ASTM E1994-09(2023)

Standard Practice for Use of Process Oriented AOQL and LTPD Sampling Plans

ABSTRACT
This practice is primarily a statement of principals for the guidance of ASTM technical committees and others in the use of average outgoing quality limit, AOQL, and lot tolerance percent defective, LTPD, sampling plans for determining acceptable of lots of product. Two general types of tables are given, one based on the concept of lot tolerance, LTPD, and the other on AOQL. For each of the types, tables are provided both for single sampling and for double sampling. Each of the individual tables constitutes a collection of solutions to the problem of minimizing the over-all amount of inspection.
SIGNIFICANCE AND USE
4.1 Two general types of tables (Note 1) are given, one based on the concept of lot tolerance, LTPD, and the other on AOQL. The broad conditions under which the different types have been found best adapted are indicated below.  
4.1.1 For each of the types, tables are provided both for single sampling and for double sampling. Each of the individual tables constitutes a collection of solutions to the problem of minimizing the over-all amount of inspection. Because each line in the tables covers a range of lot sizes, the AOQL values in the LTPD tables and the LTPD values in the AOQL tables are often conservative.
Note 1: Tables in Annex A1 – Annex A4 and parts of the text are reproduced by permission of John R. Wiley and Sons. More extensive tables and discussion of the methods will be found in that text.  
4.2 The sampling tables based on lot quality protection (LTPD) (the tables in Annex A1 and Annex A2) are perhaps best adapted to conditions where interest centers on each lot separately, for example, where the individual lot tends to retain its identity either from a shipment or a service standpoint. These tables have been found particularly useful in inspections made by the ultimate consumer or a purchasing agent for lots or shipments purchased more or less intermittently.  
4.3 The sampling tables based on average quality protection (AOQL) (the tables in Annex A3 and Annex A4) are especially adapted for use where interest centers on the average quality of product after inspection rather than on the quality of each individual lot and where inspection is, therefore, intended to serve, if necessary, as a partial screen for defective pieces. The latter point of view has been found particularly helpful, for example, in consumer inspections of continuing purchases of large quantities of a product and in manufacturing process inspections of parts where the inspection lots tend to lose their identity by merger in a common storeroom from which quantities are withdraw...
SCOPE
1.1 This practice is primarily a statement of principals for the guidance of ASTM technical committees and others in the use of average outgoing quality limit, AOQL, and lot tolerance percent defective, LTPD, sampling plans for determining acceptable of lots of product.  
1.2 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.

General Information

• Status: Published
• Publication Date: 31-Dec-2022
• ICS: 03.120.30 - Application of statistical methods
• Technical Committee: E11 - Quality and Statistics
• Drafting Committee: E11.30 - Statistical Quality Control

Relations

• Refers: ASTM E456-13a(2022)e1 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 01-Apr-2022
• Refers: ASTM E456-13A(2017)e3 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 01-Oct-2017
• Refers: ASTM E456-13A(2017)e1 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 01-Oct-2017
• Refers: ASTM E178-16 - Standard Practice for Dealing With Outlying Observations
• Effective Date: 01-Jun-2016
• Refers: ASTM E456-13ae1 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 15-Nov-2013
• Refers: ASTM E456-13ae2 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 15-Nov-2013
• Refers: ASTM E456-13a - Standard Terminology Relating to Quality and Statistics
• Effective Date: 15-Nov-2013
• Refers: ASTM E456-13ae3 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 15-Nov-2013
• Refers: ASTM E456-13 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 15-Aug-2013
• Refers: ASTM E456-12 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 01-May-2012
• Refers: ASTM E456-12e1 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 01-May-2012
• Refers: ASTM E178-08 - Standard Practice for Dealing With Outlying Observations
• Effective Date: 01-Oct-2008
• Refers: ASTM E456-08e4 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 01-Apr-2008
• Refers: ASTM E456-08 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 01-Apr-2008
• Refers: ASTM E456-08e3 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 01-Apr-2008

Overview

ASTM E1994-09(2023): Standard Practice for Use of Process Oriented AOQL and LTPD Sampling Plans, developed by ASTM, provides foundational principles and guidance for applying acceptance sampling plans based on the Average Outgoing Quality Limit (AOQL) and Lot Tolerance Percent Defective (LTPD). The document is intended for both ASTM technical committees and industry practitioners seeking effective methods to determine the acceptability of product lots using statistical quality control.

This international standard supports organizations in minimizing inspection burdens while maintaining quality assurance, aligning with World Trade Organization (WTO) principles for global standardization.

Key Topics

• Acceptance Sampling: Guidance on the selection and application of statistical sampling techniques for lot acceptance decisions.
• AOQL (Average Outgoing Quality Limit): Methods for ensuring outgoing product quality over time does not exceed a specified maximum percentage of defects, particularly useful in continuous manufacturing environments.
• LTPD (Lot Tolerance Percent Defective): Approaches focused on controlling the maximum acceptable level of defects per individual lot, suitable for intermittent or batch shipments.
• Single vs. Double Sampling Plans: The standard offers comprehensive tables and procedures for both single and double sampling, allowing users to choose based on economic considerations and process stability.
• Sampling Plan Selection:
  • Identification of item characteristics to be inspected.
  • Procedures for defining and composing lots.
  • Decision-making frameworks for choosing AOQL versus LTPD protection.
• Practical Steps and Procedures: Detailed steps for implementing sampling plans, handling rejected lots, and periodically reassessing the process average to optimize sampling.

Applications

ASTM E1994-09(2023) is highly applicable in a wide range of industries seeking to implement robust quality control measures for manufactured products and administrative processes. Key application areas include:

• Manufacturing and Production: Ensuring consistent product quality in high-volume, continuous output scenarios by applying AOQL-based plans.
• Procurement and Receiving Inspection: Acceptance inspection of incoming lots, especially when product is sourced periodically or from varied suppliers, utilizing LTPD-based plans.
• Internal Quality Audits: Assessing both incoming materials and finished goods to maintain stringent acceptance criteria.
• Consumer Product Evaluations: Supporting consumer inspections of regular purchase lots or shipments, ensuring delivered goods meet specified defect limits.
• Process Improvement Initiatives: Using AOQL and LTPD plans as incentives for ongoing process quality improvements and cost-effective inspection reduction.

The standard assists organizations in selecting appropriate sampling plans based on their control objectives, resource constraints, and product flow, resulting in enhanced operational efficiency and quality compliance.

Related Standards

For comprehensive statistical quality control, ASTM E1994-09(2023) is complemented by several related ASTM standards:

• ASTM E178: Practice for Dealing With Outlying Observations, relevant for analyzing inspection data and handling anomalies.
• ASTM E456: Terminology Relating to Quality and Statistics, providing definitions critical for understanding acceptance sampling concepts.

These standards, alongside ASTM E1994, form a robust framework for product quality assurance and inspection effectiveness.

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Keywords: acceptance sampling, AOQL, LTPD, quality control, sampling plans, ASTM E1994, statistical quality assurance, manufacturing inspection, lot acceptance, process average, consumer risk, process improvement

By following ASTM E1994-09(2023), organizations can establish data-driven, internationally aligned quality assurance processes, tailored to both lot-specific and ongoing production environments.

Standards Content (Sample)

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: E1994 − 09 (Reapproved 2023) An American National Standard
Standard Practice for
Use of Process Oriented AOQL and LTPD Sampling Plans
This standard is issued under the fixed designation E1994; 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.
INTRODUCTION
This standard is an abbreviated compilation of the sampling plans presented by H.F. Dodge and
H.G. Romig in their classic development of sampling plans for use with the process associated with
a continuing supply of products. The so called AOQL plans provide a means for disposition of product
whether or not the process is in control as well as incentives for process improvement in terms of
reduced sample size as the process average percent defective is lowered. In addition, so called LTPD
plans are provided for use with individual lots of product, not necessarily associated with a process
stream.
The sampling plans and parts of the text given here are taken from the Wiley Classics Library
Edition of the Dodge-Romig tables (copyright 1998). Additional tables and detailed discussion of the
plans, OC curves, and their derivation will be found in that text. The theoretical development of the
3,4
Dodge-Roming plans will be found in Volumes 8 and 20 of the Bell System Technical Journal and
an amplification of the plans is given in Acceptance Sampling in Quality Control.
1. Scope 2. Referenced Documents
2.1 ASTM Standards:
1.1 This practice is primarily a statement of principals for
E178 Practice for Dealing With Outlying Observations
the guidance of ASTM technical committees and others in the
E456 Terminology Relating to Quality and Statistics
use of average outgoing quality limit, AOQL, and lot tolerance
percent defective, LTPD, sampling plans for determining
3. Terminology
acceptable of lots of product.
3.1 Definitions—Terminology E456 provides a more exten-
1.2 This international standard was developed in accor-
sive list of terms in E11 standards.
dance with internationally recognized principles on standard-
3.1.1 average outgoing quality (AOQ), n—the average per-
ization established in the Decision on Principles for the
cent defective of outgoing product including all accepted lots
Development of International Standards, Guides and Recom-
or batches, after any defective units found in them are replaced
mendations issued by the World Trade Organization Technical
by acceptable units, plus all lots or batches which are not
Barriers to Trade (TBT) Committee.
accepted after such lots or batches have been effectively 100 %
inspected and all defective units replaced by acceptable units.
3.1.2 average outgoing quality limit (AOQL), n—the maxi-
This practice is under the jurisdiction of ASTM Committee E11 on Quality and
mum of the AOQs for all possible incoming percentages
Statistics and is the direct responsibility of Subcommittee E11.30 on Statistical
Quality Control. defective for the process, for a given acceptance sampling plan.
Current edition approved Jan. 1, 2023. Published February 2023. Originally
3.1.3 average quality protection, n—a type of protection in
approved in 1998. Last previous edition approved in 2018 as E1994 – 09(2018).
which there is prescribed some chosen value of average percent
DOI: 10.1520/E1994-09R23.
Available from John Wiley and Sons, Inc., 605 Third Ave., New York, NY
defective in the product after inspection (average outgoing
10158.
quality limit (AOQL), that shall not be exceeded in the long
Dodge, H. F. and Romig, H. G., “A Method of Sampling Inspection,” The Bell
System Technical Journal, Vol 8 , No. 10, 1924, pp. 613–631.
Dodge, H. F. and Romig, H. G., “Single Sampling and Double Sampling
Inspection Tables,” The Bell System Technical Journal, Vol 20, No. 1, 1941, pp. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
1–61. contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
Schilling, E. G., Acceptance Sampling in Quality Control, Marcel Dekker Inc., Standards volume information, refer to the standard’s Document Summary page on
NY, 1982, pp. 372–399. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E1994 − 09 (2023)
run no matter what may be the level of percent defective in the be accepted by sample are completely cleared of defectives.
product submitted to the inspector. Obviously, this requires a nondestructive test. The over-all
result is some average percent defective in the product as it
3.1.4 lot quality protection, n—a type of protection in which
leaves the inspector, termed the average outgoing quality,
there is prescribed some chosen value of limiting percent
which depends on the level of percent defective for incoming
defective in a lot (lot tolerance percent defective (LTPD)) and
product and the proportion of total defectives that are screened
also some chosen value for the probability (called the consum-
out.
er’s risk) of accepting a submitted lot that has a percent
defective equal to the lot tolerance percent defective.
4.5 Given a specific problem of replacing a 100 % screening
3.1.5 lot tolerance percent defective (LTPD), n—for pur- inspection by a sampling inspection, the first step is to decide
poses of acceptance sampling, the percentage of defective units
on the type of protection desired, to select the desired limit of
in a lot for which the consumer has a stated low probability of
percent defective lot tolerance (LTPD) or AOQL value for that
acceptance of the lot.
type of protection, and to choose between single and double
sampling. This results in the selection of one of the appended
3.2 Definitions of Terms Specific to This Standard:
tables. The second step is to determine whether the quality of
3.2.1 consumer’s risk, n—the probability that a lot whose
product is good enough to warrant the introduction of sam-
percentage defective is equal to the LTPD will be accepted by
pling. The economies of sampling will be realized, of course,
the plan.
only insofar as the percent defective in submitted product is
4. Significance and Use
such that the acceptance criteria of the selected sampling plan
will be met. A statistical analysis of past inspection results
4.1 Two general types of tables (Note 1) are given, one
should first be made, therefore, in order to determine existing
based on the concept of lot tolerance, LTPD, and the other on
levels and fluctuations in the percent defective for the charac-
AOQL. The broad conditions under which the different types
teristic or the group of characteristics under consideration. This
have been found best adapted are indicated below.
provides information with respect to the degree of control as
4.1.1 For each of the types, tables are provided both for
well as the usual level of percent defective to be expected
single sampling and for double sampling. Each of the indi-
under existing conditions. Determine a value from this and
vidual tables constitutes a collection of solutions to the
other information for the process average percent defective
problem of minimizing the over-all amount of inspection.
Because each line in the tables covers a range of lot sizes, the that should be used in applying the selected sampling table, if
sampling is to be introduced.
AOQL values in the LTPD tables and the LTPD values in the
AOQL tables are often conservative.
5. Procedure
NOTE 1—Tables in Annex A1 – Annex A4 and parts of the text are
reproduced by permission of John R. Wiley and Sons. More extensive
5.1 Two distinct methods of inspection are employed, single
tables and discussion of the methods will be found in that text.
sampling and double sampling. In single sampling only one
4.2 The sampling tables based on lot quality protection
sample is permitted before a decision is reached regarding the
(LTPD) (the tables in Annex A1 and Annex A2) are perhaps
disposition of the lot, and the acceptance criterion is expressed
best adapted to conditions where interest centers on each lot
as an acceptance number, c. In double sampling, a second
separately, for example, where the individual lot tends to retain
sample is permitted and two acceptance numbers are used; the
its identity either from a shipment or a service standpoint.
first, c , applying to the observed number of defectives for the
These tables have been found particularly useful in inspections
first sample alone and the second, c , applying to the observed
made by the ultimate consumer or a purchasing agent for lots
number of defectives for the first and second samples com-
or shipments purchased more or less intermittently.
bined. The specific procedures assumed in the development of
the tables are as follows:
4.3 The sampling tables based on average quality protection
(AOQL) (the tables in Annex A3 and Annex A4) are especially
5.1.1 Single Sampling Inspection Procedure:
adapted for use where interest centers on the average quality of
5.1.1.1 Inspect a sample of n pieces.
product after inspection rather than on the quality of each
5.1.1.2 If the number of defectives found in the sample does
individual lot and where inspection is, therefore, intended to
not exceed c, the acceptance number, accept the lot.
serve, if necessary, as a partial screen for defective pieces. The
5.1.1.3 If the number of defectives found in the sample
latter point of view has been found particularly helpful, for
exceeds c, inspect all the pieces in the remainder of the lot.
example, in consumer inspections of continuing purchases of
5.1.1.4 Regardless of whether or not the lot was accepted,
large quantities of a product and in manufacturing process
correct or replace all defective pieces found in the sample as
inspections of parts where the inspection lots tend to lose their
well as in any subsequent inspection of the remainder of the
identity by merger in a common storeroom from which
lot.
quantities are withdrawn on order as needed.
5.1.2 Double Sampling Inspection Procedure:
4.4 The plans based on average quality protection (AOQL)
5.1.2.1 Inspect a first sample of n pieces.
consider the degree to which the entire inspection procedure 1
screens out defectives in the product submitted to the inspector. 5.1.2.2 If the number of defectives found in the first sample
Lots accepted by sample undergo a partial screening through does not exceed c , the acceptance number for the first sample,
the elimination of defectives found in samples. Lots that fail to accept the lot.
E1994 − 09 (2023)
5.1.2.3 If the number of defectives found in the first sample each presented lot comprise material from only one of those
exceeds c , the acceptance number for the combined first and sources; otherwise have source identification information fur-
second samples, inspect all the pieces in the remainder of the nished with each lot.
lot.
5.3.2.3 To minimize the amount of inspection, make the lots
5.1.2.4 If the number of defectives found in the first sample as large as practicable, considering the limitations of available
exceeds c , but does not exceed c , inspect a second sample of storage space, delays in shipment, difficulty in handling large
1 2
n pieces.
rejected lots, etc.
5.1.2.5 If the total number of defectives found in the first
5.3.3 Choose between lot quality (LTPD) and average
and second samples combined does not exceed c , accept the
outgoing quality (AOQL) protection.
lot.
5.3.3.1 Choose AOQL if interest centers on the general level
5.1.2.6 If the total number of defectives found in the first
of quality of product after inspection. AOQL plans have been
and second samples combined exceeds c , inspect all the pieces
found generally more useful than LTPD plans in inspections of
in the remainder of the lot.
a continuing supply of product, especially in consumer’s
5.1.2.7 Regardless of whether or not the lot was accepted,
acceptance inspections and in producer’s receiving, process,
correct or replace all defective pieces found in either sample as and final inspections.
well as any in subsequent inspection or the remainder of the
5.3.3.2 Choose AOQL for a percent defective that will
lot.
almost always be safely met by the running average quality of
product after inspection.
5.2 In choosing a sampling plan for a particular application,
5.3.3.3 Choose LTPD for a percent defective that will
a number of decisions must be made which depend on the
almost always be met by each lot. (This will be a much more
conditions under which the plan is to be used. The accompa-
pessimistic figure than the AOQL value of the plan.)
nying Sequence of Steps gives an outline of a typical proce-
dure. These steps are shown in the following numbered 5.3.3.4 As a manufacturer trying to meet a consumer’s
paragraphs. stated AQL (Note 2), use for final inspection an AOQL plan
with an AOQL value equal to the specified AQL value, in order
5.3 Sequence of Steps:
to provide good assurance that outgoing quality will be found
5.3.1 Decide what characteristics will be included in the
acceptable by the consumer (or set the AOQL at one and one
inspection.
third times the AQL for reasonably good assurance).
5.3.1.1 If advantageous, use a separate sampling plan for a
single characteristic or selected group of characteristics of like NOTE 2—AQL = Acceptable Quality Level, as used to index certain
systems of sampling plans, signifying what the consumer feels to be the
importance. Sampling need not wait until all characteristics
maximum percent defective that, for sampling purposes, can be consid-
have good quality.
ered satisfactory as a process average.
5.3.1.2 If one or two characteristics give an outstandingly
5.3.3.5 When producer and consumer of a product are two
high number of defective units, treat them separately (using
departments of the same company, use AOQL plans with the
100 percent inspection; also, if possible, concentrate on cor-
provision that the producer perform the 100 percent inspection
recting the causes of trouble) and include the rest collectively
of rejected lots. Close interchange of quality findings will
in the sampling inspection.
expedite good process control of quality.
5.3.1.3 If all characteristics have satisfactory quality, in-
5.3.3.6 Wherever practicable, make arrangements for the
clude all of them collectively in the sampling inspection.
producer to perform the 100 percent inspection of rejected lots
5.3.1.4 In general, combine at one inspection station char-
under procedures acceptable to the consumer and to provide
acteristics subject to essentially similar inspection operations,
suitable certifications of work performed.
for example, all visual inspection items together, all gauging,
5.3.4 Choose a suitable figure of quality (LTPD or AOQL)
or all testing. Visual and gauging inspection operations often
for the sampling plan
combine well.
5.3.1.5 Include in any group characteristics of essentially 5.3.4.1 For LTPD, choose the value of percent defective for
lot acceptance not more than 10 % of the time (that is, reject at
the same degree of seriousness. If two degrees of seriousness
are involved, say major and minor, keep all majors together in least 90 % of the time).
one group and all minors in a second group.
5.3.4.2 For AOQL, choose the value of average percent
5.3.1.6 Consider these plans applicable to all basic types of defective in product after inspection that should not be ex-
inspection for manufactured products receiving, process, and ceeded.
final and to the inspection of administrative and clerical
5.3.4.3 In choosing a value of LTPD (or AOQL), consider
products as in paper-work quality control.
and compare the cost of inspection with the economic loss that
5.3.2 Decide what is to constitute a lot for purposes of would ensue if quality as bad as the LTPD were accepted often
sampling inspection.
(or if the average level of percent defective were greater than
the AOQL). Even though the evaluation of economic loss may
5.3.2.1 So far as practicable, require that individual lots
presented for acceptance comprise essentially homogeneous be difficult, relative values for different levels of percent
defective may often be determined.
material from a common source.
5.3.2.2 If presented material comes from two or more direct 5.3.5 Choose between single sampling and double sam-
sources not under a common system of control, arrange to have pling.
E1994 − 09 (2023)
NOTE 4—See the Dodge–Romig text for OC Curves.
5.3.5.1 In general, for economy in overall inspection effort,
use double sampling rather than single sampling.
5.3.10 From the lot, select sample units by means of a
5.3.5.2 In general, for minimum variation in the inspector’s
random procedure.
workload, use single sampling.
5.3.10.1 Consider the use of random numbers as the pre-
5.3.5.3 Consider adopting double sampling as the normal
ferred way of selecting sample units at random. Each unit in
standard for sampling plans in a given plant, with a view to
the lot is assigned a serial number usually on paper, and then
effecting overall economies.
those units whose serial numbers correspond to the numbers in
5.3.5.4 In a particular case, for a given AOQL and given
some section of a listing of random numbers are included in the
process average, compare the OC curves of the two sampling
sample.
plans (single sampling and double sampling) as an aid in
5.3.10.2 If a double sampling plan has been chosen, con-
making a choice (Note 3).
sider selecting sample units for both samples at the same time.
5.3.11 Follow the sampling inspection procedure for single
NOTE 3—See the Dodge-Romig text for OC curves.
sampling or double sampling, whichever was chosen.
5.3.6 Select the proper sampling table in Annex A1 – Annex
5.3.11.1 Inspect each unit in the sample for all the charac-
A4, on the basis of the above choices.
teristics decided on in Section 5.3.
5.3.7 Obtain an estimate of process average percent defec-
5.3.11.2 If single sampling is being used, inspect all units in
tive.
the sample even though the acceptance number is exceeded
5.3.7.1 Use recent data to estimate the process average.
before all units have been inspected. This facilitates estimation
5.3.7.2 Use rough estimates at the start, if little or no actual
of the process average.
data are available; a poor estimate merely prevents getting the
5.3.11.3 If double sampling is being used, inspect all units
most economical plan but keeps the same (LTPD or AOQL)
in the first sample; if desired, discontinue inspection of the
protection.
second sample when the acceptance number, c , is exceeded.
5.3.7.3 As more data are collected, make improved esti-
5.3.12 Keep a running check on the process average and
mates of process average.
change the sampling plan if the process average changes
5.3.7.4 Omit wild and obviously nonrepresentative sets of
sufficiently.
data in making estimates and adopt some suitable rule for
5.3.12.1 Adopt a definite plan for making periodic estimates
discarding data (see Practice E178).
of the process average, every 20 or 50 lots or every month,
5.3.8 Choose a sampling plan for the given lot size and the
quarter, or six months, depending on the production rate and
estimated process average.
the quality history.
5.3.8.1 If the estimated process average percent defective,
5.3.12.2 Keep the producing organization informed of the
PA, falls within the range of PA values in the selected table,
running quality of presented product, preferably in control
choose the sampling plan corresponding to the PA value and to
chart form, and furnish prompt information regarding any
the given lot size.
sudden adverse shifts in quality.
5.3.8.2 If the PA is unknown or is estimated to be larger than
5.3.12.3 Change from one sampling plan to another within a
the largest PA value given in the table, choose the sampling
sampling table, as the process average changes from one
plan corresponding to the largest PA in the table (last column)
general level to another. This provides a general basis for
and to the given lot size.
tightened and reduced inspection while holding to a given
5.3.8.3 Under 5.3.8.2, obtain revised estimates of the PA
AOQL or LTPD. If, with stable quality at an excellent level, it
from the lot-by-lot data and use a sampling plan with a smaller
is desired to reduce inspection even further, use a larger AOQL
sample size as soon as a revised estimate of the PA permits.
or LTPD value, twice as large as the basic AOQL or LTPD.
5.3.8.4 If, for single sampling, the sampling plan given by
the table has c = 0, consider whether it would be preferable to
6. Precision and Bias
use a plan with c = 1 to avoid making rejections on finding a
6.1 The use of this standard assumes that test methods are
single defective. There is no such problem for double
used with sufficient precision and accuracy that test results can
sampling, since c always equals 1 or more.
be safely translated into attribute (go-no go) results.
5.3.8.5 If inspection includes two classes of defects, major
and minor, with two AOQL values, choose the two sampling
7. Keywords
plans from the appropriate tables in the Annexes and use them
simultaneously. 7.1 average outgoing quality limit; lot tolerance percent
5.3.9 Check the OC curve of the chosen plan(s) (Note 4). defective; sampling; sampling plans
E1994 − 09 (2023)
ANNEXES
(Mandatory Information)
A1. SINGLE SAMPLING TABLES FOR STATED VALUES OF LOT TOLERANCE PERCENT DEFECTIVE (LTPD) WITH
CONSUMER’S RISK OF 0.10
0.5 % LTPD, 1.0 % LTPD, 2.0 % LTPD, 5.0 % LTPD, 10.0 % LTPD
A1.1 Tables A1.1-A1.5 illustrate single sampling stated
values of lot tolerance percent.
TABLE A1.1 Single Sampling Table for Lot Tolerance Percent Defective (LTPD) = 0.5 %
NOTE 1—n = sample size; c = acceptance number; AOQL = average outgoing quality limit; “all” indicates that each piece in the lot is to be inspected.
Process Average Process Average Process Average Process Average Process Average Process Average
0 to 0.005 % 0.006 to 0.050 % 0.051 to 0.100 % 0.101 to 0.150 % 0.151 to 0.200 % 0.201 to 0.250 %
Lot Size
AOQL AOQL AOQL AOQL AOQL AOQL
n c n c n c n c n c n c
% % % % % %
1–180 all 0 0 all 0 0 all 0 0 all 0 0 all 0 0 all 0 0
181–210 180 0 0.02 180 0 0.02 180 0 0.02 180 0 0.02 180 0 0.02 180 0 0.02
211–250 210 0 0.03 210 0 0.03 210 0 0.03 210 0 0.03 210 0 0.03 210 0 0.03
251–300 240 0 0.03 240 0 0.03 240 0 0.03 240 0 0.03 240 0 0.03 240 0 0.03
301–400 275 0 0.04 275 0 0.04 275 0 0.04 275 0 0.04 275 0 0.04 275 0 0.04
401–500 300 0 0.05 300 0 0.05 300 0 0.05 300 0 0.05 300 0 0.05 300 0 0.05
501–600 320 0 0.05 320 0 0.05 320 0 0.05 320 0 0.05 320 0 0.05 320 0 0.05
601–800 350 0 0.06 350 0 0.06 350 0 0.06 350 0 0.06 350 0 0.06 350 0 0.06
801–1000 365 0 0.06 365 0 0.06 365 0 0.06 365 0 0.06 365 0 0.06 365 0 0.06
1001–2000 410 0 0.07 410 0 0.07 410 0 0.07 670 1 0.08 670 1 0.08 670 1 0.08
2001–3000 430 0 0.07 430 0 0.07 705 1 0.09 705 1 0.09 955 2 0.10 955 2 0.10
3001–4000 440 0 0.07 440 0 0.07 730 1 0.09 985 2 0.10 1230 3 0.11 1230 3 0.11
4001–5000 445 0 0.08 740 1 0.10 1000 2 0.11 1000 2 0.11 1250 3 0.12 1480 4 0.12
5001–7000 450 0 0.08 750 1 0.10 1020 2 0.12 1280 3 0.12 1510 4 0.13 1760 5 0.14
7001–10 000 455 0 0.08 760 1 0.10 1040 2 0.12 1530 4 0.14 1790 5 0.14 2240 7 0.16
10 001–20 000 460 0 0.08 775 1 0.10 1330 3 0.14 1820 5 0.16 2300 7 0.17 2780 9 0.18
20 001–50 000 775 1 0.11 1050 2 0.13 1600 4 0.15 2080 5 0.18 3060 10 0.20 4200 15 0.22
50 001–100 000 780 1 0.11 1060 2 0.13 1840 5 0.17 2590 8 0.19 3780 13 0.22 5140 19 0.24
E1994 − 09 (2023)
TABLE A1.2 Single Sampling Table for Lot Tolerance Percent Defective (LTPD) = 1.0 %
NOTE 1—n = sample size; c = acceptance number; AOQL = average outgoing quality limit; “all” indicates that each piece in the lot is to be inspected.
Process Average Process Average Process Average Process Average Process Average Process Average
0 to 0.010 % 0.011 to 0.10 % 0.11 to 0.20 % 0.21 to 0.30 % 0.31 to 0.40 % 0.41 to 0.50 %
Lot Size
AOQL AOQL AOQL AOQL AOQL AOQL
n c n c n c n c n c n c
% % % % % %
1–120 all 0 0 all 0 0 all 0 0 all 0 0 all 0 0 all 0 0
121–150 120 0 0.06 120 0 0.06 120 0 0.06 120 0 0.06 120 0 0.06 120 0 0.06
151–200 140 0 0.08 140 0 0.08 140 0 0.08 140 0 0.08 140 0 0.08 140 0 0.08
201–300 165 0 0.10 165 0 0.10 165 0 0.10 165 0 0.10 165 0 0.10 165 0 0.10
301–400 175 0 0.12 175 0 0.12 175 0 0.12 175 0 0.12 175 0 0.12 175 0 0.12
401–500 180 0 0.13 180 0 0.13 180 0 0.13 180 0 0.13 180 0 0.13 180 0 0.13
501–600 190 0 0.13 190 0 0.13 190 0 0.13 190 0 0.13 190 0 0.13 305 1 0.14
601–800 200 0 0.14 200 0 0.14 200 0 0.14 330 1 0.15 330 1 0.15 330 1 0.15
801–1000 205 0 0.14 205 0 0.14 205 0 0.14 335 1 0.17 335 1 0.17 335 1 0.17
1001–2000 220 0 0.15 220 0 0.15 360 1 0.19 490 2 0.21 490 2 0.21 610 3 0.22
2001–3000 220 0 0.15 375 1 0.20 505 2 0.23 630 3 0.24 745 4 0.26 870 5 0.26
3001–4000 225 0 0.15 380 1 0.20 510 2 0.24 645 3 0.25 880 5 0.28 1000 6 0.29
4001–5000 225 0 0.16 380 1 0.20 520 2 0.24 770 4 0.28 895 5 0.29 1120 7 0.31
5001–7000 230 0 0.15 385 1 0.21 655 3 0.27 780 4 0.29 1020 6 0.32 1260 8 0.34
7001–10 000 230 0 0.16 520 2 0.25 660 3 0.28 910 5 0.32 1150 7 0.34 1500 10 0.37
10 001–20 000 390 1 0.21 525 2 0.26 785 4 0.31 1040 6 0.35 1400 9 0.39 1980 14 0.43
20 001–50 000 390 1 0.21 530 2 0.26 920 5 0.34 1300 8 0.39 1890 13 0.44 2570 19 0.48
50 001–100 000 390 1 0.21 670 3 0.29 1040 6 0.36 1420 9 0.41 2120 15 0.47 3150 23 0.50
TABLE A1.3 Single Sampling Table for Lot Tolerance Percent Defective (LTPD) = 2.0 %
NOTE 1—n = sample size; c = acceptance number; AOQL = average outgoing quality limit; “all” indicates that each piece in the lot is to be inspected.
Process Average Process Average Process Average Process Average Process Average Process Average
0 to 0.02 % 0.03 to 0.20 % 0.21 to 0.40 % 0.41 to 0.60 % 0.61 to 0.80 % 0.81 to 1.00 %
Lot Size
AOQL AOQL AOQL AOQL AOQL AOQL
n c n c n c n c n c n c
% % % % % %
1–75 all 0 0 all 0 0 all 0 0 all 0 0 all 0 0 all 0 0
76–100 70 0 0.16 70 0 0.16 70 0 0.16 70 0 0.16 70 0 0.16 70 0 0.16
101–200 85 0 0.25 85 0 0.25 85 0 0.25 85 0 0.25 85 0 0.25 85 0 0.25
201–300 95 0 0.26 95 0 0.26 95 0 0.26 95 0 0.26 95 0 0.26 95 0 0.26
301–400 100 0 0.28 100 0 0.28 100 0 0.28 160 1 0.32 160 1 0.32 160 1 0.32
401–500 105 0 0.28 105 0 0.28 105 0 0.28 165 1 0.34 165 1 0.34 165 1 0.34
501–600 105 0 0.29 105 0 0.29 175 1 0.34 175 1 0.34 175 1 0.34 235 2 0.36
601–800 110 0 0.29 110 0 0.29 180 1 0.36 240 2 0.40 240 2 0.40 300 3 0.41
801–1000 115 0 0.28 115 0 0.28 185 1 0.37 245 2 0.42 305 3 0.44 305 3 0.44
1001–2000 115 0 0.30 190 1 0.40 255 2 0.47 325 3 0.50 380 4 0.54 440 5 0.56
2001–3000 115 0 0.31 190 1 0.41 260 2 0.48 385 4 0.58 450 5 0.60 565 7 0.64
3001–4000 115 0 0.31 195 1 0.41 330 3 0.54 450 5 0.63 510 6 0.65 690 9 0.70
4001–5000 195 1 0.41 260 2 0.50 335 3 0.54 455 5 0.63 575 7 0.69 750 10 0.74
5001–7000 195 1 0.42 265 2 0.50 335 3 0.55 515 6 0.69 640 8 0.73 870 12 0.80
7001–10 000 195 1 0.42 265 2 0.50 395 4 0.62 520 6 0.69 760 10 0.79 1050 15 0.86
10 001–20 000 200 1 0.42 265 2 0.51 460 5 0.67 650 8 0.77 885 12 0.86 1230 18 0.94
20 001–50 000 200 1 0.42 335 3 0.58 520 6 0.73 710 9 0.81 1060 15 0.93 1520 23 1.0
50 001–100 000 200 1 0.42 335 3 0.58 585 7 0.76 770 10 0.84 1180 17 0.97 1690 26 1.1
E1994 − 09 (2023)
TABLE A1.4 Single Sampling Table for Lot Tolerance Percent Defective (LTPD) = 5.0 %
NOTE 1—n = sample size; c = acceptance number; AOQL = average outgoing quality limit; “all” indicates that each piece in the lot is to be inspected.
Process Average Process Average Process Average Process Average Process Average Process Average
0 to 0.05 % 0.06 to 0.50 % 0.51 to 1.00 % 1.01 to 1.50 % 1.51 to 2.00 % 2.01 to 2.50 %
Lot Size
AOQL AOQL AOQL AOQL AOQL AOQL
n c n c n c n c n c n c
% % % % % %
1–30 all 0 0 all 0 0 all 0 0 all 0 0 all 0 0 all 0 0
31–50 30 0 0.49 30 0 0.49 30 0 0.49 30 0 0.49 30 0 0.49 30 0 0.49
51–100 37 0 0.63 37 0 0.63 37 0 0.63 37 0 0.63 37 0 0.63 37 0 0.63
101–200 40 0 0.74 40 0 0.74 40 0 0.74 40 0 0.74 40 0 0.74 40 0 0.74
201–300 43 0 0.74 43 0 0.74 70 1 0.92 70 1 0.92 95 2 0.99 95 2 0.99
301–400 44 0 0.74 44 0 0.74 70 1 0.99 100 2 1.0 120 3 1.1 145 4 1.1
401–500 45 0 0.75 75 1 0.95 100 2 1.1 100 2 1.1 125 3 1.2 150 4 1.2
501–600 45 0 0.76 75 1 0.98 100 2 1.1 125 3 1.2 150 4 1.3 175 5 1.3
601–800 45 0 0.77 75 1 1.0 100 2 1.2 130 3 1.2 175 5 1.4 200 6 1.4
801–1000 45 0 0.78 75 1 1.0 105 2 1.2 155 4 1.4 180 5 1.4 225 7 1.5
1001–2000 45 0 0.80 75 1 1.0 130 3 1.4 180 5 1.6 230 7 1.7 280 9 1.8
2001–3000 75 1 1.1 105 2 1.3 135 3 1.4 210 6 1.7 280 9 1.9 370 13 2.1
3001–4000 75 1 1.1 105 2 1.3 160 4 1.5 210 6 1.7 305 10 2.0 420 15 2.2
4001–5000 75 1 1.1 105 2 1.3 160 4 1.5 235 7 1.8 330 11 2.0 440 16 2.2
5001–7000 75 1 1.1 105 2 1.3 185 5 1.7 260 8 1.9 350 12 2.2 490 18 2.4
7001–10 000 75 1 1.1 105 2 1.3 185 5 1.7 260 8 1.9 380 13 2.2 535 20 2.5
10 001–20 000 75 1 1.1 135 3 1.4 210 6 1.8 285 9 2.0 425 15 2.3 610 23 2.6
20 001–50 000 75 1 1.1 135 3 1.4 235 7 1.9 305 10 2.1 470 17 2.4 700 27 2.7
50 001–100 000 75 1 1.1 160 4 1.6 235 7 1.9 355 12 2.2 515 19 2.5 770 30 2.8
TABLE A1.5 Single Sampling Table for Lot Tolerance Percent Defective (LTPD) = 10.0 %
NOTE 1—n = sample size; c = acceptance number; AOQL = average outgoing quality limit; “all” indicates that each piece in the lot is to be inspected.
Process Average Process Average Process Average Process Average Process Average Process Average
0 to 0.10 % 0.11 to 1.00 % 1.01 to 2.00 % 2.01 to 3.00 % 3.01 to 4.00 % 4.01 to 5.00 %
Lot Size
AOQL AOQL AOQL AOQL AOQL AOQL
n c n c n c n c n c n c
% % % % % %
1–20 all 0 0 all 0 0 all 0 0 all 0 0 all 0 0 all 0 0
21–50 17 0 1.3 17 0 1.3 17 0 1.3 17 0 1.3 17 0 1.3 17 0 1.3
51–100 20 0 1.5 20 0 1.5 20 0 1.5 33 1 1.7 33 1 1.7 33 1 1.7
101–200 22 0 1.5 22 0 1.5 35 1 2.0 48 2 2.2 48 2 2.2 60 3 2.4
201–300 23 0 1.5 38 1 1.9 50 2 2.3 65 3 2.4 75 4 2.6 85 5 2.7
301–400 23 0 1.5 38 1 2.0 50 2 2.4 65 3 2.5 90 5 2.7 100 6 2.9
401–500 23 0 1.5 38 1 2.0 50 2 2.5 75 4 2.8 90 5 2.9 110 7 3.2
501–600 23 0 1.5 38 1 2.1 65 3 2.7 80 4 3.0 100 6 3.2 125 8 3.3
601–800 23 0 1.6 38 1 2.1 65 3 2.8 90 5 3.1 100 6 3.3 140 9 3.4
801–1000 39 1 2.1 50 2 2.6 65 3 2.8 90 5 3.2 115 7 3.4 150 10 3.7
1001–2000 39 1 2.1 50 2 2.6 80 4 3.1 105 6 3.4 140 9 3.9 195 14 4.4
2001–3000 39 1 2.1 50 2 2.6 80 4 3.1 115 7 3.7 165 11 4.1 230 17 4.7
3001–4000 39 1 2.1 50 2 2.6 90 5 3.4 130 8 3.8 190 13 4.4 255 19 4.8
4001–5000 39 1 2.1 50 2 2.6 90 5 3.5 130 8 3.9 200 14 4.5 270 20 4.9
5001–7000 39 1 2.1 65 3 3.0 105 6 3.6 140 9 4.1 200 14 4.6 295 22 5.0
7001–10 000 39 1 2.2 65 3 3.0 105 6 3.6 150 10 4.2 210 15 4.7 315 24 5.2
10 001-20 000 39 1 2.2 65 3 3.0 120 7 3.7 150 10 4.3 240 17 4.8 340 26 5.4
20 001–50 000 39 1 2.2 80 4 3.2 120 7 3.7 165 11 4.4 260 19 5.0 380 30 5.7
50 001–100 000 39 1 2.2 95 5 3.3 130 8 4.0 180 12 4.4 270 20 5.1 380 30 5.7
E1994 − 09 (2023)
A2. DOUBLE SAMPLING TABLES FOR STATED VALUES OF LOT TOLERANCE PERCENT DEFECTIVE (LTPD) WITH
CONSUMER’S RISK OF 0.10
0.5 % LTPD, 1.0 % LTPD, 2.0 % LTPD, 5.0 % LTPD, 10.0 % LTPD
A2.1 Tables A2.1-A2.5 illustrate double sampling stated
values of lot tolerance percent.
TABLE A2.1 Double Sampling Table for Lot Tolerance Percent Defective (LTPD) = 0.50 %
Process Average Process Average Process Average
0 to 0.005 % 0.006 to 0.050 % 0.051 to 0.100 %
Lot Size
A B C C
Trial 1 Trial 2 Trial 1 Trial 2 AOQL Trial 1 Trial 2
AOQL AOQL
in % in %
n c n n + n c n c n n + n c in % n c n n + n c
1 1 2 1 2 2 1 1 2 1 2 2 1 1 2 1 2 2
D
1–180 all 0 . . . . . . . . . 0 all 0 . . . . . . . . . 0 all 0 . . . . . . . . . 0
181–210 180 . . . . . . . . . 0.02 180 0 . . . . . . . . . 0.02 180 0 . . . . . . . . . 0.02
211–250 210 0 . . . . . . . . . 0.03 210 0 . . . . . . . . . 0.03 210 0 . . . . . . . . . 0.03
251–300 240 0 . . . . . . . . . 0.03 240 0 . . . . . . . . . 0.03 240 0 . . . . . . . . . 0.03
301–400 275 0 . . . . . . . . . 0.04 275 0 . . . . . . . . . 0.04 275 0 . . . . . . . . . 0.04
401–450 290 0 . . . . . . . . . 0.04 290 0 . . . . . . . . . 0.04 290 0 . . . . . . . . . 0.04
451–500 340 0 110 450 1 0.04 340 0 110 450 1 0.04 340 0 110 450 1 0.04
501–550 350 0 130 480 1 0.05 350 0 130 480 1 0.05 350 0 130 480 1 0.05
551–600 360 0 150 510 1 0.05 360 0 150 510 1 0.05 360 0 150 510 1 0.05
601–800 400 0 185 585 1 0.06 400 0 185 585 1 0.06 400 0 185 585 1 0.06
801–1000 430 0 200 630 1 0.07 430 0 200 630 1 0.07 430 0 200 630 1 0.07
1001–2000 490 0 265 755 1 0.08 490 0 265 755 1 0.08 490 0 265 755 1 0.08
2001–3000 520 0 290 810 1 0.09 520 0 290 810 1 0.09 520 0 530 1050 2 0.10
3001–4000 530 0 310 840 1 0.09 530 0 570 1100 2 0.11 530 0 570 1100 2 0.11
4001–5000 540 0 305 845 1 0.09 540 0 580 1120 2 0.11 540 0 830 1370 3 0.12
5001–7000 545 0 315 860 1 0.10 545 0 615 1160 2 0.11 545 0 865 1410 3 0.12
7001–10 000 550 0 330 880 1 0.10 550 0 620 1170 2 0.12 550 0 1130 1680 4 0.14
10 001–20 000 555 0 345 900 1 0.10 555 0 925 1480 3 0.13 555 0 1185 1740 4 0.15
20 001–50 000 560 0 650 1210 2 0.12 560 0 940 1500 3 0.14 900 1 1400 2300 6 0.16
50 001–100 000 560 0 650 1210 2 0.12 560 0 1210 1770 4 0.15 905 1 1655 2560 7 0.17
Process Average Process Average Process Average
0.101 to 0.150 % 0.151 to 0.200 % 0.201 to 0.250 %
Lot Size
A B
C
Trial 1 Trial 2 Trial 1 Trial 2 AOQL Trial 1 Trial 2 AOQL
AOQL
in %
n c n n + n c n c n n + n c in % n c n n + n c in %
1 1 2 1 2 2 1 1 2 1 2 2 1 1 2 1 2 2
D
1–180 all 0 . . . . . . . . . 0 all 0 . . . . . . . . . 0 all 0 . . . . . . . . . 0
181–210 180 0 . . . . . . . . . 0.02 180 0 . . . . . . . . . 0.02 180 0 . . . . . . . . . 0.02
211–250 210 0 . . . . . . . . . 0.03 210 0 . . . . . . . . . 0.03 210 0 . . . . . . . . . 0.03
251–300 240 0 . . . . . . . . . 0.03 240 0 . . . . . . . . . 0.03 240 0 . . . . . . . . . 0.03
301–400 275 0 . . . . . . . . . 0.04 275 0 . . . . . . . . . 0.04 275 0 . . . . . . . . . 0.04
401–450 290 0 . . . . . . . . . 0.04 290 0 . . . . . . . . . 0.04 290 0 . . . . . . . . . 0.04
451–500 340 0 110 450 1 0.04 340 0 110 450 1 0.04 340 0 110 450 1 0.04
501–550 350 0 130 480 1 0.05 350 0 130 480 1 0.05 350 0 130 480 1 0.05
551–600 360 0 150 510 1 0.05 360 0 150 510 1 0.05 360 0 150 510 1 0.05
601–800 400 0 185 585 1 0.06 400 0 185 585 1 0.06 400 0 185 585 1 0.06
801–1000 430 0 200 630 1 0.07 430 0 200 630 1 0.07 430 0 200 630 1 0.07
1001–2000 490 0 500 990 2 0.09 490 0 500 990 2 0.09 490 0 500 990 2 0.09
2001–3000 520 0 530 1050 2 0.10 520 0 760 1280 3 0.11 520 0 980 1500 4 0.11
3001–4000 530 0 810 1340 3 0.11 530 0 1030 1560 4 0.12 840 1 1160 2000 6 0.13
4001–5000 540 0 1060 1600 4 0.13 845 1 1205 2050 6 0.14 845 1 1425 2270 7 0.14
5001–7000 545 0 1105 1650 4 0.13 860 1 1490 2350 7 0.15 860 1 1700 2560 8 0.16
7001–10 000 880 1 1300 2180 6 0.15 880 1 1770 2650 8 0.16 1170 2 2160 3330 11 0.17
10 001–20 000 900 1 1840 2740 8 0.18 1200 2 2250 3450 11 0.19 1740 4 2620 4360 15 0.21
20 001–50 000 1210 2 2330 3540 11 0.20 1500 3 2980 4480 15 0.22 2300 6 4240 6540 24 0.24
50 001–100 000 1210 2 2590 3800 12 0.21 1770 4 3690 5460 19 0.23 2560 7 5420 7980 30 0.26
A
Trial 1: n = first sample size; c = acceptance number for first sample.
1 1
B
Trial 2: n = second sample size; c = acceptance number for first and second samples combined.
2 2
C
AOQL = average outgoing quality limit.
D
“all” indicates that each piece in the lot is to be inspected.
E1994 − 09 (2023)
TABLE A2.2 Double Sampling Table for Lot Tolerance Percent Defective (LTPD) = 1.0 %
Process Average Process Average Process Average
0 to 0.010 % 0.011 to 0.10 % 0.11 to 0.20 %
Lot Size
A B C
Trial 1 Trial 2 Trial 1 Trial 2 AOQL Trial 1 Trial 2 AOQL
AOQL
in %
n c n n + n c n c n n + n c in % n c n n + n c in %
1 1 2 1 2 2 1 1 2 1 2 2 1 1 2 1 2 2
D
1–120 all 0 . . . . . . . . . 0 all 0 . . . . . . . . . 0 all 0 . . . . . . . . . 0
121–150 120 0 . . . . . . . . . 0.06 120 0 . . . . . . . . . 0.06 120 0 . . . . . . . . . 0.06
151–200 140 0 . . . . . . . . . 0.08 140 0 . . . . . . . . . 0.08 140 0 . . . . . . . . . 0.08
201–260 165 0 . . . . . . . . . 0.10 165 0 . . . . . . . . . 0.10 165 0 . . . . . . . . . 0.10
261–300 180 0 75 255 1 0.10 180 0 75 255 1 0.10 180 0 75 255 1 0.10
301–400 200 0 90 290 1 0.12 200 0 90 290 1 0.12 200 0 90 290 1 0.12
401–500 215 0 100 315 1 0.14 215 0 100 315 1 0.14 215 0 100 315 1 0.14
501–600 225 0 115 340 1 0.15 225 0 115 340 1 0.15 225 0 115 340 1 0.15
601–800 235 0 125 360 1 0.16 235 0 125 360 1 0.16 235 0 125 360 1 0.16
801–1000 245 0 135 380 1 0.17 245 0 135 380 1 0.17 245 0 250 495 2 0.19
1001–2000 265 0 155 420 1 0.18 265 0 155 420 1 0.18 265 0 285 550 2 0.21
2001–3000 270 0 160 430 1 0.19 270 0 300 570 2 0.22 270 0 420 690 3 0.25
3001–4000 275 0 160 435 1 0.19 275 0 305 580 2 0.22 275 0 435 710 3 0.25
4001–5000 275 0 165 440 1 0.19 275 0 310 585 2 0.23 275 0 565 840 4 0.28
5001–7000 275 0 170 445 1 0.20 275 0 315 590 2 0.23 275 0 580 855 4 0.29
7001–10 000 280 0 320 600 2 0.24 280 0 460 740 3 0.26 280 0 590 870 4 0.30
10 001–20 000 280 0 325 605 2 0.24 280 0 465 745 3 0.27 450 1 700 1150 6 0.33
20 001–50 000 280 0 325 605 2 0.25 280 0 605 885 4 0.30 450 1 830 1280 7 0.36
50 001–100 000 280 0 325 605 2 0.25 280 0 605 885 4 0.30 450 1 960 1410 8 0.38
Process Average Process Average Process Average
0.21 to 0.30 % 0.31 to 0.40 % 0.41 to 0.50 %
Lot Size
A B
C
Trial 1 Trial 2 AOQL Trial 1 Trial 2 AOQL Trial 1 Trial 2 AOQL
in %
n c n n + n c n c n n + n c in % n c n n + n c in %
1 1 2 1 2 2 1 1 2 1 2 2 1 1 2 1 2 2
D
1–120 all 0 . . . . . . . . . 0 all 0 . . . . . . . . . 0 all 0 . . . . . . . . . 0
121–150 120 0 . . . . . . . . . 0.06 120 0 . . . . . . . . . 0.06 120 0 . . . . . . . . . 0.06
151–200 140 0 . . . . . . . . . 0.08 140 0 . . . . . . . . . 0.08 140 0 . . . . . . . . . 0.08
201–260 165 0 . . . . . . . . . 0.10 165 0 . . . . . . . . . 0.10 165 0 . . . . . . . . . 0.10
261–300 180 0 75 255 1 0.10 180 0 75 255 1 0.10 180 0 75 255 1 0.10
301–400 200 0 90 290 1 0.12 200 0 90 290 1 0.12 200 0 90 290 1 0.12
401–500 215 0 100 315 1 0.14 215 0 100 315 1 0.14 215 0 100 315 1 0.14
501–600 225 0 115 340 1 0.15 225 0 115 340 1 0.15 225 0 205 430 2 0.16
601–800 235 0 230 465 2 0.18 235 0 230 465 2 0.18 235 0 230 465 2 0.18
801–1000 245 0 250 495 2 0.19 245 0 250 495 2 0.19 245 0 250 495 2 0.19
1001–2000 265 0 405 670 3 0.23 265 0 515 780 4 0.24 265 0 515 780 4 0.24
2001–3000 270 0 545 815 4 0.26 430 1 620 1050 6 0.28 430 1 830 1260 8 0.30
3001–4000 435 1 645 1080 6 0.29 435 1 865 1300 8 0.30 580 2 940 1520 10 0.33
4001–5000 440 1 660 1100 6 0.30 440 1 1000 1440 9 0.33 585 2 1075 1660 11 0.35
5001–7000 445 1 785 1230 7 0.33 590 2 990 1580 10 0.36 730 3 1190 1920 13 0.38
7001–10 000 450 1 920 1370 8 0.35 600 2 1240 1840 12 0.39 870 4 1540 2410 17 0.41
10 001–20 000 605 2 1035 1640 10 0.39 745 3 1485 2230 15 0.43 1150 6 1990 3140 23 0.44
20 001–50 000 605 2 1295 1900 12 0.42 885 4 1845 2730 19 0.47 1280 7 2600 3880 29 0.52
50 001–100 000 605 2 1545 2150 14 0.44 885 4 2085 2970 21 0.49 1410 8 3280 4690 36 0.55
A
Trial 1: n = first sample size; c = acceptance number for first sample.
1 1
B
Trial 2: n = second sample size; c = acceptance number for first and second samples combined.
2 2
C
AOQL = average outgoing quality limit.
D
“all” indicates that each piece in the lot is to be inspected.
E1994 − 09 (2023)
TABLE A2.3 Double Sampling Table for Lot Tolerance Percent Defective (LTPD) = 2.0 %
Process Average Process Average Process Average
0 to 0.02 % 0.03 to 0.20 % 0.21 to 0.40 %
Lot Size
A B C
Trial 1 Trial 2 Trial 1 Trial 2 AOQL Trial 1 Trial 2 AOQL
AOQL
in %
n c n n + n c n c n n + n c in % n c n n + n c in %
1 1 2 1 2 2 1 1 2 1 2 2 1 1 2 1 2 2
D
1–75 all 0 . . . . . . . . . 0 all 0 . . . . . . . . . 0 all 0 . . . . . . . . . 0
76–100 70 0 . . . . . . . . . 0.16 70 0 . . . . . . . . . 0.16 70 0 . . . . . . . . . 0.16
101–200 85 0 . . . . . . . . . 0.25 85 0 . . . . . . . . . 0.25 85 0 . . . . . . . . . 0.25
201–300 115 0 50 165 1 0.29 115 0 50 165 1 0.29 115 0 50 165 1 0.29
301–400 120 0 60 180 1 0.32 120 0 60 180 1 0.32 120 0 60 180 1 0.32
401–500 125 0 65 190 1 0.33 125 0 65 190 1 0.33 125 0 120 245 2 0.37
501–600 125 0 70 195 1 0.34 125 0 70 195 1 0.34 125 0 130 255 2 0.39
601–800 130 0 75 205 1 0.35 130 0 75 205 1 0.35 130 0 125 265 2 0.41
801–1000 135 0 75 210 1 0.36 135 0 140 275 2 0.42 135 0 140 275 2 0.42
1001–2000 135 0 85 220 1 0.38 135 0 155 290 2 0.45 135 0 220 355 3 0.50
2001–3000 140 0 85 225 1 0.39 140 0 155 295 2 0.46 140 0 285 425 4 0.56
3001–4000 140 0 85 225 1 0.40 140 0 225 365 3 0.52 140 0 290 430 4 0.57
4001–5000 140 0 160 300 2 0.47 140 0 230 370 3 0.53 140 0 360 500 5 0.61
5001–7000 140 0 160 300 2 0.48 140 0 230 370 3 0.54 140 0 365 505 5 0.62
7001–10 000 140 0 160 300 2 0.48 140 0 235 375 3 0.54 225 1 350 575 6 0.66
10 001–20 000 140 0 165 305 2 0.49 140 0 235 375 3 0.54 225 1 415 640 7 0.71
20 001–50 000 140 0 165 305 2 0.49 140 0 305 445 4 0.59 225 1 480 705 8 0.75
50 001–100 000 140 0 165 305 2 0.49 140 0 305 445 4 0.60 225 1 545 770 9 0.78
Process Average Process Average Process Average
0.41 to 0.60 % 0.61 to 0.80 % 0.81 to 1.00 %
Lot Size
A B C
Trial 1 Trial 2 Trial 1 Trial 2 AOQL Trial 1 Trial 2 AOQL
AOQL
in %
n c n n + n c n c n n + n c in % n c n n + n c in %
1 1 2 1 2 2 1 1 2 1 2 2 1 1 2 1 2 2
D
1–75 all 0 . . . . . . . . . 0 all 0 . . . . . . . . . 0 all 0 . . . . . . . . . 0
76–100 70 0 . . . . . . . . . 0.16 70 0 . . . . . . . . . 0.16 70 0 . . . . . . . . . 0.16
101–200 85 0 . . . . . . . . 0.25 85 0 . . . . . . . . . 0.25 85 0 . . . . . . . . . 0.25
201–300 115 0 50 165 1 0.29 115 0 50 165 1 0.29 115 0 50 165 1 0.29
301–400 120 0 115 235 2 0.34 120 0 115 235 2 0.34 120 0 115 235 2 0.34
401–500 125 0 120 245 2 0.37 125 0 120 245 2 0.37 125 0 120 245 2 0.37
501–600 125 0 130 255 2 0.39 125 0 185 310 3 0.41 125 0 185 310 3 0.41
601–800 130 0 195 325 3 0.44 130 0 250 380 4 0.45 130 0 250 380 4 0.45
801–1000 135 0 200 335 3 0.46 135 0 255 390 4 0.48 210 1 290 500 6 0.54
1001–2000 135 0 285 420 4 0.54 220 1 375 595 7 0.62 220 1 485 705 9 0.65
2001–3000 225 1 385 610 7 0.65 295 2 435 730 9 0.69 360 3 535 895 12 0.72
3001–4000 225 1 455 680 8 0.69 295 2 555 850 11 0.74 365 3 715 1080 15 0.77
4001–5000 225 1 460 685 8 0.70 300 2 620 920 12 0.77 435 4 775 1210 17 0.81
5001–7000 300 2 450 750 9 0.74 370 3 680 1050 14 0.82 505 5 935 1440 21 0.89
7001–10 000 300 2 520 820 10 0.77 375 3 735 1110 15 0.85 575 6 1055 1630 24 0.95
10 001–20 000 305 2 645 950 12 0.83 375 3 935 1310 18 0.92 640 7 1240 1880 28 1.0
20 001–50 000 305 2 715 1020 13 0.86 445 4 1045 1490 21 0.98 705 8 1635 2340 36 1.1
50 001–100 000 305 2 830 1135 15 0.90 510 5 1150 1660 24 1.0 770 9 1850 2620 41 1.2
A
Trial 1: n = first sample size; c = acceptance number for first sample.
1 1
B
Trial 2: n = second sample size; c = acceptance number for first and second samples combined.
2 2
C
AOQL = average outgoing quality limit.
D
“all” indicates that each piece in the lot is to be inspected.
E1994 − 09 (2023)
TABLE A2.4 Double Sampling Table for Lot Tolerance Percent Defective (LTPD) = 5.0 %
Process Average Process Average Process Average
0 to 0.05 % 0.06 to 0.50 % 0.51 to 1.00 %
Lot Size
A B C
Trial 1 Trial 2 Trial 1 Trial 2 AOQL Trial 1 Trial 2 AOQL
AOQL
in %
n c n n + n c n c n n + n c in % n c n n + n c in %
1 1 2 1 2 2 1 1 2 1 2 2 1 1 2 1 2 2
D
1–30 all 0 . . . . . . . . . 0 all 0 . . . . . . . . . 0 all 0 . . . . . . . . . 0
31–50 30 0 . . . . . . . . . 0.49 30 0 . . . . . . . . . 0.49 30 0 . . . . . . . . . 0.49
51–75 38 0 . . . . . . . . . 0.59 38 0 . . . . . . . . . 0.59 38 0 . . . . . . . . . 0.59
76–100 44 0 21 65 1 0.64 44 0 21 65 1 0.64 44 0 21 65 1 0.64
101–200 49 0 26 75 1 0.84 49 0 26 75 1 0.84 49 0 26 75 1 0.84
201–300 50 0 30 80 1 0.91 50 0 30 80 1 0.91 50 0 55 105 2 1.0
301–400 55 0 30 85 1 0.92 55 0 55 110 2 1.1 55 0 55 110 2 1.1
401–500 55 0 30 85 1 0.93 55 0 55 110 2 1.1 55 0 80 135 3 1.2
501–600 55 0 30 85 1 0.94 55 0 60 115 2 1.1 55 0 85 140 3 1.2
601–800 55 0 35 90 1 0.95 55 0 65 120 2 1.1 55 0 85 140 3 1
...