ASTM E2234-09(2023)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: E2234 − 09 (Reapproved 2023) An American National Standard
Standard Practice for
Sampling a Stream of Product by Attributes Indexed by
AQL
This standard is issued under the fixed designation E2234; 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 Standard:
MIL-STD-105E Sampling Procedures and Tables for In-
1.1 This practice establishes lot or batch sampling plans and
spection by Attributes
procedures for inspection by attributes using MIL-STD-105E
as a basis for sampling a steady stream of lots indexed by
3. Terminology
acceptance quality limit (AQL).
3.1 Definitions—For a more extensive list of terms in E11
1.2 This practice provides the sampling plans of MIL-STD-
standards, see Terminology E456.
105E in ASTM format for use by ASTM committees and
3.1.1 acceptance quality limit (AQL), n—quality limit that is
others. It recognizes the continuing usage of MIL-STD-105E the worst tolerable process average when a continuing series of
in industries supported by ASTM. Most of the original text in
lots is submitted for acceptance sampling.
MIL-STD-105E is preserved in Sections 4 – 6 of this practice. 3.1.1.1 Discussion—This definition supersedes that given in
MIL-STD-105E.
1.3 No system of units is specified in this standard.
3.1.2 average outgoing quality (AOQ), n—the average per-
1.4 This standard does not purport to address all of the
cent defective of outgoing product including all accepted lots
safety concerns, if any, associated with its use. It is the
or batches after any defectives found in them are replaced by
responsibility of the user of this standard to establish appro-
acceptable units, plus all lots or batches which are not accepted
priate safety, health, and environmental practices and deter-
after such lots or batches have been effectively 100 %
mine the applicability of regulatory limitations prior to use.
inspected and all defective units replaced by acceptable units.
E1994
1.5 This international standard was developed in accor-
dance with internationally recognized principles on standard-
3.1.3 average outgoing quality limit (AOQL), n—the AOQL
ization established in the Decision on Principles for the
is the maximum of the AOQ’s for all possible incoming
Development of International Standards, Guides and Recom-
percentages defective for the process for a given acceptance
mendations issued by the World Trade Organization Technical sampling plan. E1994
Barriers to Trade (TBT) Committee.
3.1.4 classification of defects, n—the enumeration of pos-
sible defects of the unit of product classified according to their
2. Referenced Documents
seriousness, that is, critical, major, or minor defect.
3.1.5 critical defect, n—a defect that judgment and experi-
2.1 ASTM Standards:
ence indicate would result in hazardous or unsafe conditions
E456 Terminology Relating to Quality and Statistics
for individuals using, maintaining, or depending upon the
E1994 Practice for Use of Process Oriented AOQL and
product, or a defect that judgment and experience indicate is
LTPD Sampling Plans
likely to prevent performance of the function of a major end
E2586 Practice for Calculating and Using Basic Statistics
item.
3.1.6 defect, n—any nonconformance of the unit of product
with specified requirements.
This practice is under the jurisdiction of ASTM Committee E11 on Quality and
Statistics and is the direct responsibility of Subcommittee E11.30 on Statistical
3.1.7 double sampling plan, n—a multiple sampling plan in
Quality Control.
which up to two samplings can be taken and evaluated to
Current edition approved Jan. 1, 2023. Published February 2023. Originally
accept or reject a lot.
approved in 2005. Last previous edition approved in 2018 as E2234 – 09(2018).
DOI: 10.1520/E2234-09R23.
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
Standards volume information, refer to the standard’s Document Summary page on Available from American 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
E2234 − 09 (2023)
3.1.8 inspection, n—the process of measuring, examining, 3.2.5 defects per hundred units, n—any given quantity of
testing, or otherwise comparing the unit of product with the units of product is one hundred times the number of defects
requirements. contained therein (one or more defects being possible in any
unit of product) divided by the total number of units of product,
3.1.9 inspection by attributes, n—inspection whereby either
that is:
the unit of product is classified simply as defective or non-
defective, or the number of defects in the unit of product is Number of defects × 100
Defects per hundred units5 (1)
counted, with respect to a given requirement or set of require-
Number of units inspected
ments.
3.2.6 lot, n—see batch.
3.1.10 inspection lot, n—a collection of units of product
3.2.7 lot size, n—see batch size.
produced under conditions that are considered uniform and
3.2.8 major defective, n—a unit of product which contains
from which a sample is drawn and inspected.
one or more major defects, and may also contain minor defects
3.1.11 major defect, n—a defect, other than critical, that is
but contains no critical defect.
likely to result in failure, or to reduce materially the usability
3.2.9 minor defective, n—a unit of product which contains
of the unit of product for its intended purpose.
one or more minor defects but contains no critical or major
3.1.12 minor defect, n—a defect that is not likely to reduce
defect.
materially the usability of the unit of product for its intended
3.2.10 percent defective, n—any given quantity of units of
purpose, or is a departure from established standards having
product one hundred times the number of defective units of
little bearing on the effective use or operation of the unit.
product contained therein divided by the total number of units
3.1.13 multiple sampling plan, n—a sampling plan in which
of product, that is:
successive samples from a lot are drawn and after each sample
Number of defectives × 100
is inspected a decision is made to accept the lot, reject the lot,
Percent Defective5 (2)
Number of units inspected
or to take another sample, based on quality level of the
3.2.11 process average (in inspection), n—the average per-
combined samples.
cent defective or average number of defects per hundred units
3.1.13.1 Discussion—When the quality is much less or
(whichever is applicable) of product submitted by the supplier
much more than the AQL, the decision can be made on the first
for original inspection.
sample, which is smaller than that of a single sampling plan
3.2.11.1 Discussion—Original inspection is the first inspec-
with equivalent acceptance quality level. For samples that are
tion of a particular quantity of product as distinguished from
close to the AQL in quality, additional samples are required and
the inspection of product which has been resubmitted after
the total sample size will be larger than the corresponding
prior rejection.
single sampling plan.
3.2.12 sample size code letter, n—a device used along with
3.1.14 operating characteristic, n—probability of accep-
the AQL for locating a sampling plan on a table of sampling
tance using a specified acceptance sampling plan, as a function
plans.
of parameters describing quality of the lot.
3.2.13 sampling plan (in inspection), n—a plan that indi-
3.1.15 sample, n—a group of observations, test results,
cates the number of units of product from each lot or batch
taken from a large collection of observations, test results,
which are to be inspected (sample size or series of sample
which serves to provide information that may be used as a basis
sizes) and the criteria for determining the acceptability of the
for making a decision concerning the larger collection. E2586
lot or batch (acceptance and rejection numbers).
3.1.15.1 Discussion—A sample consists of one or more
3.2.14 unit of product, n—that which is inspected in order to
units of product drawn from an inspection lot, the units of the
sample being selected at random without regard to their determine its classification as defective or non-defective or to
count the number of defects.
quality. The number of units of product in the sample is the
sample size. 3.2.14.1 Discussion—It may be a single article, a pair, a set,
a length, an area, an operation, a volume, a component of an
3.2 Definitions of Terms Specific to This Standard:
end product, or the end product itself. The unit of product may
3.2.1 batch (in inspection), n—a collection of units of
or may not be the same as the unit of purchase, supply,
product produced under conditions that are considered uniform
production, or shipment.
and from which a sample is drawn and inspected, and may
differ from a collection of units designated as a batch for other
4. Significance and Use
purposes, for example, production, shipment, etc.
4.1 Purpose—This publication establishes lot or batch sam-
3.2.2 batch size, n—the number of units of product in a
pling plans and procedures for inspection by attributes. This
batch.
publication shall not be interpreted to supersede or conflict
3.2.3 critical defective, n—a unit of product which contains
with any contractual requirements. The words “accept,”
one or more critical defects and may also contain major or
“acceptance,” “acceptable,” etc, refer only to the contractor’s
minor defects, or both.
use of the sampling plans contained in this standard and do not
3.2.4 defective, n—a unit of product which contains one or imply an agreement by the customer (formerly “Government”
more defects. in original text) to accept any product. Determination of
E2234 − 09 (2023)
acceptability by the customer shall be as described in contrac- 5.5 Critical Defect—A critical defect is a defect that judg-
tual documents. The sampling plans described in this standard ment and experience indicate would result in hazardous or
are applicable to AQL’s of 0.01 % or higher and are therefore unsafe conditions for individuals using, maintaining, or de-
not suitable for applications where quality levels in the range of pending upon the product, or a defect that judgment and
parts per million levels can be realized. experience indicate is likely to prevent performance of the
tactical function of a major end item such as a ship, aircraft,
4.2 Application—Sampling plans designated in this publi-
tank, missile, or space vehicle.
cation are applicable, but not limited, to inspection of the
following: (1) end items, (2) components and raw materials, (3)
5.6 Critical Defective—A critical defective is a unit of
operations or services, (4) materials in process, (5) supplies in
product which contains one or more critical defects and may
storage, (6) maintenance operations, (7) data or records, (8)
also contain major or minor defects, or both.
administrative procedures. These plans are intended primarily
5.7 Defect—A defect is any nonconformance of the unit of
to be used for a continuing series of lots or batches. The plans
product with specified requirements.
may also be used for the inspection of isolated lots or batches,
5.8 Defective—A defective is a unit of product which
but, in this latter case, the user is cautioned to consult the
contains one or more defects.
operating characteristic curves to find a plan which will yield
the desired protection (see 6.11).
5.9 Defects per Hundred Units—The number of defects per
hundred units of any given quantity of units of product is one
5. Definitions
hundred times the number of defects contained therein (one or
more defects being possible in any unit of product) divided by
5.1 Acceptable Quality Level (AQL)—When a continuous
the total number of units of product, that is:
series of lots is considered, the AQL is the quality level which,
for the purposes of sampling inspection, is the limit of a
Number of defects × 100
Defects per hundred units5
satisfactory process average (see 5.19).
Number of units inspected
5.1.1 A sampling plan and an AQL are chosen in accor-
5.10 Inspection—Inspection is the process of measuring,
dance with the risk assumed. Use of a value of AQL for a
examining, testing, or otherwise comparing the unit of product
certain defect or group of defects indicates that the sampling
with the requirements.
plan will accept the great majority of the lots or batches
provided the process average level of percent defective (or
5.11 Inspection by Attributes—Inspection by attributes is
defects per hundred units) in these lots or batches be no greater
inspection whereby either the unit of product is classified
than the designated value of AQL. Thus, the AQL is a
simply as defective or non-defective, or the number of defects
designated value of percent defective (or defects per hundred
in the unit of product is counted, with respect to a given
units) for which lots will be accepted most of the time by the
requirement or set of requirements.
sampling procedure being used.
5.12 Lot or Batch—The term lot or batch shall mean
5.1.2 The sampling plans provided herein are so arranged
“inspection lot” or “inspection batch”, that is, a collection of
that the probability of acceptance at the designated AQL value
units of product from which a sample is to be drawn and
depends upon the sample size, being generally higher for large
inspected and may differ from a collection of units designated
samples than for small ones, for a given AQL. The AQL alone
as a lot or batch for other purposes (for example, production,
does not identify the chances of accepting or rejecting indi-
shipment, etc.).
vidual lots or batches but more directly relates to what might be
5.13 Lot or Batch Size—The lot or batch size is the number
expected from a series of lots or batches, provided the steps
of units of product in a lot or batch.
indicated in this publication are taken. It is necessary to refer to
the operating characteristic curve of the plan to determine the
5.14 Major Defect—A major defect is a defect, other than
relative risks.
critical, that is likely to result in failure, or to reduce materially
5.2 Average Outgoing Quality (AOQ)—For a particular the usability of the unit of product for its intended purpose.
process average, the AOQ is the average quality of outgoing
5.15 Major Defective—A major defective is a unit of prod-
product including all accepted lots or batches, plus all rejected
uct which contains one or more major defects, and may also
lots or batches after the rejected lots or batches have been
contain minor defects but contains no critical defect.
effectively 100 % inspected and all defectives replaced by
5.16 Minor Defect—A minor defect is a defect that is not
non-defectives.
likely to reduce materially the usability of the unit of product
5.3 Average Outgoing Quality Limit (AOQL)—The AOQL
for its intended purpose, or is a departure from established
is the maximum AOQ for a given acceptance sampling plan.
standards having little bearing on the effective use or operation
Factors for computing AOQL values are given in Table V-A for
of the unit.
each of the single sampling plans for normal inspection and in
5.17 Minor Defective—A minor defective is a unit of
Table V-B for each of the single sampling plans for tightened
product which contains one or more minor defects but contains
inspection.
no critical or major defect.
5.4 Classification of Defects—A classification of defects is
the enumeration of possible defects of the unit of product 5.18 Percent Defective—The percent defective of any given
classified according to their seriousness quantity of units of product is one hundred times the number of
E2234 − 09 (2023)
defective units of product contained therein divided by the total 6.4.3 Choosing AQLs—Different AQLs may be chosen for
number of units of product, that is: groups of defects considered collectively, or for individual
defects. An AQL for a group of defects may be chosen in
Number of defectives × 100
Percent defective5
addition to AQLs for individual defects, or subgroups, within
Number of units inspected
that group. AQL values of 10.0 or less may be expressed either
5.19 Process Average—The process average is the average
in percent defective or in defects per hundred units; those over
percent defective or average number of defects per hundred
10.0 shall be expressed in defects per hundred units only.
units (whichever is applicable) of product submitted by the
6.5 Sampling:
supplier for original inspection. Original inspection is the first
inspection of a particular quantity of product as distinguished 6.5.1 Representative (Stratified) Sampling—When
from the inspection of product which has been resubmitted
appropriate, the number of units in the sample shall be selected
after prior rejection. in proportion to the size of sublots or sub-batches, or parts of
the lot or batch, identified by some rational criterion. When
5.20 Sample—A sample consists of one or more units of
representative sampling is used, the units from each sublot,
product drawn from a lot or batch, the units of the sample being
sub-batch, or part of the lot or batch shall be selected at
selected at random without regard to their quality. The number
random.
of units of product in the sample is the sample size.
6.5.2 Time of Sampling—A sample may be drawn after all
5.21 Sample Size Code Letter—The sample size code letter
the units comprising the lot or batch have been assembled, or
is a device used along with the AQL for locating a sampling
sample units may be drawn during assembly of the lot or batch,
plan on a table of sampling plans.
in which case the size of the lot or batch will be determined
5.22 Sampling Plan—A sampling plan indicates the number
before any sample units are drawn. If the sample units are
of units of product from each lot or batch which are to be
drawn during assembly of the lot or batch, and if the rejection
inspected (sample size or series of sample sizes) and the
number is reached before the lot is completed, that portion of
criteria for determining the acceptability of the lot or batch
the lot already completed shall be rejected. The cause of the
(acceptance and rejection numbers).
defective product shall be determined and corrective action
taken, after which a new lot or batch shall be begun.
5.23 Unit of Product—The unit of product is the thing
inspected in order to determine its classification as defective or 6.5.3 Double or Multiple Sampling—When double or mul-
non-defective or to count the number of defects. It may be a tiple sampling is to be used, each sample shall be selected over
single article, a pair, a set, a length, an area, an operation, a the entire lot or batch.
volume, a component of an end product, or the end product
6.6 Inspection Procedures—Normal inspection will be used
itself. The unit of product may or may not be the same as the
at the start of inspection. Normal, tightened or reduced
unit of purchase, supply, production, or shipment.
inspection shall continue unchanged for each class of defects or
6. General Requirements defectives on successive lots or batches except where the
switching procedures given below require change. The switch-
6.1 Written Procedures—Written procedures are ordinarily
ing procedures shall be applied to each class of defects or
developed and made available for the customer’s review, upon
defectives independently.
request. When the written procedures indicate use of this
standard, they shall comply with the requirements of this
6.7 Switching Procedures:
standard and reference appropriate parts as necessary.
6.7.1 Normal to Tightened—When normal inspection is in
effect, tightened inspection shall be instituted when 2 out of 2,
6.2 Nonconformance—The extent of nonconformance of
product shall be expressed either in terms of percent defective 3, 4, or 5 consecutive lots or batches have been rejected on
original inspection (that is, ignoring resubmitted lots or batches
or in terms of defects per hundred units.
for this procedure).
6.3 Formation and Identification of Lots or Batches—The
6.7.2 Tightened to Normal—When tightened inspection is in
product shall be assembled into identifiable lots, sublots,
effect, normal inspection shall be instituted when 5 consecutive
batches, or in such other manner as may be prescribed. Each lot
lots or batches have been considered acceptable on original
or batch shall, as far as is practicable, consist of units of
inspection.
product of a single type, grade, class, size, and composition,
manufactured under essentially the same conditions, and at 6.7.3 Normal to Reduced—When normal inspection is in
essentially the same time. The lots or batches shall be identified effect, reduced inspection shall be instituted provided that all of
by the contractor and shall be kept intact in adequate and the following conditions are satisfied:
suitable storage space.
6.7.3.1 The preceding 10 lots or batches (or more, as
indicated by the note to Table VIII) have been on normal
6.4 AQL:
inspection and all have been accepted on original inspection;
6.4.1 AQL Use—The AQL, together with the Sample Size
and
Code Letter, is used for indexing the sampling plans provided
herein. 6.7.3.2 The total number of defectives (or defects) in the
6.4.2 Limitation—The selection or use of an AQL shall not samples from the preceding 10 lots or batches (or such other
imply that the contractor has the right to supply any defective number as was used for condition “a” above) is equal to or less
unit of product. than the applicable number given in Table VIII. If double or
E2234 − 09 (2023)
multiple sampling is in use, all samples inspected should be 6.9.4 Types of Sampling Plans—Three types of sampling
included, not “first” samples only; and plans; Single, Double, and Multiple, are given in Tables II, III,
6.7.3.3 Production is at a steady rate; and and IV, respectively. When several types of plans are available
6.7.3.4 Reduced inspection is considered desirable.
for a given AQL and code letter, any one may be used. A
6.7.4 Reduced to Normal—When reduced inspection is in decision as to type of plan, either single, double, or multiple,
effect, normal inspection shall be instituted if any of the
when available for a given AQL and code letter, will usually be
following occur on original inspection: based upon the comparison between the administrative diffi-
6.7.4.1 A lot or batch is rejected; or culty and the average sample sizes of the available plans. The
6.7.4.2 A lot or batch is considered acceptable under the average sample size of multiple plans is less than for double
procedures of 6.10.1.4, or (except in the case corresponding to single acceptance number
6.7.4.3 Production becomes irregular or delayed; or
1) and both of these are always less than a single sample size
6.7.4.4 Other conditions warrant that normal inspection
...