ASTM E1994-98
(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
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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Standards Content (Sample)
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Designation: E 1994 – 98
Standard Practice for
Use of Process Oriented AOQL and LTPD Sampling Plans
This standard is issued under the fixed designation E 1994; 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 (e) 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 3.2 average outgoing quality (AOQ)—the average percent
defective of outgoing product including all accepted lots or
1.1 This practice is primarily a statement of principals for
batches, after any defective units found in them are replaced by
the guidance of ASTM technical committees and others in the
acceptable units, plus all lots or batches which are not accepted
use of Average Outgoing Quality Limit, AOQL, and Lot
after such lots or batches have been effectively 100 % in-
Tolerance Percent Defective, LTPD, sampling plans for deter-
spected and all defective units replaced by acceptable units.
mining acceptable of lots of product.
3.3 average outgoing quality limit (AOQL)—the maximum
2. Referenced Documents of the AOQs for all possible incoming percentages defective
for the process, for a given acceptance sampling plan.
2.1 ASTM Standards:
3.4 lot quality protection—a type of protection in which
E 178 Practice for Dealing with Outlying Observations
there is prescribed some chosen value of limiting percent
E 456 Terminology Relating to Quality and Statistics
defective in a lot (lot tolerance percent defective, (LTPD)) and
3. Terminology
also some chosen value for the probability (called the consum-
er’s risk) of accepting a submitted lot that has a percent
3.1 lot tolerance percent defective (LTPD)—the percentage
defective equal to the lot tolerance percent defective.
of defective units in a batch or lot for which, for purposes of
3.5 average quality protection—a type of protection in
acceptance sampling, the consumer wishes the probability of
which there is prescribed some chosen value of average percent
acceptance to be restricted to a specified low value, specifically
defective in the product after inspection (average outgoing
10 % for this practice. This is also referred to by the more
quality limit (AOQL), that shall not be exceeded in the long
general term limiting quality taken at 10 % consumer risk.
run no matter what may be the level of percent defective in the
product submitted to the inspector.
This practice is under the jurisdiction of ASTM Committee E-11 on Quality and
3.6 consumer’s risk—the probability that a lot whose per-
Statistics and is the direct responsibility of Subcommittee E11.10 on Sampling and
centage defective is equal to the LTPD will be accepted by the
Data Analysis.
Current edition approved Nov. 10, 1998. Published January 1999.
plan.
Available from John Wiley and Sons, Inc., 605 Third Ave., New York, NY
10158.
4. Significance and Use
Dodge, H.F. and Romig, H.G., “A Method of Sampling Inspection,” The Bell
4.1 Two general types of tables (Note 1) are given, one
System Technical Journal, Vol 8, No. 10, 1924, pp. 613–631.
Dodge, H.F. and Romig, H.G., “Single Sampling and Double Sampling
based on the concept of lot tolerance, LTPD, and the other on
Inspection Tables, The Bell System Technical Journal, Vol 20, No. 1, 1941, pp. 1–61.
AOQL. The broad conditions under which the different types
Schilling, E.G., “Acceptance Sampling in Quality Control,” Marcel Dekker
have been found best adapted are indicated below.
Inc., NY, 1982, pp. 372–399.
Annual Book of ASTM Standards, Vol 14.02. 4.1.1 For each of the types, tables are provided both for
Copyright © ASTM, 100 Barr Harbor Drive, West Conshohocken, PA 19428-2959, United States.
NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
E 1994
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
5. Procedure
AOQL tables are often conservative.
5.1 Two distinct methods of inspection are employed, single
NOTE 1—Tables in Annex A1-Annex A4 and parts of the text are
sampling and double sampling. In single sampling only one
reproduced by permission of John R. Wiley and Sons. More extensive
sample is permitted before a decision is reached regarding the
tables and discussion of the methods will be found in that text.
disposition of the lot, and the acceptance criterion is expressed
4.2 The sampling tables based on lot quality protection
as an acceptance number, c. In double sampling, a second
(LTPD) (the tables in Annex A1 and Annex A2) are perhaps
sample is permitted and two acceptance numbers are used; the
best adapted to conditions where interest centers on each lot
first, c , applying to the observed number of defectives for the
separately, for example, where the individual lot tends to retain
first sample alone and the second, c , applying to the observed
its identity either from a shipment or a service standpoint.
number of defectives for the first and second samples com-
These tables have been found particularly useful in inspections
bined. The specific procedures assumed in the development of
made by the ultimate consumer or a purchasing agent for lots
the tables are as follows:
or shipments purchased more or less intermittently.
5.1.1 Single Sampling Inspection Procedure:
4.3 The sampling tables based on average quality protection
5.1.1.1 Inspect a sample of n pieces.
(AOQL) (the tables in Annex A3 and Annex A4) are especially
5.1.1.2 If the number of defectives found in the sample does
adapted for use where interest centers on the average quality of
not exceed c, the acceptance number, accept the lot.
product after inspection rather than on the quality of each
5.1.1.3 If the number of defectives found in the sample
individual lot and where inspection is, therefore, intended to
exceeds c, inspect all the pieces in the remainder of the lot.
serve, if necessary, as a partial screen for defective pieces. The
5.1.1.4 Regardless of whether or not the lot was accepted,
latter point of view has been found particularly helpful, for
correct or replace all defective pieces found in the sample as
example, in consumer inspections of continuing purchases of
well as in any subsequent inspection of the remainder of the
large quantities of a product and in manufacturing process
lot.
inspections of parts where the inspection lots tend to lose their
5.1.2 Double Sampling Inspection Procedure:
identity by merger in a common storeroom from which
5.1.2.1 Inspect a first sample of n pieces.
quantities are withdrawn on order as needed.
5.1.2.2 If the number of defectives found in the first sample
4.4 The plans based on average quality protection (AOQL)
does not exceed c , the acceptance number for the first sample,
consider the degree to which the entire inspection procedure
accept the lot.
screens out defectives in the product submitted to the inspector. 5.1.2.3 If the number of defectives found in the first sample
Lots accepted by sample undergo a partial screening through
exceeds c , the acceptance number for the combined first and
the elimination of defectives found in samples. Lots that fail to second samples, inspect all the pieces in the remainder of the
be accepted by sample are completely cleared of defectives.
lot.
Obviously, this requires a nondestructive test. The over-all 5.1.2.4 If the number of defectives found in the first sample
result is some average percent defective in the product as it
exceeds c , but does not exceed c , inspect a second sample of
1 2
leaves the inspector, termed the average outgoing quality,
n pieces.
which depends on the level of percent defective for incoming
5.1.2.5 If the total number of defectives found in the first
product and the proportion of total defectives that are screened
and second samples combined does not exceed c , accept the
out.
lot.
4.5 Given a specific problem of replacing a 100 % screening 5.1.2.6 If the total number of defectives found in the first
inspection by a sampling inspection, the first step is to decide and second samples combined exceeds c , inspect all the pieces
on the type of protection desired, to select the desired limit of in the remainder of the lot.
percent defective lot tolerance (LTPD) or AOQL value for that 5.1.2.7 Regardless of whether or not the lot was accepted,
type of protection, and to choose between single and double correct or replace all defective pieces found in either sample as
sampling. This results in the selection of one of the appended
well as any in subsequent inspection or the remainder of the
tables. The second step is to determine whether the quality of lot.
product is good enough to warrant the introduction of sam-
5.2 In choosing a sampling plan for a particular application,
pling. The economies of sampling will be realized, of course, a number of decisions must be made which depend on the
only insofar as the percent defective in submitted product is conditions under which the plan is to be used. The accompa-
such that the acceptance criteria of the selected sampling plan nying Sequence of Steps gives an outline of a typical proce-
will be met. A statistical analysis of past inspection results dure. These steps are shown in the following numbered
should first be made, therefore, in order to determine existing paragraphs.
levels and fluctuations in the percent defective for the charac- 5.3 Sequence of Steps:
teristic or the group of characteristics under consideration. This 5.3.1 Decide what characteristics will be included in the
provides information with respect to the degree of control as inspection.
well as the usual level of percent defective to be expected 5.3.1.1 If advantageous, use a separate sampling plan for a
NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
E 1994
systems of sampling plans, signifying what the consumer feels to be the
single characteristic or selected group of characteristics of like
maximum percent defective that, for sampling purposes, can be consid-
importance. Sampling need not wait until all characteristics
ered satisfactory as a process average.
have good quality.
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
under procedures acceptable to the consumer and to provide
5.3.1.4 In general, combine at one inspection station char-
suitable certifications of work performed.
acteristics subject to essentially similar inspection operations,
5.3.4 Choose a suitable figure of quality (LTPD or AOQL)
for example, all visual inspection items together, all gauging,
for the sampling plan
or all testing. Visual and gauging inspection operations often
5.3.4.1 For LTPD, choose the value of percent defective for
combine well.
lot acceptance not more than 10 % of the time (that is, reject at
5.3.1.5 Include in any group characteristics of essentially
least 90 % of the time).
the same degree of seriousness. If two degrees of seriousness
5.3.4.2 For AOQL, choose the value of average percent
are involved, say major and minor, keep all majors together in
defective in product after inspection that should not be ex-
one group and all minors in a second group.
ceeded.
5.3.1.6 Consider these plans applicable to all basic types of
5.3.4.3 In choosing a value of LTPD (or AOQL), consider
inspection for manufactured products receiving, process, and
and compare the cost of inspection with the economic loss that
final and to the inspection of administrative and clerical
would ensue if quality as bad as the LTPD were accepted often
products as in paper-work quality control.
(or if the average level of percent defective were greater than
5.3.2 Decide what is to constitute a lot for purposes of
the AOQL). Even though the evaluation of economic loss may
sampling inspection.
be difficult, relative values for different levels of percent
5.3.2.1 So far as practicable, require that individual lots
defective may often be determined.
presented for acceptance comprise essentially homogeneous
5.3.5 Choose between single sampling and double sam-
material from a common source.
pling.
5.3.2.2 If presented material comes from two or more direct
5.3.5.1 In general, for economy in overall inspection effort,
sources not under a commo
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