n without determination
t
of lot acceptability, inspection terminates and the acceptance and non-acceptance of the lot is then
determined using the curtailment values of the acceptance and rejection numbers.
For sequential sampling plans in common use, curtailment usually represents a deviation from their
intended usage, leading to a distortion of their operating characteristics. In this International Standard,
however, the operating characteristics of the sequential sampling plans have been determined with
curtailment taken into account, so curtailment is an integral component of the provided plans.
Sequential sampling plans for inspection by attributes are also provided in ISO 2859-5. However, the
design principle of those plans is fundamentally different from that of this International Standard. The
sampling plans in ISO 2859-5 are designed to supplement the ISO 2859-1 acceptance sampling system
for inspection by attributes. Thus, they should be used for the inspection of a continuing series of lots,
that is, a series long enough to permit the switching rules of the ISO 2859 system to function. The
application of the switching rules is the only means of providing enhanced protection to the consumer
(by means of tightened sampling inspection criteria or discontinuation of sampling inspection) when
the sequential sampling plans from ISO 2859-5 are used. However, in certain circumstances, there
is a strong need to have both the producer's and the consumer's risks under strict control. Such
circumstances occur, for example, when sampling is performed for regulatory reasons, to demonstrate
the quality of the production processes or to test hypotheses. In such cases, individual sampling plans
selected from the ISO 2859-5 sampling scheme may be inappropriate. The sampling plans from this
International Standard have been designed in order to meet these specific requirements.
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INTERNATIONAL STANDARD ISO 28591:2017(E)
Sequential sampling plans for inspection by attributes
1 Scope
This International Standard specifies sequential sampling plans and procedures for inspection by
attributes of discrete items.
The plans are indexed in terms of the producer's risk point and the consumer's risk point. Therefore,
they can be used not only for the purposes of acceptance sampling, but for a more general purpose of
the verification of simple statistical hypotheses for proportions.
The purpose of this International Standard is to provide procedures for sequential assessment of
inspection results that may be used to induce the supplier, through the economic and psychological
pressure of non-acceptance of lots of inferior quality, to supply lots of a quality having a high probability
of acceptance. At the same time, the consumer is protected by a prescribed upper limit to the probability
of accepting lots of poor quality.
This International Standard provides sampling plans that are applicable, but not limited, to inspection
in different fields, such as:
— end items,
— components and raw materials,
— operations,
— materials in process,
— supplies in storage,
— maintenance operations,
— data or records, and
— administrative procedures.
This International Standard contains sampling plans for inspection by attributes of discrete items.
The sampling plans may be used when the extent of nonconformity is expressed either in terms of
proportion (or percent) nonconforming items or in terms of nonconformities per item (per 100 items).
The sampling plans are based on the assumption that nonconformities occur randomly and with
statistical independence. There may be good reasons to suspect that one nonconformity in an item
could be caused by a condition also likely to cause others. If so, it would be better to consider the items
just as conforming or not, and ignore multiple nonconformities.
The sampling plans from this International Standard should primarily be used for the analysis of
samples taken from processes. For example, they may be used for the acceptance sampling of lots taken
from a process that is under statistical control. However, they may also be used for the acceptance
sampling of an isolated lot when its size is large, and the expected fraction nonconforming is small
(significantly smaller than 10 %).
In the case of the acceptance sampling of continuing series of lots, the system of sequential sampling
plans indexed by acceptance quality limit (AQL) for lot-by-lot inspection published in ISO 2859-5 should
be applied.
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ISO 28591:2017(E)
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 3534-1, Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in
probability
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 3534-1 and the following 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
inspection
conformity evaluation by observation and judgement accompanied as appropriate by measurement,
testing or gauging
[SOURCE: ISO 3534-2:2006, 4.1.2]
3.2
inspection by attributes
inspection (3.1) by noting the presence, or absence, of one or more particular characteristic(s) in each
of the items in the group under consideration, and counting how many items do, or do not, possess the
characteristic(s), or how many such events occur in the item, group or opportunity space
Note 1 to entry: When inspection is performed by simply noting whether the item is nonconforming or not, the
inspection is termed inspection for nonconforming items. When inspection is performed by noting the number of
nonconformities on each unit, the inspection is termed inspection for number of nonconformities.
[SOURCE: ISO 3534-2:2006, 4.1.3]
3.3
item
entity
anything that can be described and considered separately
EXAMPLE A discrete physical item; a defined amount of bulk material; a service, activity, person, system or
some combination thereof.
[SOURCE: ISO 3534-2:2006, 1.2.11]
3.4
nonconformity
non-fulfilment of a requirement
[SOURCE: ISO 3534-2:2006, 3.1.11]
Note 1 to entry: See notes to 3.5.
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ISO 28591:2017(E)
3.5
defect
non-fulfilment of a requirement related to an intended or specified use
Note 1 to entry: The distinction between the concepts defect and nonconformity (3.4) 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 information, such as operating
or maintenance instructions, provided by the customer.
[SOURCE: ISO 3534-2:2006, 3.1.12]
3.6
nonconforming item
item (3.3) with one or more nonconformities (3.4)
[SOURCE: ISO 3534-2:2006, 1.2.12]
3.7
percent nonconforming
〈in a sample〉 one hundred times the number of nonconforming items (3.6) in the sample (3.13) divided
by the sample size (3.14), viz:
d
100 ×
n
where
d is the number of nonconforming items in the sample;
n is the sample size
[SOURCE: ISO 2859-1:1999, 3.1.8]
3.8
percent nonconforming
〈in a population or lot〉 one hundred times the number of nonconforming items (3.6) in the population or
lot (3.11) divided by the population or lot size (3.12), viz:
D
ni
100 ×=p 100 ×
ni
N
where
p is the proportion of nonconforming items;
ni
D is the number of nonconforming items in the population or lot;
ni
N is the population or lot size
Note 1 to entry: Adapted from ISO 2859-1:1999, 3.1.9.
Note 2 to entry: In this International Standard, the terms percent nonconforming (3.7 and 3.8) or nonconformities
per 100 items (3.9 and 3.10) 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.
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ISO 28591:2017(E)
3.9
nonconformities per 100 items
〈in a sample〉 one hundred times the number of nonconformities (3.4) in the sample (3.13) divided by the
sample size (3.14), viz:
d
100×
n
where
d is the number of nonconformities in the sample;
n is the sample size
[SOURCE: ISO 2859-1:1999, 3.1.10]
3.10
nonconformities per 100 items
〈in a population or lot〉 100 times the number of nonconformities (3.4) in the population or lot (3.11)
divided by the population or lot size (3.12), viz:
D
nt
100×=p 100×
nt
N
where
p is the number of nonconformities per item;
nt
D is the number of nonconformities in the population or lot;
nt
N is the population or lot size
Note 1 to entry: Adapted from ISO 2859-1:1999, 3.1.11.
Note 2 to entry: An item may contain one or more nonconformities.
3.11
lot
definite part of a population constituted under essentially the same conditions as the population with
respect to the sampling purpose
Note 1 to entry: The sampling purpose can, for example, be to determine lot acceptability, or to estimate the
mean value of a particular characteristic.
[SOURCE: ISO 3534-2:2006, 1.2.4]
3.12
lot size
number of items (3.3) in a lot (3.11)
[SOURCE: ISO 2859-1:1999, 3.1.14]
3.13
sample
subset of a population made up of one or more sampling units
[SOURCE: ISO 3534-2:2006, 1.2.17]
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ISO 28591:2017(E)
3.14
sample size
number of sampling units in a sample (3.13)
[SOURCE: ISO 3534-2:2006, 1.2.26]
3.15
acceptance sampling plan
plan which states the sample size(s) (3.14) to be used and the associated criteria for lot acceptance
[SOURCE: ISO 3534-2:2006, 4.3.3]
3.16
consumer's risk quality
Q
CR
〈acceptance sampling〉 quality level of a lot (3.11) or process which, in the acceptance sampling plan
(3.15), corresponds to a specified consumer's risk
[SOURCE: ISO 3534-2:2006, 4.6.9]
Note 1 to entry: The specified consumer's risk is usually 10 %.
3.17
producer's risk quality
Q
PR
〈acceptance sampling〉 quality level of a lot (3.11) or process which, in the acceptance sampling plan
(3.15), corresponds to a specified producer's risk
[SOURCE: ISO 3534-2:2006, 4.6.10]
Note 1 to entry: The specified producer's risk is usually 5 %.
3.18
count
when inspection by attributes is performed, the result of the inspection of each sample item
Note 1 to entry: In the case of the inspection for nonconforming items, the count is set to 1 if the sample
item is nonconforming. In the case of the inspection for nonconformities, the count is set to the number of
nonconformities found in the sample item.
3.19
cumulative count
when a sequential sampling plan is used, the sum of the counts during inspection, counting from the
start of the inspection of the lot up to, and including, the sample item last inspected
3.20
cumulative sample size
when a sequential sampling plan is used, the total number of sample items during inspection, counting
from the start of the inspection of the lot up to, and including, the sample item last inspected
3.21
acceptance value
〈for sequential sampling〉 value used in the graphical method for determination of acceptance of the lot,
that is derived from the specified parameters of the sampling plan and the cumulative sample size
3.22
acceptance number
〈for sequential sampling〉 number used in the numerical method for determination of acceptance of the
lot, that is obtained by rounding the acceptance value down to the nearest integer
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ISO 28591:2017(E)
3.23
rejection value
〈for sequential sampling〉 value used in the graphical method for determination of non-acceptance of the
lot, that is derived from the specified parameters of the sampling plan and the cumulative sample size
3.24
rejection number
〈for sequential sampling〉 number used in the numerical method for determination of non-acceptance of
the lot, that is obtained by rounding the rejection value up to the nearest integer
3.25
acceptability table
table used for the lot acceptability determination in the numerical method
3.26
acceptability chart
chart used for the lot acceptability determination in the graphical method, consisting of the following
three zones:
— acceptance zone;
— rejection zone;
— indecision zone;
the borders being acceptance, rejection and curtailment lines
4 Symbols and abbreviated terms
The symbols and abbreviations used in this International Standard are as follows:
A acceptance value (for sequential sampling plan)
Ac acceptance number
Ac acceptance number for a corresponding single sampling plan
0
Ac acceptance number at curtailment (curtailment value)
t
d count
D cumulative count
g parameter giving the slope of the acceptance and rejection lines
h parameter givin
...
SLOVENSKI STANDARD
SIST ISO 28591:2018
01-julij-2018
1DGRPHãþD
SIST ISO 8422:2008
6HNYHQþQLQDþUWLY]RUþHQMD]DNRQWURORSRRSLVQLKVSUHPHQOMLYNDK
Sequential sampling plans for inspection by attributes
Plans d'échantillonnage progressif pour le contrôle par attributs
Ta slovenski standard je istoveten z: ISO 28591:2017
ICS:
03.120.30 8SRUDEDVWDWLVWLþQLKPHWRG Application of statistical
methods
SIST ISO 28591:2018 en,fr
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST ISO 28591:2018
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SIST ISO 28591:2018
INTERNATIONAL ISO
STANDARD 28591
First edition
2017-10
Sequential sampling plans for
inspection by attributes
Plans d'échantillonnage progressif pour le contrôle par attributs
Reference number
ISO 28591:2017(E)
©
ISO 2017
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SIST ISO 28591:2018
ISO 28591:2017(E)
COPYRIGHT PROTECTED DOCUMENT
© 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
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SIST ISO 28591:2018
ISO 28591:2017(E)
Contents Page
Foreword .iv
Introduction .vi
1 Scope . 1
2 Normative references . 2
3 Terms and definitions . 2
4 Symbols and abbreviated terms . 6
5 Principles of sequential sampling plans for inspection by attributes .7
6 Selection of a sampling plan . 7
6.1 Producer’s risk point and consumer’s risk point . 7
6.2 Preferred values of Q and Q .
PR CR 8
6.3 Pre-operation preparations . 8
6.3.1 Obtaining the parameters h , h and g .8
A R
6.3.2 Obtaining the curtailment values . 8
7 Operation of a sequential sampling plan . 8
7.1 Specification of the plan . 8
7.2 Drawing a sample item . 8
7.3 Count and cumulative count . 8
7.3.1 Count . 8
7.3.2 Cumulative count . 8
7.4 Choice between numerical and graphical methods . 8
7.5 Numerical method . 9
7.5.1 Preparation of the acceptability table . 9
7.5.2 Making decisions . 9
7.6 Graphical method .10
7.6.1 Preparation of the acceptability chart .10
7.6.2 Making decisions .11
8 Numerical example .12
9 Tables .12
Annex A (informative) Statistical properties of the sequential sampling plan
for inspection by attributes.30
Bibliography .39
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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 28591 cancels and replaces ISO 8422:2006, of which it constitutes a minor
revision to change the reference number from 8422 to 28591.
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
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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
In contemporary production processes, quality is often expected to reach such high levels that the
−6
number of nonconforming items is reported in parts per million (10 ). Under such circumstances,
popular acceptance sampling plans, such as those presented in ISO 2859-1, require prohibitively large
sample sizes. To overcome this problem, users apply acceptance sampling plans with higher probabilities
of wrong decisions or, in extreme situations, abandon the use of acceptance sampling procedures
altogether. However, in many situations there is still a need to accept products of high quality using
standardized statistical methods. In such cases, there is a need to apply statistical procedures that
require the smallest possible sample sizes. Sequential sampling plans are the only statistical procedures
that satisfy that need as, among all possible sampling plans having similar statistical properties, the
sequential sampling plan has the smallest average sample size.
The principal advantage of sequential sampling plans is the reduction in the average sample size. The
average sample size is the weighted average of all the sample sizes that may occur under a sampling
plan for a given lot or process quality level. Like double and multiple sampling plans, the use of
sequential sampling plans leads to a smaller average sample size than single sampling plans having
the equivalent operating characteristic. However, the average savings are even greater when using a
sequential sampling plan than when a double or multiple sampling plan is used. For lots of very good
quality, the maximum savings for sequential sampling plans may reach 85 %, as compared to 37 % for
double sampling plans and 75 % for multiple sampling plans. On the other hand, when using a double,
multiple or sequential sampling plan, the actual number of items inspected for a particular lot may
exceed the sample size, n , of the corresponding single sampling plan. For double and multiple sampling
0
plans, there is an upper limit of 1,25 n to the actual number of items to be inspected. For classical
0
sequential sampling plans, there is no such limit, and the actual number of inspected items may exceed
the corresponding single sample size, n , or be even as large as the lot size, N. For the sequential sampling
0
plans in this International Standard, a curtailment rule has been introduced involving an upper limit n
t
on the actual number of items to be inspected.
Other factors that should be taken into account include:
a) Simplicity
The rules of a sequential sampling plan are more easily misunderstood by inspectors than the simple
rules for a single sampling plan.
b) Variability in the amount of inspection
As the actual number of items inspected for a particular lot is not known in advance, the use of
sequential sampling plans brings about various organisational difficulties. For example, scheduling of
inspection operations may be difficult.
c) Ease of drawing sample items
If drawing sample items at different times is expensive, the reduction in the average sample size by
sequential sampling plans may be cancelled out by the increased sampling cost.
d) Duration of test
If the test of a single item is of long duration and a number of items can be tested simultaneously,
sequential sampling plans are much more time-consuming than the corresponding single sampling plans.
e) Variability of quality within the lot
If the lot consists of two or more sublots from different sources and if there is likely to be a substantial
difference between the qualities of the sublots, drawing of a representative sample under a sequential
sampling plan is far more awkward than under the corresponding single sampling plan.
The advantages and disadvantages of double and multiple sampling plans always lie between those of
single and sequential sampling plans. The balance between the advantage of a smaller average sample
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size and the above disadvantages leads to the conclusion that sequential sampling plans are suitable
only when inspection of individual items is costly in comparison with inspection overheads.
The choice between single, double, multiple and sequential sampling plans shall be made before the
inspection of a lot is started. During inspection of a lot, it is not permitted to switch from one type
to another, because the operating characteristics of the plan may be drastically changed if the actual
inspection results influence the choice of acceptability criteria.
Although use of sequential sampling plans is on average much more economical than the use of
corresponding single sampling plans, acceptance or non-acceptance may occur at a very late stage
due to the cumulative count of nonconforming items (or nonconformities) remaining between the
acceptance number and the rejection number for a long time. When using the graphical method, this
corresponds to the random progress of the step curve remaining in the indecision zone. Such a situation
is most likely to occur when the lot or process quality level (in terms of percent nonconforming or in
nonconformities per 100 items) is close to (100g), where g is the parameter giving the slope of the
acceptance and rejection lines.
To improve upon this situation, the sample size curtailment value is set before the inspection of a
lot is begins. If the cumulative sample size reaches the curtailment value n without determination
t
of lot acceptability, inspection terminates and the acceptance and non-acceptance of the lot is then
determined using the curtailment values of the acceptance and rejection numbers.
For sequential sampling plans in common use, curtailment usually represents a deviation from their
intended usage, leading to a distortion of their operating characteristics. In this International Standard,
however, the operating characteristics of the sequential sampling plans have been determined with
curtailment taken into account, so curtailment is an integral component of the provided plans.
Sequential sampling plans for inspection by attributes are also provided in ISO 2859-5. However, the
design principle of those plans is fundamentally different from that of this International Standard. The
sampling plans in ISO 2859-5 are designed to supplement the ISO 2859-1 acceptance sampling system
for inspection by attributes. Thus, they should be used for the inspection of a continuing series of lots,
that is, a series long enough to permit the switching rules of the ISO 2859 system to function. The
application of the switching rules is the only means of providing enhanced protection to the consumer
(by means of tightened sampling inspection criteria or discontinuation of sampling inspection) when
the sequential sampling plans from ISO 2859-5 are used. However, in certain circumstances, there
is a strong need to have both the producer's and the consumer's risks under strict control. Such
circumstances occur, for example, when sampling is performed for regulatory reasons, to demonstrate
the quality of the production processes or to test hypotheses. In such cases, individual sampling plans
selected from the ISO 2859-5 sampling scheme may be inappropriate. The sampling plans from this
International Standard have been designed in order to meet these specific requirements.
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INTERNATIONAL STANDARD ISO 28591:2017(E)
Sequential sampling plans for inspection by attributes
1 Scope
This International Standard specifies sequential sampling plans and procedures for inspection by
attributes of discrete items.
The plans are indexed in terms of the producer's risk point and the consumer's risk point. Therefore,
they can be used not only for the purposes of acceptance sampling, but for a more general purpose of
the verification of simple statistical hypotheses for proportions.
The purpose of this International Standard is to provide procedures for sequential assessment of
inspection results that may be used to induce the supplier, through the economic and psychological
pressure of non-acceptance of lots of inferior quality, to supply lots of a quality having a high probability
of acceptance. At the same time, the consumer is protected by a prescribed upper limit to the probability
of accepting lots of poor quality.
This International Standard provides sampling plans that are applicable, but not limited, to inspection
in different fields, such as:
— end items,
— components and raw materials,
— operations,
— materials in process,
— supplies in storage,
— maintenance operations,
— data or records, and
— administrative procedures.
This International Standard contains sampling plans for inspection by attributes of discrete items.
The sampling plans may be used when the extent of nonconformity is expressed either in terms of
proportion (or percent) nonconforming items or in terms of nonconformities per item (per 100 items).
The sampling plans are based on the assumption that nonconformities occur randomly and with
statistical independence. There may be good reasons to suspect that one nonconformity in an item
could be caused by a condition also likely to cause others. If so, it would be better to consider the items
just as conforming or not, and ignore multiple nonconformities.
The sampling plans from this International Standard should primarily be used for the analysis of
samples taken from processes. For example, they may be used for the acceptance sampling of lots taken
from a process that is under statistical control. However, they may also be used for the acceptance
sampling of an isolated lot when its size is large, and the expected fraction nonconforming is small
(significantly smaller than 10 %).
In the case of the acceptance sampling of continuing series of lots, the system of sequential sampling
plans indexed by acceptance quality limit (AQL) for lot-by-lot inspection published in ISO 2859-5 should
be applied.
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2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 3534-1, Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in
probability
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 3534-1 and the following 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
inspection
conformity evaluation by observation and judgement accompanied as appropriate by measurement,
testing or gauging
[SOURCE: ISO 3534-2:2006, 4.1.2]
3.2
inspection by attributes
inspection (3.1) by noting the presence, or absence, of one or more particular characteristic(s) in each
of the items in the group under consideration, and counting how many items do, or do not, possess the
characteristic(s), or how many such events occur in the item, group or opportunity space
Note 1 to entry: When inspection is performed by simply noting whether the item is nonconforming or not, the
inspection is termed inspection for nonconforming items. When inspection is performed by noting the number of
nonconformities on each unit, the inspection is termed inspection for number of nonconformities.
[SOURCE: ISO 3534-2:2006, 4.1.3]
3.3
item
entity
anything that can be described and considered separately
EXAMPLE A discrete physical item; a defined amount of bulk material; a service, activity, person, system or
some combination thereof.
[SOURCE: ISO 3534-2:2006, 1.2.11]
3.4
nonconformity
non-fulfilment of a requirement
[SOURCE: ISO 3534-2:2006, 3.1.11]
Note 1 to entry: See notes to 3.5.
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3.5
defect
non-fulfilment of a requirement related to an intended or specified use
Note 1 to entry: The distinction between the concepts defect and nonconformity (3.4) 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 information, such as operating
or maintenance instructions, provided by the customer.
[SOURCE: ISO 3534-2:2006, 3.1.12]
3.6
nonconforming item
item (3.3) with one or more nonconformities (3.4)
[SOURCE: ISO 3534-2:2006, 1.2.12]
3.7
percent nonconforming
〈in a sample〉 one hundred times the number of nonconforming items (3.6) in the sample (3.13) divided
by the sample size (3.14), viz:
d
100 ×
n
where
d is the number of nonconforming items in the sample;
n is the sample size
[SOURCE: ISO 2859-1:1999, 3.1.8]
3.8
percent nonconforming
〈in a population or lot〉 one hundred times the number of nonconforming items (3.6) in the population or
lot (3.11) divided by the population or lot size (3.12), viz:
D
ni
100 ×=p 100 ×
ni
N
where
p is the proportion of nonconforming items;
ni
D is the number of nonconforming items in the population or lot;
ni
N is the population or lot size
Note 1 to entry: Adapted from ISO 2859-1:1999, 3.1.9.
Note 2 to entry: In this International Standard, the terms percent nonconforming (3.7 and 3.8) or nonconformities
per 100 items (3.9 and 3.10) 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.
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3.9
nonconformities per 100 items
〈in a sample〉 one hundred times the number of nonconformities (3.4) in the sample (3.13) divided by the
sample size (3.14), viz:
d
100×
n
where
d is the number of nonconformities in the sample;
n is the sample size
[SOURCE: ISO 2859-1:1999, 3.1.10]
3.10
nonconformities per 100 items
〈in a population or lot〉 100 times the number of nonconformities (3.4) in the population or lot (3.11)
divided by the population or lot size (3.12), viz:
D
nt
100×=p 100×
nt
N
where
p is the number of nonconformities per item;
nt
D is the number of nonconformities in the population or lot;
nt
N is the population or lot size
Note 1 to entry: Adapted from ISO 2859-1:1999, 3.1.11.
Note 2 to entry: An item may contain one or more nonconformities.
3.11
lot
definite part of a population constituted under essentially the same conditions as the population with
respect to the sampling purpose
Note 1 to entry: The sampling purpose can, for example, be to determine lot acceptability, or to estimate the
mean value of a particular characteristic.
[SOURCE: ISO 3534-2:2006, 1.2.4]
3.12
lot size
number of items (3.3) in a lot (3.11)
[SOURCE: ISO 2859-1:1999, 3.1.14]
3.13
sample
subset of a population made up of one or more sampling units
[SOURCE: ISO 3534-2:2006, 1.2.17]
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3.14
sample size
number of sampling units in a sample (3.13)
[SOURCE: ISO 3534-2:2006, 1.2.26]
3.15
acceptance sampling plan
plan which states the sample size(s) (3.14) to be used and the associated criteria for lot acceptance
[SOURCE: ISO 3534-2:2006, 4.3.3]
3.16
consumer's risk quality
Q
CR
〈acceptance sampling〉 quality level of a lot (3.11) or process which, in the acceptance sampling plan
(3.15), corresponds to a specified consumer's risk
[SOURCE: ISO 3534-2:2006, 4.6.9]
Note 1 to entry: The specified consumer's risk is usually 10 %.
3.17
producer's risk quality
Q
PR
〈acceptance sampling〉 quality level of a lot (3.11) or process which, in the acceptance sampling plan
(3.15), corresponds to a specified producer's risk
[SOURCE: ISO 3534-2:2006, 4.6.10]
Note 1 to entry: The specified producer's risk is usually 5 %.
3.18
count
when inspection by attributes is performed, the result of the inspection of each sample item
Note 1 to entry: In the case of the inspection for nonconforming items, the count is set to 1 if the sample
item is nonconforming. In the case of the inspection for nonconformities, the count is set to the number of
nonconformities found in the sample item.
3.19
cumulative count
when a sequential sampling plan is used, the sum of the counts during inspection, counting from the
start of the inspection of the lot up to, and including, the sample item last inspected
3.20
cumulative sample size
when a sequential sampling plan is used, the total number of sample items during inspection, counting
from the start of the inspection of the lot up to, and including, the sample item last inspected
3.21
acceptance value
〈for sequential sampling〉 value used in the graphical method for determination of acceptance of the lot,
that is derived from the specified parameters of the sampling plan and the cumulative sample size
3.22
acceptance number
〈for sequential sampling〉 number used in the numerical method for determination of acceptance of the
lot, that is obtained by rounding the acceptance value down to the nearest integer
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3.23
rejection value
〈for sequential sampling〉 value used in the graphical method for determination of non-acceptance of the
lot, that is derived from the specified parameter
...
NORME ISO
INTERNATIONALE 28591
Première édition
2017-10
Plans d'échantillonnage progressif
pour le contrôle par attributs
Sequential sampling plans for inspection by attributes
Numéro de référence
ISO 28591:2017(F)
©
ISO 2017
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ISO 28591:2017(F)
DOCUMENT PROTÉGÉ PAR COPYRIGHT
© ISO 2017, Publié en Suisse
Droits de reproduction réservés. Sauf indication contraire, 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, l’affichage sur
l’internet ou sur un Intranet, sans autorisation écrite préalable. Les demandes d’autorisation peuvent être adressées à l’ISO à
l’adresse ci-après ou au comité membre de l’ISO dans le pays du demandeur.
ISO copyright office
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Tel. +41 22 749 01 11
Fax +41 22 749 09 47
copyright@iso.org
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ii © ISO 2017 – Tous droits réservés
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ISO 28591:2017(F)
Sommaire Page
Avant-propos .iv
Introduction .vi
1 Domaine d'application . 1
2 Références normatives . 2
3 Termes et définitions . 2
4 Symboles et termes abrégés . 6
5 Principes des plans d'échantillonnage progressif pour contrôle par attributs .7
6 Sélection d'un plan d'échantillonnage . 7
6.1 Point du risque fournisseur et point du risque client . 7
6.2 Valeurs recommandées de Q et de Q .
RF RC 8
6.3 Opérations préliminaires . 8
6.3.1 Obtention des paramètres h , h et g .8
A R
6.3.2 Obtention des valeurs de troncage. 8
7 Mise en œuvre d'un plan d'échantillonnage progressif . 8
7.1 Spécification du plan . 8
7.2 Prélèvement d'un individu. 8
7.3 Cumul et résultat du cumul . 8
7.3.1 Cumul . 8
7.3.2 Résultat du cumul . 9
7.4 Choix entre méthode numérique et méthode graphique . 9
7.5 Méthode numérique . 9
7.5.1 Préparation de la table d'acceptabilité . 9
7.5.2 Prise de décisions .10
7.6 Méthode graphique .10
7.6.1 Préparation du graphique d'acceptabilité .10
7.6.2 Prise de décisions .11
8 Exemple numérique .12
9 Tableaux .12
Annexe A (informative) Propriétés statistiques du plan d'échantillonnage progressif pour
contrôle par attributs .31
Bibliographie .40
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ISO 28591:2017(F)
Avant-propos
L'ISO (Organisation internationale de normalisation) est une fédération mondiale d'organismes
nationaux de normalisation (comités membres de l'ISO). L'élaboration des Normes internationales est
en général confiée aux comités techniques de l'ISO. Chaque comité membre intéressé par une étude
a le droit de faire partie du comité technique créé à cet effet. Les organisations internationales,
gouvernementales et non gouvernementales, en liaison avec l'ISO participent également aux travaux.
L'ISO collabore étroitement avec la Commission électrotechnique internationale (IEC) en ce qui
concerne la normalisation électrotechnique.
Les procédures utilisées pour élaborer le présent document et celles destinées à sa mise à jour sont
décrites dans les Directives ISO/IEC, Partie 1. Il convient, en particulier de prendre note des différents
critères d'approbation requis pour les différents types de documents ISO. Le présent document a été
rédigé conformément aux règles de rédaction données dans les Directives ISO/IEC, Partie 2 (voir www.
iso.org/directives).
L'attention est appelée sur le fait que certains des éléments du présent document peuvent faire l'objet de
droits de propriété intellectuelle ou de droits analogues. L'ISO ne saurait être tenue pour responsable
de ne pas avoir identifié de tels droits de propriété et averti de leur existence. Les détails concernant
les références aux droits de propriété intellectuelle ou autres droits analogues identifiés lors de
l'élaboration du document sont indiqués dans l'Introduction et/ou dans la liste des déclarations de
brevets reçues par l'ISO (voir www.iso.org/brevets).
Les appellations commerciales éventuellement mentionnées dans le présent document sont données
pour information, par souci de commodité, à l’intention des utilisateurs et ne sauraient constituer un
engagement.
Pour une explication de la nature volontaire des normes, la signification des termes et expressions
spécifiques de l'ISO liés à l'évaluation de la conformité, ou pour toute information au sujet de l'adhésion
de l'ISO aux principes de l’Organisation mondiale du commerce (OMC) concernant les obstacles
techniques au commerce (OTC), voir le lien suivant: www.iso.org/iso/fr/avant-propos.html
Le présent document a été élaboré par le comité technique ISO/TC 69, Application des méthodes
statistiques, sous-comité SC 5, Échantillonnage en vue d'acceptation.
Cette première édition de l’ISO 28591 annule et remplace l’ISO 8422:2006, qui a fait l’objet d’une révision
mineure pour changer l’ancien numéro de référence, 8422, par le nouveau, 28591.
En vue d’obtenir un portfolio plus cohérent, le TC 69/SC 5 a renuméroté simultanément les normes
suivantes, par le biais de révisions mineures:
Ancienne référence Nouvelle référence Titre
ISO 2859-10:2006 ISO 28590:2017 Règles d'échantillonnage pour les contrôles par attributs
— Introduction au système d'échantillonnage pour les
contrôles par attributs de l'ISO 2859
ISO 8422:2006 ISO 28591:2017 Plans d'échantillonnage progressif pour le contrôle par
attributs
ISO 28801:2011 ISO 28592:2017 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)
ISO 18414:2006 ISO 28593:2017 Procédures d'échantillonnage par attributs pour accepta-
tion — Système d'échantillonnage de tolérance zéro-défaut
basé sur le principe de crédit pour le contrôle de la qualité à
la sortie
ISO 21247:2005 ISO 28594:2017 Systèmes d'échantillonnage de tolérance zéro-défaut et pro-
cédures de maîtrise des processus combinés pour l'accepta-
tion de produits
iv © ISO 2017 – Tous droits réservés
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ISO 28591:2017(F)
ISO 14560:2004 ISO 28597:2017 Règles d'échantillonnage par attributs en vue d'acceptation
— Niveaux spécifiés de qualité en termes d'individus non
conformes pour un million d'individus
ISO 13448-1:2005 ISO 28598-1:2017 Règles d'échantillonnage pour acceptation fondées sur le
principe d'attribution de priorités (APP) — Partie 1: Lignes
directrices relatives à l'approche APP
ISO 13448-2:2004 ISO 28598-2:2017 Règles d'échantillonnage pour acceptation fondées sur le
principe d'attribution de priorités (APP) — Partie 2: Plans
d'échantillonnage simple coordonnés pour l'échantillonnage
pour acceptation par attributs
Les références croisées entre les documents énumérés ci-dessous ont été corrigées dans les révisions
mineures.
Une liste de tous les documents de la nouvelle série de normes ISO 28590 - ISO 28599 se trouve sur le
site Web de l’ISO.
© ISO 2017 – Tous droits réservés v
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ISO 28591:2017(F)
Introduction
Les processus de production actuels prévoient le plus souvent d'atteindre des niveaux élevés de qualité
−6
tels que le nombre d'individus non conformes est exprimé en parties par million (10 ). Dans de telles
circonstances, les plans d'échantillonnage pour acceptation les plus utilisés, tels que ceux présentés
dans l'ISO 2859-1, nécessitent des effectifs d'échantillon d'une importance telle qu'il est difficile de
les traiter. Pour pallier ce problème, les utilisateurs appliquent des plans d'échantillonnage pour
acceptation présentant des probabilités très élevées de décisions erronées ou, dans des cas extrêmes,
ils préfèrent ne pas utiliser du tout les règles d'échantillonnage pour acceptation. Cependant, dans
bon nombre de situations, l'acceptation de produits de haute qualité nécessite encore d'utiliser des
méthodes statistiques normalisées. Dans ce cas, il est nécessaire d'appliquer des règles statistiques
impliquant les plus faibles effectifs d'échantillon possibles. Les plans d'échantillonnage progressif
constituent les seules règles statistiques permettant de satisfaire cette nécessité dans la mesure où
parmi tous les plans d'échantillonnage disponibles ayant des propriétés statistiques similaires, le plan
d'échantillonnage progressif a l'effectif moyen d'échantillon le plus faible.
Les plans d'échantillonnage progressif présentent le principal avantage de réduire l'effectif moyen
d'échantillon. L'effectif moyen d'échantillon est la moyenne pondérée de tous les effectifs d'échantillon
susceptibles d'être obtenus pour un plan d'échantillonnage pour un niveau de qualité d'un lot ou
processus donné. Comme pour les plans d'échantillonnage double et multiple, l'utilisation de plans
d'échantillonnage progressif conduit à un effectif moyen d'échantillon inférieur à celui qu'il faut pour
des plans d'échantillonnage simple ayant la même efficacité. Cependant, les économies moyennes sont
souvent plus importantes lors de l'utilisation d'un plan d'échantillonnage progressif que d'un plan
d'échantillonnage double ou multiple. Pour des lots de très bonne qualité, les économies maximales
pour des plans d'échantillonnage progressif peuvent atteindre 85 %, comparées à une économie de
37 % pour des plans d'échantillonnage double et de 75 % pour des plans d'échantillonnage multiple.
D'autre part, le nombre réel d'individus contrôlés pour un lot particulier en plan d'échantillonnage
double, multiple ou progressif, peut dépasser l'effectif d'échantillon, n , du plan d'échantillonnage simple
0
correspondant. Pour des plans d'échantillonnage double et multiple, il existe une limite supérieure de
1,25n au nombre réel d'individus à contrôler. Pour les plans d'échantillonnage progressif classiques, il
0
n'existe pas une telle limite et le nombre réel d'individus contrôlés peut excéder l'effectif d'échantillon
du plan d'échantillonnage simple correspondant, n , voire dépasser l'effectif du lot, N. Pour les plans
0
d'échantillonnage progressif de la présente Norme internationale, une règle de troncage a été introduite
qui implique une limite supérieure n au nombre réel d'individus à contrôler.
t
Les autres facteurs dont il convient de tenir compte comprennent:
a) Simplicité
Les règles d'un plan d'échantillonnage progressif sont plus facilement mal interprétées par les
contrôleurs que les règles plus faciles d'un plan d'échantillonnage simple.
b) Variabilité du nombre de contrôles
Dans la mesure où le nombre réel d'individus contrôlés pour un lot particulier n'est pas connu à l'avance,
l'utilisation de plans d'échantillonnage progressif peut présenter des difficultés organisationnelles. Par
exemple, des difficultés de planification des opérations de contrôle.
c) Facilité de prélèvement des individus
Si le prélèvement des individus à différents moments se révèle coûteux, l'intérêt de réduire l'effectif
moyen d'échantillon en utilisant des plans d'échantillonnage progressif peut être annulé par
l'augmentation du coût d'échantillonnage.
d) Durée de l'essai
vi © ISO 2017 – Tous droits réservés
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ISO 28591:2017(F)
Lorsque la durée de l'essai d'un individu simple est longue et qu'il est possible de vérifier un certain
nombre d'individus en même temps, les plans d'échantillonnage progressif sont plus longs à réaliser
que les plans d'échantillonnage simples correspondants.
e) Variabilité de la qualité au sein du lot
Si le lot comprend deux sous-lots ou plus provenant de différentes sources et s'il est probable qu'il
existe une différence substantielle en termes de qualité des sous-lots, le prélèvement d'un échantillon
représentatif pour un plan d'échantillonnage progressif est beaucoup plus difficile à réaliser que pour
le plan d'échantillonnage simple correspondant.
Les avantages et les inconvénients des plans d'échantillonnage double et multiple sont toujours fonction
de ceux que présentent les plans d'échantillonnage simple et progressif. Le résultat de la balance entre
l'avantage d'un effectif moyen d'échantillon plus petit et les inconvénients cités ci-dessus est que les
plans d'échantillonnage progressif ne sont appropriés que lorsque le contrôle des individus discrets est
coûteux par rapport aux frais généraux de contrôle.
Le choix entre des plans d'échantillonnage simple, double, multiple et progressif doit être fait avant le
début du contrôle d'un lot. Il n'est pas possible pendant le contrôle d'un lot de changer un type de plan
d'échantillonnage pour un autre, car l'efficacité du plan peut être radicalement modifiée si les résultats
du contrôle réel influencent le choix du critère d'acceptation.
Bien que l'utilisation de plans d'échantillonnage progressif soit en moyenne plus économique que
l'utilisation des plans d'échantillonnage simple correspondants, l'acceptation ou la non-acceptation peut
survenir à un stade très tardif, le résultat du cumul d'individus non conformes (ou de non-conformités)
restant compris très longtemps entre les critères d'acceptation et de rejet. Pour la méthode graphique,
cela se traduit par la progression aléatoire de la courbe en escalier dans la zone d'indécision. Une
telle situation est d'autant plus probable que le niveau de qualité du lot ou du processus (en termes de
pourcentage de non conformes ou en nombre de non-conformités pour 100 individus) est proche de
100g, où g représente le paramètre donnant la pente des lignes d'acceptation et de rejet.
Afin d'améliorer cette situation, la valeur de troncage de l'effectif d'échantillon est établie avant le début
du contrôle d'un lot. Si l'effectif cumulé d'échantillon atteint la valeur de troncage n sans détermination
t
de l'acceptabilité du lot, le contrôle est arrêté; l'acceptation ou la non-acceptation du lot est alors
déterminée selon les valeurs de troncage des critères d'acceptation et de rejet.
Pour les plans d'échantillonnage progressif d'usage courant, le troncage représente généralement un
écart par rapport à leurs usages prévus, donnant lieu à une déformation de leurs efficacités. Cependant,
dans la présente Norme internationale, les efficacités des plans d'échantillonnage progressif ont été
déterminées en tenant compte du troncage de sorte qu'il fasse partie intégrante des plans fournis.
L'ISO 2859-5 fournit également des plans d'échantillonnage progressif pour le contrôle par attributs.
Cependant, le principe de conception de ces plans est fondamentalement différent de celui spécifié
dans la présente Norme internationale. Les plans d'échantillonnage de l'ISO 2859-5 sont conçus pour
compléter le système d'échantillonnage pour acceptation pour le contrôle par attributs de l'ISO 2859-1.
Il convient par conséquent de les utiliser pour le contrôle d'une série continue de lots, c'est-à-dire une
série suffisamment longue pour pouvoir appliquer les règles de modification (passage) du système de
l'ISO 2859. L'application des règles de modification constitue le seul moyen de renforcer la protection
du client (au moyen de critères de contrôle par échantillonnage renforcé ou l'interruption du contrôle
par échantillonnage) lorsqu'on utilise les plans d'échantillonnage progressif de l'ISO 2859-5. Cependant,
dans certaines circonstances, il est absolument nécessaire de totalement maîtriser les risques
fournisseur et client. De telles situations peuvent par exemple survenir lorsque l'échantillonnage est
réalisé pour des raisons d'ordre réglementaire, pour démontrer la qualité des processus de production
ou pour vérifier des hypothèses. Dans ce cas, le choix d'utiliser les plans d'échantillonnage individuels
spécifiés dans les procédures d'échantillonnage de l'ISO 2859-5 peut se révéler inapproprié. Les plans
d'échantillonnage donnés dans la présente Norme internationale ont été conçus pour satisfaire ces
conditions spécifiques.
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NORME INTERNATIONALE ISO 28591:2017(F)
Plans d'échantillonnage progressif pour le contrôle par
attributs
1 Domaine d'application
La présente Norme internationale spécifie des plans et des règles d'échantillonnage progressif pour le
contrôle par attributs d'individus discrets.
Les plans sont indexés en termes de point du risque fournisseur et de point du risque client. Par
conséquent, ils peuvent être utilisés pour l'échantillonnage pour acceptation mais également à des fins
plus générales de vérification d'hypothèses statistiques simples concernant des proportions.
La présente Norme internationale fournit des règles, basées sur la détermination progressive des
résultats de contrôle, pouvant être utilisées pour inciter le fournisseur, par des pressions économiques
et psychologiques liées à la non-acceptation de lots de qualité inférieure, à fournir des lots de qualité
ayant une forte probabilité d'acceptation. En même temps, le client est protégé par une limite supérieure
imposée de la probabilité d'accepter des lots de faible qualité.
La présente Norme internationale fournit des plans d'échantillonnage, d'une manière non limitative,
notamment aux contrôles ci-après:
— produits finis;
— composants et matières premières;
— opérations;
— matériaux en cours de fabrication;
— fournitures en stock;
— opérations d'entretien;
— informations ou enregistrements;
— procédures administratives.
La présente Norme internationale contient des plans d'échantillonnage pour le contrôle par attributs
d'individus discrets. Les plans d'échantillonnage peuvent être utilisés lorsque l'évaluation de la non-
conformité s'exprime soit en termes de proportion (ou pourcentage) d'individus non conformes, soit en
termes de non-conformités par individu (pour 100 individus).
Les plans d'échantillonnage sont fondés sur l'hypothèse selon laquelle les non-conformités surviennent
de façon aléatoire et sont statistiquement indépendantes. Il peut exister de bonnes raisons de supposer
qu'une non-conformité dans un individu puisse être provoquée par une condition qui provoquerait des
non-conformités également dans d'autres individus. Dans ce cas, mieux vaudrait considérer les individus
comme étant simplement conformes ou non conformes, et ignorer les non-conformités multiples.
Il convient d'utiliser les plans d'échantillonnage de la présente Norme internationale principalement
pour l'analyse d'échantillons prélevés de processus. Par exemple, ils peuvent être utilisés pour
l'échantillonnage pour acceptation de lots prélevés d'un processus sous maîtrise statistique. Par ailleurs,
ils peuvent également être utilisés pour l'échantillonnage pour acceptation d'un lot isolé dont l'effectif
est important et la proportion prévue de non-conformités est faible (sensiblement inférieure à 10 %).
Dans le cas de l'échantillonnage pour acceptation d'une série continue de lots, il convient d'appliquer le
système des plans d'échantillonnage progressif pour le contrôle lot par lot, indexés d'après le niveau de
qualité acceptable (NQA) de l'ISO 2859-5.
© ISO 2017 – Tous droits réservés 1
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ISO 28591:2017(F)
2 Références normatives
Les documents suivants cités dans le texte constituent, pour tout ou partie de leur contenu, des
exigences du présent document. Pour les références datées, seule l’édition citée s’applique. Pour les
références non datées, la dernière édition du document de référence s'applique (y compris les éventuels
amendements).
ISO 3534-1, Statistique — Vocabulaire et symboles — Partie 1: Termes statistiques généraux et termes
utilisés en calcul des probabilités
3 Termes et définitions
Pour les besoins du présent document, les termes et définitions donnés dans l'ISO 3534-1 ainsi que les
suivants s'appliquent.
L'ISO et l'IEC tiennent à jour des bases de données terminologiques destinées à être utilisées en
normalisation, consultables aux adresses suivantes:
— IEC Electropedia: disponible à l’adresse http://www.electropedia.org/.
— ISO Online browsing platform: disponible à l’adresse http://www.iso.org/obp.
3.1
contrôle
évaluation de la conformité par observation et jugement, accompagnés le cas échéant par des mesurages,
essais et passages au calibre
[SOURCE: ISO 3534-2:2006, 4.1.2]
3.2
contrôle par attributs
contrôle (3.1) consistant à noter la présence ou l'absence d'une ou plusieurs caractéristiques pour
chacun des individus du groupe considéré, et à compter combien de ces individus possèdent ou ne
possèdent pas cette (ces) caractéristique(s), ou encore à compter combien d'événements de même
nature se produisent dans l'individu, le groupe ou l'aire d'occurrence
Note 1 à l'article: Lorsque le contrôle consiste uniquement à noter si l'individu est conforme ou non conforme, le
contrôle est appelé contrôle d'individus non conformes. Lorsque le contrôle consiste à noter le nombre de non-
conformités par unité, le contrôle est appelé contrôle du nombre de non-conformités.
[SOURCE: ISO 3534-2:2006, 4.1.3]
3.3
individu
entité
tout ce qui peut être décrit et considéré individuellement
EXEMPLE Une entité physique discrète, une quantité définie de matériau en vrac, un service, une activité,
une personne, un système ou une combinaison de l'ensemble.
[SOURCE: ISO 3534-2:2006, 1.2.11]
3.4
non-conformité
non-satisfaction d'une exigence
[SOURCE: ISO 3534-2:2006, 3.1.11]
Note 1 à l'article: Voir les notes au 3.5.
2 © ISO 2017 – Tous droits réservés
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ISO 28591:2017(F)
3.5
défaut
non-satisfaction d'une exigence relative à une utilisation prévue ou spécifiée
Note 1 à l'article: La distinction faite entre les concepts «défaut» et non-conformité (3.4) est importante car elle
comporte des connotations juridiques, particulièrement celles liées à la responsabilité du fait du produit. En
conséquence, il convient d'utiliser le terme «défaut» avec une extrême précaution.
Note 2 à l'article: L'utilisation prévue, telle que prévue par le client, peut être affectée par la nature des
informations, par exemple les notices d'utilisation ou d'entretien, transmises par le client.
[SOURCE: ISO 3534-2:2006, 3.1.12]
3.6
individu non conforme
individu (3.3) avec une ou plusieurs non-conformités (3.4)
[SOURCE: ISO 3534-2:2006, 1.2.12]
3.7
pourcentage de non-conformes
〈dans un échantillon〉 cent fois le nombre d'individus non conformes (3.6) de l'échantillon (3.13) divisé
par l'effectif d'échantillon (3.14), soit:
d
100 ×
n
où
d est le nombre d'individus non conformes de l'échantillon;
n est l'effectif d'échantillon
[SOURCE: ISO 2859-1:1999, 3.1.8]
3.8
pourcentage de non-conformes
〈dans une population ou dans un lot〉 cent fois le nombre d'individus non conformes (3.6) de la population
ou du lot (3.11) divisé par l'effectif du lot (3.12) ou de la population, soit:
D
ni
100×=p 100×
ni
N
où
p est la proportion d'individus non conformes;
ni
D est le nombre d'individus non conformes de la population ou du lot;
ni
N est l'effectif de la population ou du lot
Note 1 à l'article: Adapté de l'ISO 2859-1:1999, 3.1.9.
Note 2 à l'article: Dans la présente Norme internationale, les termes pourcentage de non-conformes (3.7 et 3.8)
et nombre de non-conformités pour 100 individus (3.9 et 3.10) 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.
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ISO 28591:2017(F)
3.9
nombre de non-conformités pour 100 individus
〈dans un échantillon〉 cent fois le nombre de non-conformités (3.4) de l'échantillon (3.13) divisé par
l'effectif d'échantillon (3.14), soit:
d
100×
n
où
d est le nombre de non-conformités trouvées dans l'échantillon;
n est l'effectif d'échantillon
[SOURCE: ISO 2859-1:1999, 3.1.10]
3.10
nombre de non-conformités pour 100 individus
〈dans une population ou dans un lot〉 100 fois le nombre de non-conformités (3.4) de la population ou du
lot (3.11) divisé par l'effectif du lot (3.12) ou de la population, soit:
D
nt
100×=p 100×
nt
N
où
p est le nombre de non-conformités par individu;
nt
D est le nombre de non-conformités de la population ou du lot;
nt
N est l'effectif de la population ou du lot
Note 1 à l'article: Adapté de l'ISO 2859-1:1999, 3.1.11.
Note 2 à l'article: Un individu peut contenir une ou plusieurs non-conformités.
3.11
lot
partie définie d'une population constituée essentiellement dans les mêmes conditions que la population
pour ce qui concerne l'échantillonnage
Note 1 à l'article: L'échantillonnage peut par exemple être réalisé pour déterminer l'acceptabilité d'un lot ou pour
estimer la valeur moyenne d'une caractéristique particulière.
[SOURCE: ISO 3534-2:2006, 1.2.4]
3.12
effectif du lot
nombre d'individus (3.3) dans un lot (3.11)
[SOURCE: ISO 2859-1:1999, 3.1.14]
3.13
échantillon
sous-ensemble d'une population constitué d'une ou de plusieurs unités d'échantillonnage
[SOURCE: ISO 3534-2:2006, 1.2.17]
4 © ISO 2017 – Tous droits réservés
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ISO 28591:2017(F)
3.14
taille de l'échantillon
nombre d'unités d'échantillonnage constituant un échantillon (3.13)
[SOURCE:
...
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