ASTM E2334-08
(Practice)Standard Practice for Setting an Upper Confidence Bound For a Fraction or Number of Non-Conforming items, or a Rate of Occurrence for Non-conformities, Using Attribute Data, When There is a Zero Response in the Sample
Standard Practice for Setting an Upper Confidence Bound For a Fraction or Number of Non-Conforming items, or a Rate of Occurrence for Non-conformities, Using Attribute Data, When There is a Zero Response in the Sample
SIGNIFICANCE AND USE
In Case 1, the sample is selected from a process or a very large population of interest. The population is essentially unlimited, and each item either has or has not the defined attribute. The population (process) has an unknown fraction of items p (long run average process non-conforming) having the attribute. The sample is a group of n discrete items selected at random from the process or population under consideration, and the attribute is not exhibited in the sample. The objective is to determine an upper confidence bound, pu, for the unknown fraction p whereby one can claim that p ≤ pu with some confidence coefficient (probability) C. The binomial distribution is the sampling distribution in this case.
In Case 2, a sample of n items is selected at random from a finite lot of N items. Like Case 1, each item either has or has not the defined attribute, and the population has an unknown number, D, of items having the attribute. The sample does not exhibit the attribute. The objective is to determine an upper confidence bound, Du, for the unknown number D, whereby one can claim that D ≤ Du with some confidence coefficient (probability) C. The hypergeometric distribution is the sampling distribution in this case.
In Case 3, there is a process, but the output is a continuum, such as area (for example, a roll of paper or other material, a field of crop), volume (for example, a volume of liquid or gas), or time (for example, hours, days, quarterly, etc.) The sample size is defined as that portion of the “continuum” sampled, and the defined attribute may occur any number of times over the sampled portion. There is an unknown average rate of occurrence, λ, for the defined attribute over the sampled interval of the continuum that is of interest. The sample does not exhibit the attribute. For a roll of paper this might be blemishes per 100 ft2; for a volume of liquid, microbes per cubic litre; for a field of crop, spores per acre; for a time interval, calls per hour, c...
SCOPE
1.1 This practice presents methodology for the setting of an upper confidence bound regarding a unknown fraction or quantity non-conforming, or a rate of occurrence for nonconformities, in cases where the method of attributes is used and there is a zero response in a sample. Three cases are considered.
1.1.1 The sample is selected from a process or a very large population of discrete items, and the number of non-conforming items in the sample is zero.
1.1.2 A sample of items is selected at random from a finite lot of discrete items, and the number of non-conforming items in the sample is zero.
1.1.3 The sample is a portion of a continuum (time, space, volume, area etc.) and the number of non-conformities in the sample is zero.
1.2 Allowance is made for misclassification error in this standard, but only when misclassification rates are well understood or known and can be approximated numerically.
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An American National Standard
Designation: E2334 – 08
Standard Practice for
Setting an Upper Confidence Bound For a Fraction or
Number of Non-Conforming items, or a Rate of Occurrence
for Non-conformities, Using Attribute Data, When There is a
1
Zero Response in the Sample
This standard is issued under the fixed designation E2334; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope ISO 3534-1 Statistics—Vocabulary and Symbols, Part 1:
3
Probability and General Statistical Terms
1.1 This practice presents methodology for the setting of an
ISO 3534-2 Statistics—Vocabulary and Symbols, Part 2:
upper confidence bound regarding a unknown fraction or
3
Statistical Quality Control
quantity non-conforming, or a rate of occurrence for noncon-
formities, in cases where the method of attributes is used and
NOTE 1—Samples discussed in this standard should meet the require-
there is a zero response in a sample. Three cases are consid-
ments (or approximately so) of a probability sample as defined in
Terminologies E1402 or E456.
ered.
1.1.1 The sample is selected from a process or a very large
3. Terminology
population of discrete items, and the number of non-
3.1 Definitions: Terminology E456 provides a more exten-
conforming items in the sample is zero.
sive list of terms in E11 standards.
1.1.2 Asample of items is selected at random from a finite
3.1.1 attributes, method of, n—measurement of quality by
lot of discrete items, and the number of non-conforming items
the method of attributes consists of noting the presence (or
in the sample is zero.
absence)ofsomecharacteristicorattributeineachoftheunits
1.1.3 The sample is a portion of a continuum (time, space,
in the group under consideration, and counting how many of
volume, area etc.) and the number of non-conformities in the
the units do (or do not) possess the quality attribute, or how
sample is zero.
many such events occur in the unit, group or area.
1.2 Allowance is made for misclassification error in this
3.1.2 confidence bound, n—see confidence limit.
standard, but only when misclassification rates are well under-
3.1.3 confidence coeffıcient, n—the value, C, of the prob-
stood or known and can be approximated numerically.
ability associated with a confidence interval or statistical
2. Referenced Documents
coverage interval. It is often expressed as a percentage.
2
ISO 3534-1
2.1 ASTM Standards:
3.1.4 confidence interval, n—an interval estimate of a
E141 Practice for Acceptance of Evidence Based on the
population parameter, calculated such that there is a given
Results of Probability Sampling
long-run probability that the parameter is included in the
E456 Terminology Relating to Quality and Statistics
interval.
E1402 Guide for Sampling Design
3.1.4.1 Discussion—Aone-sided confidence interval is one
E1994 Practice for Use of Process Oriented AOQL and
for which one of the limits is plus infinity, minus infinity, or a
LTPD Sampling Plans
natural fixed limit (such as zero).
E2586 Practice for Calculating and Using Basic Statistics
3.1.5 confidence level, n—see confidence coeffıcient.
2.2 ISO Standards:
3.1.6 confidence limit, n—the upper or lower limit of a
confidence interval.
1
ThispracticeisunderthejurisdictionofASTMCommitteeE11onQualityand 3.1.7 item, n—an object or quantity of material on which a
Statistics and is the direct responsibility of Subcommittee E11.30 on Statistical
set of observations can be made.
Quality Control.
3.1.7.1 Discussion—As used in this standard, “set” denotes
Current edition approved Oct. 15, 2008. Published January 2009. Originally
´1
a single variable (the defined attribute). The term “sampling
approved in 2003. Last previous edition approved in 2003 as E2334–03 . DOI:
10.1520/E2334-08.
unit” is also used to denote an “item” (see Practice E141).
2
For referenced ASTM Standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
3
Standardsvolume information, refer to teh standard’s Document Summary page on Available fromAmerican National Standards Institute (ANSI), 25 W. 43rd St.,
the ASTM website. 4th Floor, New York, NY 10036, http://www.ansi.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
1
---------------------- Page: 1 ----------------------
E2334 – 08
3.1.8 non-conforming item, n—an item containing at least 3.3.17 u —the probability of classifying a non-conforming
2
one non-conformity. ISO 3534-2 item as conforming; or of failing to find a non-conformity
where one should have been found.
3.1.8.1 Di
...
This document is not anASTM standard and is intended only to provide the user of anASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately,ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
An American National Standard
´1
Designation:E2334–03 Designation: E 2334 – 08
Standard Practice for
Setting an Upper Confidence Bound For a Fraction or
Number of Non-Conforming items, or a Rate of Occurrence
for Non-conformities, Using Attribute Data, When There is a
1
Zero Response in the Sample
This standard is issued under the fixed designation E2334; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1
´ NOTE—Eq 4 was corrected editorially in May 2007.
1. Scope
1.1 This practice presents methodology for the setting of an upper confidence bound regarding a unknown fraction or quantity
non-conforming, or a rate of occurrence for nonconformities, in cases where the method of attributes is used and there is a zero
response in a sample. Three cases are considered.
1.1.1 The sample is selected from a process or a very large population of discrete items, and the number of non-conforming
items in the sample is zero.
1.1.2 Asample of items is selected at random from a finite lot of discrete items, and the number of non-conforming items in
the sample is zero.
1.1.3 Thesampleisaportionofacontinuum(time,space,volume,areaetc.)andthenumberofnon-conformitiesinthesample
is zero.
1.2 Allowance is made for misclassification error in this standard, but only when misclassification rates are well understood or
known and can be approximated numerically.
2. Referenced Documents
2
2.1 ASTM Standards:
E141 Practice for Acceptance of Evidence Based on the Results of Probability Sampling
E456 Terminology Relating to Quality and Statistics
E1402 Terminology Relating to Sampling
E1994 PracticeforUseofProcessOrientedAOQLandLTPDSamplingPlansPracticeforUseofProcessOrientedAOQLand
LTPD Sampling Plans
E2586 Practice for Calculating and Using Basic Statistics
2.2 ISO Standards:
3
ISO 3534-1 Statistics—Vocabulary and Symbols, Part 1: Probability and General Statistical Terms
3
ISO 3534-2 Statistics—Vocabulary and Symbols, Part 2: Statistical Quality Control
NOTE 1—Samples discussed in this standard should meet the requirements (or approximately so) of a probability sample as defined in Terminologies
E1402 or E456.
3. Terminology
3.1 Definitions: Terminology E456 provides a more extensive list of terms in E11 standards.
3.1.1 attributes, method of, n—measurementofqualitybythemethodofattributesconsistsofnotingthepresence(orabsence)
of some characteristic or attribute in each of the units in the group under consideration, and counting how many of the units do
(or do not) possess the quality attribute, or how many such events occur in the unit, group or area. E456
1
This practice is under the jurisdiction of ASTM Committee E11 on Quality and Statistics and is the direct responsibility of Subcommittee E11.30 on Data Analysis.
Current edition approved Oct. 1, 2003. Published February 2004.
1
This practice is under the jurisdiction ofASTM Committee E11 on Quality and Statistics and is the direct responsibility of Subcommittee E11.30 on Statistical Quality
Control.
´1
Current edition approved Oct. 15, 2008. Published January 2009. Originally approved in 2003. Last previous edition approved in 2003 as E2334–03 .
2
For referenced ASTM Standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Standardsvolume information, refer to teh standard’s Document Summary page on the ASTM website.
3
Available from American National Standards Institute, 11 W. 42nd Street, 13th Floor, New York, NY 10036.
3
Available from American National Standards Institute (ANSI), 25 W. 43rd St., 4th Floor, New York, NY 10036, http://www.ansi.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
1
---------------------- Page: 1 ----------------------
E2334–08
3.1.2 confidence bound, n—see confidence limit.
3.1.3 confidence coeffıcient, n—the value, C, of the probability associated with a confidence interval or statistical coverage
interval. It is often expressed as a percentage. ISO 3534-1
3.1.4 confidence interval, n—an interval estimate of a population parameter, calculated such that there is a given long-run
probability that the parameter is included in the interval.
3.1.4.1 Discussion—Aone-sidedconfidenceintervalisoneforwhichoneofthelimitsisplusinfinity,minusinfinity,oranatu
...
This document is not anASTM standard and is intended only to provide the user of anASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately,ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
An American National Standard
´1
Designation:E2334–03 Designation: E 2334 – 08
Standard Practice for
Setting an Upper Confidence Bound For a Fraction or
Number of Non-Conforming items, or a Rate of Occurrence
for Non-conformities, Using Attribute Data, When There is a
1
Zero Response in the Sample
This standard is issued under the fixed designation E2334; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1
´ NOTE—Eq 4 was corrected editorially in May 2007.
1. Scope
1.1 This practice presents methodology for the setting of an upper confidence bound regarding a unknown fraction or quantity
non-conforming, or a rate of occurrence for nonconformities, in cases where the method of attributes is used and there is a zero
response in a sample. Three cases are considered.
1.1.1 The sample is selected from a process or a very large population of discrete items, and the number of non-conforming
items in the sample is zero.
1.1.2 Asample of items is selected at random from a finite lot of discrete items, and the number of non-conforming items in
the sample is zero.
1.1.3 Thesampleisaportionofacontinuum(time,space,volume,areaetc.)andthenumberofnon-conformitiesinthesample
is zero.
1.2 Allowance is made for misclassification error in this standard, but only when misclassification rates are well understood or
known and can be approximated numerically.
2. Referenced Documents
2
2.1 ASTM Standards:
E141 Practice for Acceptance of Evidence Based on the Results of Probability Sampling
E456 Terminology Relating to Quality and Statistics
E1402 Guide for Sampling Design
E1994 PracticeforUseofProcessOrientedAOQLandLTPDSamplingPlansPracticeforUseofProcessOrientedAOQLand
LTPD Sampling Plans
E2586 Practice for Calculating and Using Basic Statistics
2.2 ISO Standards:
3
ISO 3534-1 Statistics—Vocabulary and Symbols, Part 1: Probability and General Statistical Terms
3
ISO 3534-2 Statistics—Vocabulary and Symbols, Part 2: Statistical Quality Control
NOTE 1—Samples discussed in this standard should meet the requirements (or approximately so) of a probability sample as defined in Terminologies
E1402 or E456.
3. Terminology
3.1 Definitions: Terminology E456 provides a more extensive list of terms in E11 standards.
3.1.1 attributes, method of, n—measurementofqualitybythemethodofattributesconsistsofnotingthepresence(orabsence)
of some characteristic or attribute in each of the units in the group under consideration, and counting how many of the units do
(or do not) possess the quality attribute, or how many such events occur in the unit, group or area. E456
1
This practice is under the jurisdiction of ASTM Committee E11 on Quality and Statistics and is the direct responsibility of Subcommittee E11.30 on Data Analysis.
Current edition approved Oct. 1, 2003. Published February 2004.
1
This practice is under the jurisdiction ofASTM Committee E11 on Quality and Statistics and is the direct responsibility of Subcommittee E11.30 on Statistical Quality
Control.
´1
Current edition approved Oct. 15, 2008. Published January 2009. Originally approved in 2003. Last previous edition approved in 2003 as E2334–03 .
2
For referenced ASTM Standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Standardsvolume information, refer to teh standard’s Document Summary page on the ASTM website.
3
Available from American National Standards Institute, 11 W. 42nd Street, 13th Floor, New York, NY 10036.
3
Available from American National Standards Institute (ANSI), 25 W. 43rd St., 4th Floor, New York, NY 10036, http://www.ansi.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
1
---------------------- Page: 1 ----------------------
E2334–08
3.1.2 confidence bound, n—see confidence limit.
3.1.3 confidence coeffıcient, n—the value, C, of the probability associated with a confidence interval or statistical coverage
interval. It is often expressed as a percentage. ISO 3534-1
3.1.4 confidence interval, n—an interval estimate of a population parameter, calculated such that there is a given long-run
probability that the parameter is included in the interval.
3.1.4.1 Discussion—Aone-sidedconfidenceintervalisoneforwhichoneofthelimitsisplusinfinity,minusinfinity,oranatural
fixe
...
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