SIST ISO 16269-6:2006

INTERNATIONAL ISO
STANDARD 16269-6
First edition
2005-04-01
Statistical interpretation of data —
Part 6:
Determination of statistical tolerance
intervals
Interprétation statistique des données —
Partie 6: Détermination des intervalles statistiques de tolérance

Reference number
©
ISO 2005
PDF disclaimer
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©  ISO 2005
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 2005 – All rights reserved

Contents Page
Foreword. iv
Introduction . v
1 Scope. 1
2 Normative references . 1
3 Terms, definitions and symbols . 1
3.1 Terms and definitions. 1
3.2 Symbols . 2
4 Procedures . 3
4.1 Normal population with known variance and known mean. 3
4.2 Normal population with known variance and unknown mean . 3
4.3 Normal population with unknown variance and unknown mean. 3
4.4 Any continuous distribution of unknown type . 3
5 Examples. 3
5.1 Data. 3
5.2 Example 1: One-sided statistical tolerance interval under known variance. 4
5.3 Example 2: Two-sided statistical tolerance interval under known variance . 4
5.4 Example 3: One-sided statistical tolerance interval under unknown variance . 5
5.5 Example 4: Two-sided statistical tolerance interval under unknown variance. 6
5.6 Example 5: Distribution-free statistical tolerance interval for continuous distribution . 6
Annex A (informative) Forms for tolerance intervals. 8
Annex B (normative) One-sided statistical tolerance limit factors, k (n; p; 1 − α), for known σ . 14
Annex C (normative) Two-sided statistical tolerance limit factors, k (n; p; 1 − α), for known σ. 17
Annex D (normative) One-sided statistical tolerance limit factors, k (n; p; 1 − α), for unknown σ. 20
Annex E (normative) Two-sided statistical tolerance limit factors, k (n; p; 1 − α), for unknown σ. 23
Annex F (normative) One-sided distribution-free statistical tolerance intervals. 26
Annex G (normative) Two-sided distribution-free statistical tolerance intervals. 27
Annex H (informative) Construction of a distribution-free statistical tolerance interval for any type
of distribution . 28
Annex I (informative) Computation of factors for two-sided parametric statistical tolerance
intervals. 29
Bibliography . 30

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 16269-6 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods.
This first edition of ISO 16269-6 cancels and replaces ISO 3207:1975, which has been technically revised.
ISO 16269 consists of the following parts, under the general title Statistical interpretation of data:
 Part 6: Determination of statistical tolerance intervals
 Part 7: Median — Estimation and confidence intervals
 Part 8: Determination of prediction intervals

iv © ISO 2005 – All rights reserved

Introduction
A statistical tolerance interval is an estimated interval, based on a sample, which can be asserted with
confidence 1 − α, for example 95 %, to contain at least a specified proportion p of the items in the population.
The limits of a statistical tolerance interval are called statistical tolerance limits. The confidence level 1 − α is
the probability that a statistical tolerance interval constructed in the prescribed manner will contain at least a
proportion p of the population. Conversely, the probability that this interval will contain less than the proportion
p of the population is α. This part of ISO 16269 describes both one-sided and two-sided statistical tolerance
intervals; a one-sided interval is constructed with an upper or a lower limit while a two-sided interval is
constructed with both an upper and a lower limit.
Tolerance intervals are functions of the observations of the sample, i.e. statistics, and they will generally take
different values for different samples. It is necessary that the observations be independent for the procedures
provided in this part of ISO 16269 to be valid.
Two types of tolerance interval are provided in this part of ISO 16269, parametric and distribution-free. The
parametric approach is based on the assumption that the characteristic being studied in the population has a
normal distribution; hence the confidence that the calculated statistical tolerance interval contains at least a
proportion p of the population can only be taken to be 1 − α if the normality assumption is true. For normally
distributed characteristics, the statistical tolerance interval is determined using one of the Forms A, B, C or D
given in Annex A.
Parametric methods for distributions other than the normal are not considered in this part of ISO 16269. If
departure from normality is suspected in the population, distribution-free statistical tolerance intervals may be
constructed. The procedure for the determination of a statistical tolerance interval for any continuous
distribution is provided in Forms E and F of Annex A.
The tolerance limits discussed in this part of ISO 16269 can be used to compare the natural capability of a
process with one or two given specification limits, either an upper one U or a lower one L or both in statistical
process management. An indication of this is the fact that these tolerance limits have also been called natural
process limits. See ISO 3534-2:1993, 3.2.4, and the general remarks in ISO 3207 which will be cancelled and
replaced by this part of ISO 16269.
Above the upper specification limit U there is the upper fraction nonconforming p (ISO 3534-2:—, 3.2.5.5 and
U
3.3.1.4) and below the lower specification limit L there is the lower fraction nonconforming p (ISO 3534-2:—,
L
3.2.5.6 and 3.3.1.5). The sum p + p = p is called the total fraction nonconforming. (ISO 3534-2:—, 3.2.5.7).
U L T
Between the specification limits U and L there is the fraction conforming 1 − p .
T
In statistical process management the limits U and L are fixed in advance and the fractions p , p and p are
U L T
either calculated, if the distribution is assumed to be known, or otherwise estimated. There are many
applications of statistical tolerance intervals, although the above shows an example to a quality control
problem. Wider applications and more statistical intervals are introduced in many textbooks such as Hahn and
[10]
Meeker .
In contrast, for the tolerance intervals considered in this part of ISO 16269, the confidence level for the interval
estimator and the proportion of the distribution within the interval (corresponding to the fraction conforming
mentioned above) are fixed in advance, and the limits are estimated. These limits may be compared with U
and L. Hence the appropriateness of the given specification limits U and L can be compared with the actual
properties of the process. The one-sided tolerance intervals are used when only either the upper specification
limit U or the lower specification limit L is relevant, while the two-sided intervals are used when both the upper
and the lower specification limits are considered simultaneously.
The terminology with regard to these different limits and intervals has been confusing as the “specification
limits” were earlier also called “tolerance limits” (see the terminology standard ISO 3534-2:1993, 1.4.3, where
both these terms as well as the term “limiting values” were all used as synonyms for this concept). In the latest
revision of ISO 3534-2:—, only the term specification limits have been kept for this concept. Furthermore, the
[5]
Guide for the expression of uncertainty in measurement uses the term “coverage factor” defined as a
“numerical factor used as a multiplier of the combined standard uncertainty in order to obtain an expanded
uncertainty”. This use of “coverage” differs from the use of the term in this part of ISO 16269.
vi © ISO 2005 – All rights reserved

INTERNATIONAL STANDARD ISO 16269-6:2005(E)

Statistical interpretation of data —
Part 6:
Determination of statistical tolerance intervals
1 Scope
This part of ISO 16269 describes procedures for establishing tolerance intervals that include at least a
specified proportion of the population with a specified confidence level. Both one-sided and two-sided
statistical tolerance intervals are provided, a one-sided interval having either an upper or a lower limit while a
two-sided interval has both upper and lower limits. Two methods are provided, a parametric method for the
case where the characteristic being studied has a normal distribution and a distribution-free method for the
case where nothing is known about the distribution except that it is continuous.
2 Normative references
The following referenced documents are indispensable for the application 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: Probability and general statistical terms
1)
ISO 3534-2:— , Statistics — Vocabulary and symbols — Part 2: Applied statistics
3 Terms, definitions and symbols
3.1 Terms and definitions
For the purposes of this document, the terms and definition given in ISO 3534-1, ISO 3534-2 and the following
apply.
3.1.1
statistical tolerance interval
interval determined from a random sample in such a way that one may have a specified level of confidence
that the interval covers at least a specified proportion of the sampled population
NOTE The confidence level in this context is the long-run
...

SLOVENSKI STANDARD
01-april-2006
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Statistical interpretation of data -- Part 6: Determination of statistical tolerance intervals
Interprétation statistique des données -- Partie 6: Détermination des intervalles
statistiques de tolérance
Ta slovenski standard je istoveten z: ISO 16269-6:2005
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 16269-6
First edition
2005-04-01
Statistical interpretation of data —
Part 6:
Determination of statistical tolerance
intervals
Interprétation statistique des données —
Partie 6: Détermination des intervalles statistiques de tolérance

Reference number
©
ISO 2005
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 2005
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 2005 – All rights reserved

Contents Page
Foreword. iv
Introduction . v
1 Scope. 1
2 Normative references . 1
3 Terms, definitions and symbols . 1
3.1 Terms and definitions. 1
3.2 Symbols . 2
4 Procedures . 3
4.1 Normal population with known variance and known mean. 3
4.2 Normal population with known variance and unknown mean . 3
4.3 Normal population with unknown variance and unknown mean. 3
4.4 Any continuous distribution of unknown type . 3
5 Examples. 3
5.1 Data. 3
5.2 Example 1: One-sided statistical tolerance interval under known variance. 4
5.3 Example 2: Two-sided statistical tolerance interval under known variance . 4
5.4 Example 3: One-sided statistical tolerance interval under unknown variance . 5
5.5 Example 4: Two-sided statistical tolerance interval under unknown variance. 6
5.6 Example 5: Distribution-free statistical tolerance interval for continuous distribution . 6
Annex A (informative) Forms for tolerance intervals. 8
Annex B (normative) One-sided statistical tolerance limit factors, k (n; p; 1 − α), for known σ . 14
Annex C (normative) Two-sided statistical tolerance limit factors, k (n; p; 1 − α), for known σ. 17
Annex D (normative) One-sided statistical tolerance limit factors, k (n; p; 1 − α), for unknown σ. 20
Annex E (normative) Two-sided statistical tolerance limit factors, k (n; p; 1 − α), for unknown σ. 23
Annex F (normative) One-sided distribution-free statistical tolerance intervals. 26
Annex G (normative) Two-sided distribution-free statistical tolerance intervals. 27
Annex H (informative) Construction of a distribution-free statistical tolerance interval for any type
of distribution . 28
Annex I (informative) Computation of factors for two-sided parametric statistical tolerance
intervals. 29
Bibliography . 30

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 16269-6 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods.
This first edition of ISO 16269-6 cancels and replaces ISO 3207:1975, which has been technically revised.
ISO 16269 consists of the following parts, under the general title Statistical interpretation of data:
 Part 6: Determination of statistical tolerance intervals
 Part 7: Median — Estimation and confidence intervals
 Part 8: Determination of prediction intervals

iv © ISO 2005 – All rights reserved

Introduction
A statistical tolerance interval is an estimated interval, based on a sample, which can be asserted with
confidence 1 − α, for example 95 %, to contain at least a specified proportion p of the items in the population.
The limits of a statistical tolerance interval are called statistical tolerance limits. The confidence level 1 − α is
the probability that a statistical tolerance interval constructed in the prescribed manner will contain at least a
proportion p of the population. Conversely, the probability that this interval will contain less than the proportion
p of the population is α. This part of ISO 16269 describes both one-sided and two-sided statistical tolerance
intervals; a one-sided interval is constructed with an upper or a lower limit while a two-sided interval is
constructed with both an upper and a lower limit.
Tolerance intervals are functions of the observations of the sample, i.e. statistics, and they will generally take
different values for different samples. It is necessary that the observations be independent for the procedures
provided in this part of ISO 16269 to be valid.
Two types of tolerance interval are provided in this part of ISO 16269, parametric and distribution-free. The
parametric approach is based on the assumption that the characteristic being studied in the population has a
normal distribution; hence the confidence that the calculated statistical tolerance interval contains at least a
proportion p of the population can only be taken to be 1 − α if the normality assumption is true. For normally
distributed characteristics, the statistical tolerance interval is determined using one of the Forms A, B, C or D
given in Annex A.
Parametric methods for distributions other than the normal are not considered in this part of ISO 16269. If
departure from normality is suspected in the population, distribution-free statistical tolerance intervals may be
constructed. The procedure for the determination of a statistical tolerance interval for any continuous
distribution is provided in Forms E and F of Annex A.
The tolerance limits discussed in this part of ISO 16269 can be used to compare the natural capability of a
process with one or two given specification limits, either an upper one U or a lower one L or both in statistical
process management. An indication of this is the fact that these tolerance limits have also been called natural
process limits. See ISO 3534-2:1993, 3.2.4, and the general remarks in ISO 3207 which will be cancelled and
replaced by this part of ISO 16269.
Above the upper specification limit U there is the upper fraction nonconforming p (ISO 3534-2:—, 3.2.5.5 and
U
3.3.1.4) and below the lower specification limit L there is the lower fraction nonconforming p (ISO 3534-2:—,
L
3.2.5.6 and 3.3.1.5). The sum p + p = p is called the total fraction nonconforming. (ISO 3534-2:—, 3.2.5.7).
U L T
Between the specification limits U and L there is the fraction conforming 1 − p .
T
In statistical process management the limits U and L are fixed in advance and the fractions p , p and p are
U L T
either calculated, if the distribution is assumed to be known, or otherwise estimated. There are many
applications of statistical tolerance intervals, although the above shows an example to a quality control
problem. Wider applications and more statistical intervals are introduced in many textbooks such as Hahn and
[10]
Meeker .
In contrast, for the tolerance intervals considered in this part of ISO 16269, the confidence level for the interval
estimator and the proportion of the distribution within the interval (corresponding to the fraction conforming
mentioned above) are fixed in advance, and the limits are estimated. These limits may be compared with U
and L. Hence the appropriateness of the given specification limits U and L can be compared with the actual
properties of the process. The one-sided tolerance intervals are used when only either the upper specification
limit U or the lower specification limit L is relevant, while the two-sided intervals are used when both the upper
and the lower specification limits are considered simultaneously.
The terminology with regard to these different limits and intervals has been confusing as the “specification
limits” were earlier also called “tolerance limits” (see the terminology standard ISO 3534-2:1993, 1.4.3, where
both these terms as well as the term “limiting values” were all used as synonyms for this concept). In the latest
revision of ISO 3534-2:—, only the term specification limits have been kept for this concept. Furthermore, the
[5]
Guide for the expression of uncertainty in measurement uses the term “coverage factor” defined as a
“numerical factor used as a multiplier of the combined standard uncertainty in order to obtain an expanded
uncertainty”. This use of “coverage” differs from the use of the term in this part of ISO 16269.
vi © ISO 2005 – All rights reserved

INTERNATIONAL STANDARD ISO 16269-6:2005(E)

Statistical interpretation of data —
Part 6:
Determination of statistical tolerance intervals
1 Scope
This part of ISO 16269 describes procedures for establishing tolerance intervals that include at least a
specified proportion of the population with a specified confidence level. Both one-sided and two-sided
statistical tolerance intervals are provided, a one-sided interval having either an upper or a lower limit while a
two-sided interval has both upper and lower limits. Two methods are provided, a parametric method for the
case where the characteristic being studied has a normal distribution and a distribution-free method for the
case where nothing is known about the distribution except that it is continuous.
2 Normative re
...

NORME ISO
INTERNATIONALE 16269-6
Première édition
2005-04-01
Version corrigée
2006-01-01
Interprétation statistique des données —
Partie 6:
Détermination des intervalles statistiques
de dispersion
Statistical interpretation of data —
Part 6: Determination of statistical tolerance intervals

Numéro de référence
©
ISO 2005
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©  ISO 2005
Droits de reproduction réservés. Sauf prescription différente, 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 et les microfilms, sans l'accord écrit
de l'ISO à l'adresse ci-après ou du comité membre de l'ISO dans le pays du demandeur.
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
Publié en Suisse
ii © ISO 2005 – Tous droits réservés

Sommaire Page
Avant-propos. iv
Introduction . v
1 Domaine d'application. 1
2 Références normatives . 1
3 Termes, définitions et symboles . 1
3.1 Termes et définitions. 1
3.2 Symboles . 2
4 Méthodes . 3
4.1 Population normale avec une variance et une moyenne connues. 3
4.2 Population normale avec une variance connue et une moyenne inconnue. 3
4.3 Population normale avec une variance et une moyenne inconnues . 3
4.4 Distribution continue quelconque de type inconnu. 3
5 Exemples . 4
5.1 Données. 4
5.2 Exemple 1: intervalle statistique de dispersion unilatéral sous variance connue . 4
5.3 Exemple 2: intervalle statistique de dispersion bilatéral sous variance connue. 5
5.4 Exemple 3: intervalle statistique de dispersion unilatéral sous variance inconnue . 5
5.5 Exemple 4: intervalle statistique de dispersion bilatéral sous variance inconnue . 6
5.6 Exemple 5: intervalle statistique de dispersion non paramétrique pour une distribution
continue . 7
Annexe A (informative) Formulaires pour les intervalles de dispersion . 8
Annexe B (normative) Facteurs de la limite statistique de dispersion unilatérale, k (n; p; 1 − α), pour
un écart-type de la population, σ, connu. 14
Annexe C (normative) Facteurs de la limite statistique de dispersion bilatérale, k (n; p; 1 − α), pour
un écart-type de la population, σ, connu. 17
Annexe D (normative) Facteurs de la limite statistique de dispersion unilatérale, k (n; p; 1 − α), pour
un écart-type de la population, σ, inconnu . 20
Annexe E (normative) Facteurs de la limite statistique de dispersion bilatérale, k (n; p; 1 − α), pour
un écart-type de la population, σ, inconnu . 23
Annexe F (normative) Intervalles statistiques de dispersion unilatéraux non paramétriques . 26
Annexe G (normative) Intervalles statistiques de dispersion bilatéraux non paramétriques. 27
Annexe H (informative) Construction d'un intervalle statistique de dispersion non paramétrique
pour un type de distribution quelconque.28
Annexe I (informative) Calculs des facteurs des intervalles statistiques de dispersion bilatéraux
paramétriques . 29
Bibliographie . 30

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 16269-6 a été élaborée par le comité technique ISO/TC 69, Application des méthodes statistiques.
Cette première édition de l'ISO 16269-6 annule et remplace l'ISO 3207:1975, qui a fait l'objet d'une révision
technique.
L'ISO 16269 comprend les parties suivantes, présentées sous le titre général Interprétation statistique des
données:
 Partie 6: Détermination des intervalles statistiques de dispersion
 Partie 7: Médiane — Estimation et intervalles de confiance
 Partie 8: Détermination des intervalles de prédiction
Dans la présente version corrigée, le terme «tolérance» a été remplacé par «dispersion» et les termes «limite
de spécification» ont été remplacés par «limite de tolérance» dans l'ensemble du document.
iv © ISO 2005 – Tous droits réservés

Introduction
Un intervalle statistique de dispersion est un intervalle estimé, d'après un échantillon, pour lequel il est
possible d'affirmer avec un niveau de confiance 1 − α, par exemple 95 %, qu'il contient au moins une
proportion donnée p d'individus de la population. Les limites d'un intervalle statistique de dispersion sont
appelées limites statistiques de dispersion. Le niveau de confiance 1 − α est la probabilité selon laquelle un
intervalle statistique de dispersion construit de la manière spécifiée contiendra au moins une proportion p
d'individus de la population. Inversement, la probabilité que cet intervalle contiendra moins que la proportion p
d'individus de la population est α. La présente partie de l'ISO 16269 décrit les intervalles statistiques de
dispersion unilatéraux et les intervalles statistiques de dispersion bilatéraux; un intervalle unilatéral est
construit avec une limite inférieure ou une limite supérieure tandis qu'un intervalle bilatéral est construit avec
une limite supérieure et une limite inférieure.
Les intervalles de dispersion sont fonction des observations de l'échantillon, c'est-à-dire des statistiques, et
leurs valeurs seront généralement différentes pour des échantillons différents. Il est nécessaire que les
observations soient indépendantes pour que les méthodes indiquées dans la présente partie de l'ISO 16269
soient valables.
La présente partie de l'ISO 16269 stipule deux types d'intervalles statistiques de dispersion: l'intervalle
paramétrique et l'intervalle non paramétrique. L'approche paramétrique se fonde sur l'hypothèse selon
laquelle la caractéristique étudiée dans la population a une distribution normale; ainsi, si l'hypothèse de
normalité est avérée, le niveau de confiance avec lequel l'intervalle statistique de dispersion contient au moins
une proportion p d'individus de la population ne peut être que de 1 − α. Pour les caractéristiques distribuées
normalement, l'intervalle statistique de dispersion est déterminé à l'aide des formulaires A, B, C et D donnés
dans l'Annexe A.
La présente partie de l'ISO 16269 ne traite pas des méthodes paramétriques s'appliquant à des distributions
autres que les distributions normales. Si des écarts par rapport à la normalité sont suspectés dans la
population, des intervalles statistiques de dispersion non paramétriques peuvent être construits. La procédure
de détermination d'un intervalle statistique de dispersion pour une distribution continue quelconque est
indiquée aux formulaires E et F de l'Annexe A.
Les limites de dispersion abordées dans la présente partie de l'ISO 16269 peuvent être utilisées pour
comparer l'aptitude naturelle d'un processus avec une ou deux limites de tolérance données, soit une limite
supérieure, U, soit une limite inférieure, L, ou encore les deux, dans la gestion d'un processus statistique.
Cela est indiqué par le fait que ces limites de dispersion ont également été appelées limites naturelles du
processus. Voir l'ISO 3534-2:1993, 3.2.4, ainsi que les remarques générales de l'ISO 3207, qui sera annulée
et remplacée par la présente partie de l'ISO 16269.
Au-dessus de la limite de tolérance supérieure, U, il y a la fraction supérieure non conforme, p
U
(ISO 3534-2:—, 3.2.5.5 et 3.3.1.4), et en dessous de la limite de tolérance inférieure, L, il y a la fraction
inférieure non conforme, p (ISO 3534-2:—, 3.2.5.6 et 3.3.1.5). La somme p + p = p est appelée fraction
L U L T
totale non conforme (ISO 3534-2:—, 3.2.5.7). Entre les limites de tolérance U et L, il y a la fraction conforme
1 – p .
T
Dans la gestion du processus statistique, les limites U et L sont fixées à l'avance et les fractions p , p et p
U L T
sont soit calculées, lorsque la distribution est supposée connue, soit estimées. Il existe beaucoup
d'applications d'intervalles statistiques de dispersion, bien que l'exemple ci-dessus montre un exemple d'un
problème de contrôle qualité. Des applications plus importantes et plus d'intervalles statistiques sont introduits
[10]
dans de nombreux ouvrages tels que Hahn et Meeker .
Par contraste, pour les intervalles de dispersion dont il est question dans la présente partie de l'ISO 16269, le
niveau de confiance pour l'estimateur d'intervalle et la proportion de distribution dans l'intervalle
(correspondant à la fraction conforme mentionnée ci-dessus) sont fixés à l'avance, et les limites sont estimées.
Ces limites peuvent être comparées à U et à L. Ainsi la justesse des limites de tolérance données U et L peut
être comparée aux propriétés réelles du processus. Les intervalles de dispersion unilatéraux sont utilisés
uniquement lorsque la limite de tolérance supérieure, U, ou la limite de tolérance inférieure, L, est appropriée,
tandis que les intervalles bilatéraux sont utilisés lorsque les limites supérieure et inférieure sont prises en
compte simultanément.
La terminologie relative à ces limites et intervalles différents est confuse car les «limites de tolérance» étaient
également autrefois appelées «limites de dispersion» (voir la Norme de terminologie ISO 3534-2:1993, 1.4.3,
où ces deux termes, mais aussi le terme «valeurs limites», étaient utilisés comme synonymes pour désigner
ce concept). Dans la dernière révision de l'ISO 3534-2:—, seul le terme «limites de tolérance» a été conservé
[5]
pour désigner ce concept. En outre, le Guide pour l'expression de l'incertitude de mesure (GUM) utilise le
terme «facteur d'élargissement», défini comme un «facteur numérique utilisé
...