ASTM E2762-10(2014)
(Practice)Standard Practice for Sampling a Stream of Product by Variables Indexed by AQL
Standard Practice for Sampling a Stream of Product by Variables Indexed by AQL
SIGNIFICANCE AND USE
5.1 This practice was prepared to meet a growing need for the use of standard sampling plans for inspection by variables in customer procurement, supply and storage, and maintenance inspection operations. The variables sampling plans apply to a single quality characteristic which can be measured on a continuous scale, and for which quality is expressed in terms of percent defective. The theory underlying the development of the variables sampling plans, including the operating characteristic curves, assumes that measurements of the quality characteristic are independent, identically distributed normal random variables.
5.2 In comparison with attributes sampling plans, variables sampling plans have the advantage of usually resulting in considerable savings in sample size for comparable assurance as to the correctness of decisions in judging a single quality characteristic, or for the same sample size, greater assurance is obtained using variables plans. Attributes sampling plans have the advantage of greater simplicity, of being applicable to either single or multiple quality characteristics, and of requiring no knowledge about the distribution of the continuous measurements of any of the quality characteristics.
5.3 It is important to note that variables sampling plans are not to be used indiscriminately, simply because it is possible to obtain variables measurement data. In considering applications where the normality or independence assumptions may be questioned, the user is advised to consult his technical agency to determine the feasibility of application.
5.4 Application—Sampling plans designated in this publication are applicable, but not limited, to inspection of the following: (1) end items, (2) components and raw materials, (3) operations or services, (4) materials in process, (5) supplies in storage, (6) maintenance operations, (7) data or records, and (8) administrative procedures.
SCOPE
1.1 Purpose—This practice establishes lot or batch sampling plans and procedures for inspection by variables using MIL-STD-414 as a basis for sampling a steady stream of lots indexed by AQL.
1.2 This practice provides the sampling plans of MIL-STD-414 in ASTM format for use by ASTM committees and others. It recognizes the continuing usage of MIL-STD-414 in industries supported by ASTM. Most of the original text in MIL-STD-414 is preserved in Sections 6 – 9 of this practice.
1.3 The values stated in inch-pound units are to be regarded as standard. No other units of measurement are included in this standard.
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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Standards Content (Sample)
NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
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Designation: E2762 − 10 (Reapproved 2014) An American National Standard
Standard Practice for
Sampling a Stream of Product by Variables Indexed by
AQL
This standard is issued under the fixed designation E2762; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 2.2 Other Standards:
MIL-STD-414 Sampling Procedures and Tables for Inspec-
1.1 Purpose—This practice establishes lot or batch sam-
tion by Variables for Percent Defective
pling plans and procedures for inspection by variables using
MIL-STD-105E Sampling Procedures and Tables for In-
MIL-STD-414 as a basis for sampling a steady stream of lots
spection by Attributes
indexed by AQL.
1.2 This practice provides the sampling plans of MIL-STD-
3. Terminology
414 inASTM format for use byASTM committees and others.
3.1 Definitions:
It recognizes the continuing usage of MIL-STD-414 in indus-
3.1.1 For a more extensive list of terms in E11 standards,
tries supported by ASTM. Most of the original text in MIL-
see Terminology E456.
STD-414 is preserved in Sections6–9 of this practice.
3.1.2 acceptance quality limit (AQL), n—qualitylimitthatis
1.3 The values stated in inch-pound units are to be regarded
the worst tolerable process average when a continuing series of
as standard. No other units of measurement are included in this
lots is submitted for acceptance sampling. E2234
standard.
3.1.2.1 Discussion—This definition supersedes that given in
1.4 This standard does not purport to address all of the
MIL-STD-105E and MIL-STD-414.
safety concerns, if any, associated with its use. It is the
3.1.3 classification of defects, n—the enumeration of pos-
responsibility of the user of this standard to establish appro-
sible defects of the unit of product classified according to their
priate safety and health practices and determine the applica-
seriousness, that is, critical, major, or minor defect. E2234
bility of regulatory limitations prior to use.
1.5 This international standard was developed in accor-
3.1.4 critical defect, n—a defect that judgment and experi-
dance with internationally recognized principles on standard-
ence indicate would result in hazardous or unsafe conditions
ization established in the Decision on Principles for the
for individuals using, maintaining, or depending upon the
Development of International Standards, Guides and Recom-
product, or a defect that judgment and experience indicate is
mendations issued by the World Trade Organization Technical
likely to prevent performance of the function of a major end
Barriers to Trade (TBT) Committee.
item. E2234
3.1.5 defect, n—any nonconformance of the unit of product
2. Referenced Documents
with specified requirements. E2234
2.1 ASTM Standards:
3.1.6 inspection, n—the process of measuring, examining,
E456 Terminology Relating to Quality and Statistics
testing, or otherwise comparing the unit of product with the
E2234 Practice for Sampling a Stream of Product by Attri-
requirements. E2234
butes Indexed by AQL
E2586 Practice for Calculating and Using Basic Statistics
3.1.7 inspection by variables, n—inspection wherein the
unit of product is measured on a continuous scale with respect
to a given requirement or set of requirements.
This practice is under the jurisdiction ofASTM Committee E11 on Quality and
3.1.8 inspection lot, n—a collection of units of product
Statistics and is the direct responsibility of Subcommittee E11.30 on Statistical
produced under conditions that are considered uniform and
Quality Control.
from which a sample is drawn and inspected. E2234
Current edition approved April 1, 2014. Published May 2014. Originally
approved in 2010. Last previous edition approved in 2010 as E2762 – 10. DOI
101520/E2762-10.
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 Available from Standardization Documents Order Desk, DODSSP, Bldg. 4,
Standards volume information, refer to the standard’s Document Summary page on Section D, 700 Robbins Ave., Philadelphia, PA 19111-5098, http://
the ASTM website. dodssp.daps.dla.mil.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2762 − 10 (2014)
3.1.9 major defect, n—a defect, other than critical, that is A1.3) have been computed for the sampling plans based on the
likely to result in failure, or to reduce materially the usability estimate of lot standard deviation of unknown variability.They
of the unit of product for its intended purpose. E2234 are equally applicable for sampling plans based on the average
range of the sample of unknown variability and those based on
3.1.10 minor defect, n—a defect that is not likely to reduce
known variability.
materially the usability of the unit of product for its intended
purpose, or is a departure from established standards having 4.5 Certain characteristics concerning the sampling plans in
little bearing on the effective use or operation of the unit. Sections 7 and 8 and those in Section 9 should be noted. Plans
E2234 based on the estimate of unknown variability require fewer
sampleunitsforcomparableassurancewhentheestimateoflot
3.1.11 operating characteristic, n—probability of accep-
standard deviation is used than when the average range of the
tance using a specified acceptance sampling plan, as a function
sample is used; on the other hand, plans using the average
of parameters describing quality of the lot. E2234
range of the sample require simpler computations. Plans using
3.1.12 sample, n—a group of observations, test results,
known variability require considerably fewer sample units for
taken from a large collection of observations, test results,
comparable assurance than either of the plans when variability
whichservestoprovideinformationthatmaybeusedasabasis
is unknown; however, the requirement of variability is a
for making a decision concerning the larger collection. E2586
stringent one. The user is advised to consult his technical
3.1.12.1 Discussion—A sample consists of one or more
agency before applying sampling plans using known variabil-
units of product drawn from an inspection lot, the units of the
ity.
sample being selected at random without regard to their
4.6 Table B-8 (see Fig. A1.11) provides values of the
quality. The number of units of product in the sample is the
factor F to compute the maximum standard deviation MSD.
sample size.
The MSD serves as a guide for the magnitude of the estimate
4. Summary of Practice
of lot standard deviation when using plans for the double
specification limit case, based on the estimate of lot standard
4.1 The main body of this practice is divided into four
deviationofunknownvariability.Similarly,TableC-8(seeFig.
sections. Section 6 (Section A in MIL-STD-414) describes
A1.19) provides values of the factor f to compute the maxi-
general procedures of the sampling plans. Sections 7 and 8
mum average range MAR. The MAR serves as a guide for the
(Sections B and C in MIL-STD-414) describe specific proce-
magnitudeoftheaveragerangeofthesamplewhenusingplans
dures and applications of the sampling plans when variability
for the double specification limit case, based on the average
is unknown. In Section 7 (Section B in MIL-STD-414) the
range of the sample of unknown variability.The estimate of lot
estimate of lot standard deviation is used as the basis for an
standard deviation or average range of the sample, if it is less
estimate of the unknown variability, and in Section 8 (Section
than the MSD or MAR respectively, helps to insure, but does
C in MIL-STD-414) the average range of the sample is used.
not guarantee, lot acceptability.
Section 9 (Section D in MIL-STD-414) describes the plans
when variability is known. 4.7 All symbols and their definitions are given in AnnexA1
for their applicable section.An illustration of the computations
4.2 Each of Sections 7, 8, and 9 is divided into three parts:
and procedures used in the sampling plans is given in the
(I) Sampling Plans for the Single Specification Limit Case, (II)
examples of Parts I and II of the applicable section. The
Sampling Plans for the Double Specification Limit Case, and
computations involve simple arithmetic operations such as
(III) Procedures for Estimation of ProcessAverage and Criteria
addition, subtraction, multiplication, and division of numbers,
for Tightened and Reduced Inspection. For the single specifi-
or at most, the taking of a square root of a number. The user
cation limit case, the acceptability criterion is given in two
should become familiar with the general procedures of Section
forms: Form 1 and Form 2. Either of the forms may be used,
6, and refer to the applicable section for detailed instructions
since they are identical as to sample size and decision for lot
regarding specific procedures, computations, and tables for the
acceptabilityorrejectability.IndecidingwhethertouseForm 1
sampling plans.
or Form 2, the following point should be borne in mind.
Form 1 provides the lot acceptability criterion without estimat-
5. Significance and Use
ing lot percent defective.The Form 2 lot acceptability criterion
5.1 This practice was prepared to meet a growing need for
requiresestimatesoflotpercentdefective.Theseestimatesalso
the use of standard sampling plans for inspection by variables
are required for estimation of the process average.
in customer procurement, supply and storage, and maintenance
4.3 Operating Characteristic Curves in Table A-3 (see Fig.
inspection operations. The variables sampling plans apply to a
A1.3)showtherelationshipbetweenqualityandpercentoflots
single quality characteristic which can be measured on a
expected to be acceptable for the quality characteristic in-
continuousscale,andforwhichqualityisexpressedintermsof
spected. As stated, these Operating Characteristic Curves are
percent defective. The theory underlying the development of
based on the assumption that measurements are selected at
the variables sampling plans, including the operating charac-
random from a normal distribution.
teristic curves, assumes that measurements of the quality
characteristic are independent, identically distributed normal
4.4 The corresponding sampling plans in Sections 7, 8, and
random variables.
9 were matched as closely as possible under a system of fixed
sample size with respect to their Operating Characteristic 5.2 In comparison with attributes sampling plans, variables
Curves. Operating Characteristic Curves in TableA-3 (see Fig. sampling plans have the advantage of usually resulting in
E2762 − 10 (2014)
considerable savings in sample size for comparable assurance These plans may be used whether procurement inspection is
as to the correctness of decisions in judging a single quality performed at the plant of a prime contractor, subcontractor or
characteristic, or for the same sample size, greater assurance is
vendor, or at destination, and also may be used when appro-
obtained using variables plans.Attributes sampling plans have priate in supply and storage, and maintenance inspection
the advantage of greater simplicity, of being applicable to
operations.
either single or multiple quality characteristics, and of requir-
6.2 Classification of Defects:
ing no knowledge about the distribution of the continuous
6.2.1 Method of Classifying Defects—A classification of
measurements of any of the quality characteristics.
defects is the enumeration of defects of the unit of product
5.3 It is important to note that variables sampling plans are
classified according to their importance.Adefect is a deviation
not to be used indiscriminately, simply because it is possible to
of the unit of product from requirements of the specifications,
obtain variables measurement data. In considering applications
drawings,purchasedescriptions,andanychangestheretointhe
where the normality or independence assumptions may be
contract or order. Defects normally belong to one of the
questioned, the user is advised to consult his technical agency
following classes; however, defects may be placed in other
to determine the feasibility of application.
classes.
5.4 Application—Sampling plans designated in this publi-
6.2.1.1 Critical Defects—A critical defect is one that judg-
cation are applicable, but not limited, to inspection of the
ment and experience indicate could result in hazardous or
following: (1)enditems, (2)componentsandrawmaterials, (3)
unsafe conditions for individuals using or maintaining the
operations or services, (4) materials in process, (5) supplies in
product; or, for major end items units of product, such as ships,
storage, (6) maintenance operations, (7) data or records, and
aircraft, or tanks, a defect that could prevent performance of
(8) administrative procedures.
their tactical function.
6.2.1.2 Major Defects—A major defect is a defect, other
6. General Description of Sampling Plans
than critical, that could result in failure, or materially reduce
6.1 Scope:
the usability of the unit of product for its intended purpose.
6.1.1 Purpose—This practice establishes sampling plans
6.2.1.3 Minor Defects—A minor defect is one that does not
and procedures for inspection by variables for use in customer
materially reduce the usability of the unit of product for its
procurement, supply and storage, and maintenance inspection
intended purpose, or is a departure from established standards
operations.Whenapplicablethispracticeshallbereferencedin
having no significant bearing on the effective use or operation
the specification, contract, or inspection instructions, and the
of the unit.
provisions set forth herein shall govern.
6.1.2 Inspection—Inspection is the process of measuring,
6.3 Percent Defective:
examining,testing,gaging,orotherwisecomparingthe“unitof
6.3.1 Expression of Nonconformance—The extent of non-
product” (see 6.1.4) with the applicable requirements.
conformance of product that shall be expressed in terms of
6.1.3 Inspection by Variables—Inspection by variables is
percent defective.
inspection wherein a specified quality characteristic (see 6.1.5)
6.3.2 Percent Defective—The percent defective for a quality
on a unit of product is measured on a continuous scale, such as
characteristic of a given lot of product is the number of units of
pounds, inches, feet per second, etc., and a measurement is
product defective for that characteristic divided by the total
recorded.
number of units of product and multiplied by one
...
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