ASTM E1994-09(2013)
(Practice)Standard Practice for Use of Process Oriented AOQL and LTPD Sampling Plans
Standard Practice for Use of Process Oriented AOQL and LTPD Sampling Plans
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parts where the inspection lots tend to lose their identity by merger in a common storeroom from which quantities are withdrawn on o...
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.
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Designation: E1994 − 09 (Reapproved 2013) 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
acontinuingsupplyofproducts.ThesocalledAOQLplansprovideameansfordispositionofproduct
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
1.1 This practice is primarily a statement of principals for 2.1 ASTM Standards:
the guidance of ASTM technical committees and others in the E178 Practice for Dealing With Outlying Observations
use of Average Outgoing Quality Limit, AOQL, and Lot E456 Terminology Relating to Quality and Statistics
Tolerance Percent Defective, LTPD, sampling plans for deter-
3. Terminology
mining 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 quality protection—a type of protection in
ization established in the Decision on Principles for the
whichthereisprescribedsomechosenvalueofaveragepercent
Development of International Standards, Guides and Recom-
defective in the product after inspection (average outgoing
mendations issued by the World Trade Organization Technical
quality limit (AOQL), that shall not be exceeded in the long
Barriers to Trade (TBT) Committee.
run no matter what may be the level of percent defective in the
1 product submitted to the inspector.
This practice is under the jurisdiction ofASTM Committee E11 on Quality and
Statistics and is the direct responsibility of Subcommittee E11.30 on Statistical
3.1.2 average outgoing quality (AOQ)—the average percent
Quality Control.
defective of outgoing product including all accepted lots or
Current edition approved April 1, 2013. Published April 2013. Originally
batches,afteranydefectiveunitsfoundinthemarereplacedby
approved in 1998. Last previous edition approved in 2009 as E1994 – 09. DOI:
10.1520/E1994-09R13.
acceptableunits,plusalllotsorbatcheswhicharenotaccepted
Available from John Wiley and Sons, Inc., 605 Third Ave., New York, NY
after such lots or batches have been effectively 100 % in-
10158.
spected and all defective units replaced by acceptable units.
Dodge, H. F. and Romig, H. G., “AMethod 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 service@astm.org. 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 (2013)
3.1.3 average outgoing quality limit (AOQL)—the maxi- the elimination of defectives found in samples. Lots that fail to
mum of the AOQs for all possible incoming percentages be accepted by sample are completely cleared of defectives.
defectivefortheprocess,foragivenacceptancesamplingplan. 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—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 Givenaspecificproblemofreplacinga100 %screening
inspection by a sampling inspection, the first step is to decide
3.1.5 lot tolerance percent defective (LTPD)—for purposes
on the type of protection desired, to select the desired limit of
of acceptance sampling, the percentage of defective units in a
percent defective lot tolerance (LTPD) orAOQLvalue for that
lot for which the consumer has a stated low probability of
type of protection, and to choose between single and double
acceptance of the lot.
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—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
teristicorthegroupofcharacteristicsunderconsideration.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.
that should be used in applying the selected sampling table, if
Because each line in the tables covers a range of lot sizes, the
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
5.1 Twodistinctmethodsofinspectionareemployed,single
reproduced by permission of John R. Wiley and Sons. More extensive
tables and discussion of the methods will be found in that text. sampling and double sampling. In single sampling only one
sample is permitted before a decision is reached regarding the
4.2 The sampling tables based on lot quality protection
disposition of the lot, and the acceptance criterion is expressed
(LTPD) (the tables in Annex A1 and Annex A2) are perhaps
as an acceptance number, c. In double sampling, a second
best adapted to conditions where interest centers on each lot
sample is permitted and two acceptance numbers are used; the
separately, for example, where the individual lot tends to retain
first, c , applying to the observed number of defectives for the
its identity either from a shipment or a service standpoint. 1
first sample alone and the second, c , applying to the observed
These tables have been found particularly useful in inspections
number of defectives for the first and second samples com-
made by the ultimate consumer or a purchasing agent for lots
bined. The specific procedures assumed in the development of
or shipments purchased more or less intermittently.
the tables are as follows:
4.3 The sampling tables based on average quality protection
5.1.1 Single Sampling Inspection Procedure:
(AOQL) (the tables in AnnexA3 and AnnexA4) are especially
5.1.1.1 Inspect a sample of n pieces.
adapted for use where interest centers on the average quality of
5.1.1.2 If the number of defectives found in thesampledoes
product after inspection rather than on the quality of each
not exceed c, the acceptance number, accept the lot.
individual lot and where inspection is, therefore, intended to
5.1.1.3 If the number of defectives found in the sample
serve, if necessary, as a partial screen for defective pieces. The
exceeds c, inspect all the pieces in the remainder of the lot.
latter point of view has been found particularly helpful, for
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:
5.1.2.1 Inspect a first sample of n pieces.
4.4 The plans based on average quality protection (AOQL)
consider the degree to which the entire inspection procedure 5.1.2.2 If the number of defectives found in the first sample
screensoutdefectivesintheproductsubmittedtotheinspector. does not exceed c , the acceptance number for the first sample,
Lots accepted by sample undergo a partial screening through accept the lot.
E1994 − 09 (2013)
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 ChooseAOQLifinterestcentersonthegenerallevel
5.1.2.6 If the total number of defectives found in the first
of quality of product after inspection. AOQL plans have been
andsecondsamplescombinedexceeds c ,inspectallthepieces
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
withanAOQLvalueequaltothespecifiedAQLvalue,inorder
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 it
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