SIST ISO 8422:2008
(Main)Sequential sampling plans for inspection by attributes
Sequential sampling plans for inspection by attributes
ISO 8422:2006 contains 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. ISO 8422:2006 provides 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.
ISO 8422:2006 provides sampling plans that are applicable, but not limited, to inspection of 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.
The sampling plans from ISO 8422:2006 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 8422:2006 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. L'ISO 8422:2006 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.
L'ISO 8422:2006 fournit des plans d'échantillonnage applicables, 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, et procédures administratives.
Il convient d'utiliser les plans d'échantillonnage de l'ISO 8422:2006 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.
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Standards Content (Sample)
INTERNATIONAL ISO
STANDARD 8422
Second edition
2006-10-01
Sequential sampling plans for inspection
by attributes
Plans d'échantillonnage progressif pour le contrôle par attributs
Reference number
©
ISO 2006
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
© ISO 2006
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2006 – All rights reserved
Contents Page
Foreword. iv
Introduction . v
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
7 Operation of a sequential sampling plan . 8
8 Numerical example . 12
9 Tables. 12
Annex A (informative) Statistical properties of the sequential sampling plan
for inspection by attributes . 25
Bibliography . 32
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
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.
ISO 8422 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 5, Acceptance sampling.
This second edition cancels and replaces the first edition (ISO 8422:1991), of which it constitutes a technical
revision. It also incorporates the Technical Corrigendum ISO 8422:1991/Cor.1:1993. The following
improvements have been introduced:
⎯ preferred values of producer's risk quality and consumer's risk quality have been changed and their series
have been extended,
⎯ values of the parameters h , h and g have been recalculated in order to provide plans that exactly meet
A R
stated requirements,
⎯ consumer's risk quality values in percent nonconforming are separated from those in nonconformities per
100 items both in the master tables and in Table A.1, which contains the average sample sizes for
sequential sampling plans.
The revised version of Annex A of ISO 8422:1991 has been published as ISO 2859-5.
iv © ISO 2006 – All rights reserved
Introduction
In contemporary production processes, quality is often expected to reach such high levels that the number of
−6
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 plans, there is an upper limit of 1,25 n to the actual
number of items to be inspected. For classical 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 plans in this International Standard, a curtailment rule has been
introduced involving an upper limit n on the actual number of items to be inspected.
t
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 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 of lot acceptability,
t
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.
vi © ISO 2006 – All rights reserved
INTERNATIONAL STANDARD ISO 8422:2006(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
...
SLOVENSKI STANDARD
01-januar-2008
6HNYHQþQLQDþUWLY]RUþHQMD]DNRQWURORSRRSLVQLKVSUHPHQOMLYNDK
Sequential sampling plans for inspection by attributes
Ta slovenski standard je istoveten z:
ICS:
03.120.30 8SRUDEDVWDWLVWLþQLKPHWRG Application of statistical
methods
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
INTERNATIONAL ISO
STANDARD 8422
Second edition
2006-10-01
Sequential sampling plans for inspection
by attributes
Plans d'échantillonnage progressif pour le contrôle par attributs
Reference number
©
ISO 2006
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
© ISO 2006
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2006 – All rights reserved
Contents Page
Foreword. iv
Introduction . v
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
7 Operation of a sequential sampling plan . 8
8 Numerical example . 12
9 Tables. 12
Annex A (informative) Statistical properties of the sequential sampling plan
for inspection by attributes . 25
Bibliography . 32
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
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.
ISO 8422 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 5, Acceptance sampling.
This second edition cancels and replaces the first edition (ISO 8422:1991), of which it constitutes a technical
revision. It also incorporates the Technical Corrigendum ISO 8422:1991/Cor.1:1993. The following
improvements have been introduced:
⎯ preferred values of producer's risk quality and consumer's risk quality have been changed and their series
have been extended,
⎯ values of the parameters h , h and g have been recalculated in order to provide plans that exactly meet
A R
stated requirements,
⎯ consumer's risk quality values in percent nonconforming are separated from those in nonconformities per
100 items both in the master tables and in Table A.1, which contains the average sample sizes for
sequential sampling plans.
The revised version of Annex A of ISO 8422:1991 has been published as ISO 2859-5.
iv © ISO 2006 – All rights reserved
Introduction
In contemporary production processes, quality is often expected to reach such high levels that the number of
−6
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 plans, there is an upper limit of 1,25 n to the actual
number of items to be inspected. For classical 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 plans in this International Standard, a curtailment rule has been
introduced involving an upper limit n on the actual number of items to be inspected.
t
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 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 of lot acceptability,
t
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.
vi © ISO 2006 – All rights reserved
INTERNATIONAL STANDARD ISO 8422:2006(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 prov
...
NORME ISO
INTERNATIONALE 8422
Deuxième édition
2006-10-01
Plans d'échantillonnage progressif pour
le contrôle par attributs
Sequential sampling plans for inspection by attributes
Numéro de référence
©
ISO 2006
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Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax. + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Publié en Suisse
ii © ISO 2006 – Tous droits réservés
Sommaire Page
Avant-propos. iv
Introduction . v
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 . 8
7 Mise en œuvre d'un plan d'échantillonnage progressif . 8
8 Exemple numérique. 12
9 Tableaux . 13
Annexe A (informative) Propriétés statistiques du plan d'échantillonnage progressif pour contrôle
par attributs . 26
Bibliographie . 33
Avant-propos
L'ISO (Organisation internationale de normalisation) est une fédération mondiale d'organismes nationaux de
normalisation (comités membres de l'ISO). L'élaboration des Normes internationales est en général confiée
aux comités techniques de l'ISO. Chaque comité membre intéressé par une étude a le droit de faire partie du
comité technique créé à cet effet. Les organisations internationales, gouvernementales et non
gouvernementales, en liaison avec l'ISO participent également aux travaux. L'ISO collabore étroitement avec
la Commission électrotechnique internationale (CEI) en ce qui concerne la normalisation électrotechnique.
Les Normes internationales sont rédigées conformément aux règles données dans les Directives ISO/CEI,
Partie 2.
La tâche principale des comités techniques est d'élaborer les Normes internationales. Les projets de Normes
internationales adoptés par les comités techniques sont soumis aux comités membres pour vote. Leur
publication comme Normes internationales requiert l'approbation de 75 % au moins des comités membres
votants.
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.
L'ISO 8422 a été élaborée par le comité technique ISO/TC 69, Application des méthodes statistiques,
sous-comité SC 5, Échantillonnage en vue d'acceptation.
Cette deuxième édition annule et remplace la première édition (ISO 8422:1991), qui a fait l'objet d'une
révision technique.Elle incorpore également le Rectificatif technique ISO 8422:1991/Cor.1:1993. Les
améliorations suivantes ont été apportées:
⎯ les valeurs recommandées de qualité du risque du fournisseur et de qualité du risque du client ont été
modifiées et leur série a été élargie,
⎯ les valeurs des paramètres h , h et g ont été recalculées afin de fournir des plans qui répondent plus
A R
exactement aux conditions déclarées,
⎯ les valeurs de qualité du risque du client en pourcentage de non-conformes sont séparées de celles
correspondant au nombre de non-conformités pour 100 individus, tant dans les tableaux principaux que
dans le Tableau A.1, comprenant les effectifs moyens d'échantillon de plans d'échantillonnage progressif.
La version révisée de l'Annexe A de l'ISO 8422:1991 a été publiée en tant que nouvelle Norme internationale,
sous la référence ISO 2859-5.
iv © ISO 2006 – Tous droits réservés
Introduction
Les processus de production actuels prévoient le plus souvent d'atteindre des niveaux élevés de qualité tels
−6
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 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 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 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
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 de
t
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 renfo
...
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