ASTM E2762-10
(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
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.
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.
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.
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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NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
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Designation: E2762 − 10 AnAmerican 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 3. Terminology
1.1 Purpose—This practice establishes lot or batch sam- 3.1 Definitions:
pling plans and procedures for inspection by variables using 3.1.1 For a more extensive list of terms in E11 standards,
MIL-STD-414 as a basis for sampling a steady stream of lots
see Terminology E456.
indexed by AQL.
3.1.2 acceptance quality limit (AQL), n—qualitylimitthatis
the worst tolerable process average when a continuing series of
1.2 This practice provides the sampling plans of MIL-STD-
lots is submitted for acceptance sampling. E2234
414 inASTM format for use byASTM committees and others.
3.1.2.1 Discussion—This definition supersedes that given in
It recognizes the continuing usage of MIL-STD-414 in indus-
MIL-STD-105E and MIL-STD-414.
tries supported by ASTM. Most of the original text in MIL-
STD-414 is preserved in Sections 6-9 of this practice. 3.1.3 classification of defects, n—the enumeration of pos-
sible defects of the unit of product classified according to their
1.3 The values stated in inch-pound units are to be regarded
seriousness, that is, critical, major, or minor defect. E2234
as standard. No other units of measurement are included in this
3.1.4 critical defect, n—a defect that judgment and experi-
standard.
ence indicate would result in hazardous or unsafe conditions
1.4 This standard does not purport to address all of the
for individuals using, maintaining, or depending upon the
safety concerns, if any, associated with its use. It is the
product, or a defect that judgment and experience indicate is
responsibility of the user of this standard to establish appro-
likely to prevent performance of the function of a major end
priate safety and health practices and determine the applica-
item. E2234
bility of regulatory limitations prior to use.
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
3.1.7 inspection by variables, n—inspection wherein the
E2586 Practice for Calculating and Using Basic Statistics
unit of product is measured on a continuous scale with respect
2.2 Other Standards:
to a given requirement or set of requirements.
MIL-STD-414 Sampling Procedures and Tables for Inspec-
3.1.8 inspection lot, n—a collection of units of product
tion by Variables for Percent Defective
produced under conditions that are considered uniform and
MIL-STD-105E Sampling Procedures and Tables for In-
from which a sample is drawn and inspected. E2234
spection by Attributes
3.1.9 major defect, n—a defect, other than critical, that is
likely to result in failure, or to reduce materially the usability
This practice is under the jurisdiction ofASTM Committee E11 on Quality and
of the unit of product for its intended purpose. E2234
Statistics and is the direct responsibility of Subcommittee E11.30 on Statistical
3.1.10 minor defect, n—a defect that is not likely to reduce
Quality Control.
Current edition approved May 1, 2010. Published November 2010. DOI materially the usability of the unit of product for its intended
101520/E2762-10.
purpose, or is a departure from established standards having
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
little bearing on the effective use or operation of the unit.
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
E2234
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website.
3.1.11 operating characteristic, n—probability of accep-
Available from Standardization Documents Order Desk, DODSSP, Bldg. 4,
tance using a specified acceptance sampling plan, as a function
Section D, 700 Robbins Ave., Philadelphia, PA 19111-5098, http://
dodssp.daps.dla.mil. of parameters describing quality of the lot. E2234
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2762 − 10
3.1.12 sample, n—a group of observations, test results, range of the sample require simpler computations. Plans using
taken from a large collection of observations, test results, known variability require considerably fewer sample units for
whichservestoprovideinformationthatmaybeusedasabasis comparable assurance than either of the plans when variability
for making a decision concerning the larger collection. E2586 is unknown; however, the requirement of variability is a
3.1.12.1 Discussion—A sample consists of one or more stringent one. The user is advised to consult his technical
units of product drawn from an inspection lot, the units of the agency before applying sampling plans using known variabil-
sample being selected at random without regard to their ity.
quality. The number of units of product in the sample is the
4.6 Table B-8 (see Fig. A1.11) provides values of the
sample size.
factor F to compute the maximum standard deviation MSD.
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
4.1 The main body of this practice is divided into four specification limit case, based on the estimate of lot standard
deviationofunknownvariability.Similarly,TableC-8(seeFig.
sections. Section 6 (Section A in MIL-STD-414) describes
general procedures of the sampling plans. Sections 7 and 8 A1.19) provides values of the factor f to compute the maxi-
mum average range MAR. The MAR serves as a guide for the
(Sections B and C in MIL-STD-414) describe specific proce-
dures and applications of the sampling plans when variability magnitudeoftheaveragerangeofthesamplewhenusingplans
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.
Section 9 (Section D in MIL-STD-414) describes the plans not guarantee, lot acceptability.
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)
Sampling Plans for the Double Specification Limit Case, and examples of Parts I and II of the applicable section. The
computations involve simple arithmetic operations such as
(III) Procedures for Estimation of ProcessAverage and Criteria
for Tightened and Reduced Inspection. For the single specifi- addition, subtraction, multiplication, and division of numbers,
or at most, the taking of a square root of a number. The user
cation limit case, the acceptability criterion is given in two
forms: Form 1 and Form 2. Either of the forms may be used, should become familiar with the general procedures of Section
6, and refer to the applicable section for detailed instructions
since they are identical as to sample size and decision for lot
acceptabilityorrejectability.IndecidingwhethertouseForm 1 regarding specific procedures, computations, and tables for the
sampling plans.
or Form 2, the following point should be borne in mind.
Form 1 provides the lot acceptability criterion without estimat-
ing lot percent defective.The Form 2 lot acceptability criterion 5. Significance and Use
requiresestimatesoflotpercentdefective.Theseestimatesalso
5.1 This practice was prepared to meet a growing need for
are required for estimation of the process average.
the use of standard sampling plans for inspection by variables
4.3 Operating Characteristic Curves in Table A-3 (see Fig. in customer procurement, supply and storage, and maintenance
A1.3)showtherelationshipbetweenqualityandpercentoflots inspection operations. The variables sampling plans apply to a
expected to be acceptable for the quality characteristic in- single quality characteristic which can be measured on a
spected. As stated, these Operating Characteristic Curves are continuousscale,andforwhichqualityisexpressedintermsof
based on the assumption that measurements are selected at percent defective. The theory underlying the development of
random from a normal distribution. the variables sampling plans, including the operating charac-
teristic curves, assumes that measurements of the quality
4.4 The corresponding sampling plans in Sections 7, 8, and
characteristic are independent, identically distributed normal
9 were matched as closely as possible under a system of fixed
random variables.
sample size with respect to their Operating Characteristic
Curves. Operating Characteristic Curves in TableA-3 (see Fig. 5.2 In comparison with attributes sampling plans, variables
A1.3) have been computed for the sampling plans based on the sampling plans have the advantage of usually resulting in
estimate of lot standard deviation of unknown variability.They considerable savings in sample size for comparable assurance
are equally applicable for sampling plans based on the average as to the correctness of decisions in judging a single quality
range of the sample of unknown variability and those based on characteristic, or for the same sample size, greater assurance is
known variability. obtained using variables plans.Attributes sampling plans have
the advantage of greater simplicity, of being applicable to
4.5 Certain characteristics concerning the sampling plans in
either single or multiple quality characteristics, and of requir-
Sections 7 and 8 and those in Section 9 should be noted. Plans
ing no knowledge about the distribution of the continuous
based on the estimate of unknown variability require fewer
measurements of any of the quality characteristics.
sampleunitsforcomparableassurancewhentheestimateoflot
standard deviation is used than when the average range of the 5.3 It is important to note that variables sampling plans are
sample is used; on the other hand, plans using the average not to be used indiscriminately, simply because it is possible to
E2762 − 10
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.
6.2.1.1 Critical Defects—A critical defect is one that judg-
5.4 Application—Sampling plans designated in this publi-
ment and experience indicate could result in hazardous or
cation are applicable, but not limited, to inspection of the
unsafe conditions for individuals using or maintaining the
following: (1)enditems, (2)componentsandrawmaterials, (3)
product; or, for major end items units of product, such as ships,
operations or services, (4) materials in process, (5) supplies in
aircraft, or tanks, a defect that could prevent performance of
storage, (6) maintenance operations, (7) data or records, and
their tactical function.
(8) administrative procedures.
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
the usability of the unit of product for its intended purpose.
6.1 Scope:
6.2.1.3 Minor Defects—A minor defect is one that does not
6.1.1 Purpose—This practice establishes sampling plans
materially reduce the usability of the unit of product for its
and procedures for inspection by variables for use in customer
intended purpose, or is a departure from established standards
procurement, supply and storage, and maintenance inspection
having no significant bearing on the effective use or operation
operations.Whenapplicablethispracticeshallbereferencedin
of the unit.
the specification, contract, or inspection instructions, and the
provisions set forth herein shall govern.
6.3 Percent Defective:
6.1.2 Inspection—Inspection is the process of measuring,
6.3.1 Expression of Nonconformance—The extent of non-
examining,testing,gaging,orotherwisecomparingthe“unitof
conformance of product that shall be expressed in terms of
product” (see 6.1.4) with the applicable requirements.
percent defective.
6.1.3 Inspection by Variables—Inspection by variables is
6.3.2 Percent Defective—The percent defective for a quality
inspection wherein a specified quality characteristic (see 6.1.5)
characteristic of a given lot of product is the number of units of
on a unit of product is measured on a continuous scale, such as
product defective for that characteristic divided by the total
pounds, inches, feet per second, etc., and a measurement is
number of units of product and multiplied by one hundred.
recorded.
Expressed as an equation:
6.1.4 Unit of Product—The unit of product is the entity of
product inspected in order to determine its measurable quality number of defectives 3100
Percent defective 5 (1)
characteristic. This may be a single article, a pair, a set, a number of units
component of a product, or the end product itself. The unit of
6.4 Acceptance Quality Level:
product may or may not be the same as the unit of purchase,
6.4.1 Acceptance Quality Level—The acceptance quality
supply, production, or shipment.
level (AQL) is a nominal value expressed in terms of percent
6.1.5 Quality Characteristic—The quality characteristic for
defective specified for a single quality characteristic. Certain
variables inspection is that characteristic of a unit of product
numerical values of AQL ranging from 0.04 to 15.00 percent
that is actually measured to determine conformance with a
are shown in TableA-1 (see Fig.A1.1). When a range ofAQL
given require
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