ASTM E1994-98(2003)
(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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An American National Standard
Designation:E1994–98 (Reapproved 2003)
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
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 acceptance sampling, the consumer wishes the probability of
acceptancetoberestrictedtoaspecifiedlowvalue,specifically
1.1 This practice is primarily a statement of principals for
10 % for this practice. This is also referred to by the more
the guidance of ASTM technical committees and others in the
general term limiting quality taken at 10 % consumer risk.
use of Average Outgoing Quality Limit, AOQL, and Lot
3.2 average outgoing quality (AOQ)—the average percent
Tolerance Percent Defective, LTPD, sampling plans for deter-
defective of outgoing product including all accepted lots or
mining acceptable of lots of product.
batches,afteranydefectiveunitsfoundinthemarereplacedby
2. Referenced Documents
acceptableunits,plusalllotsorbatcheswhicharenotaccepted
after such lots or batches have been effectively 100 % in-
2.1 ASTM Standards:
spected and all defective units replaced by acceptable units.
E 178 Practice for Dealing with Outlying Observations
3.3 average outgoing quality limit (AOQL)—the maximum
E 456 Terminology Relating to Quality and Statistics
of the AOQs for all possible incoming percentages defective
3. Terminology
for the process, for a given acceptance sampling plan.
3.4 lot quality protection—a type of protection in which
3.1 lot tolerance percent defective (LTPD)—the percentage
there is prescribed some chosen value of limiting percent
of defective units in a batch or lot for which, for purposes of
defective in a lot (lot tolerance percent defective, (LTPD)) and
also some chosen value for the probability (called the consum-
This practice is under the jurisdiction of ASTM Committee E11.30 on Data
er’s risk) of accepting a submitted lot that has a percent
Analysis.
defective equal to the lot tolerance percent defective.
Current edition approved Oct. 1, 2003. Published January 1999.
3.5 average quality protection—a type of protection in
Available from John Wiley and Sons, Inc., 605 Third Ave., New York, NY
10158.
whichthereisprescribedsomechosenvalueofaveragepercent
Dodge, H.F. and Romig, H.G., “A Method of Sampling Inspection,” The Bell
defective in the product after inspection (average outgoing
System Technical Journal, Vol 8, No. 10, 1924, pp. 613–631.
quality limit (AOQL), that shall not be exceeded in the long
Dodge, H.F. and Romig, H.G., “Single Sampling and Double Sampling
InspectionTables,TheBellSystemTechnicalJournal,Vol20,No.1,1941,pp.1–61. run no matter what may be the level of percent defective in the
Schilling, E.G., “Acceptance Sampling in Quality Control,” Marcel Dekker
product submitted to the inspector.
Inc., NY, 1982, pp. 372–399.
Annual Book of ASTM Standards, Vol 14.02.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
E1994–98 (2003)
3.6 consumer’s risk—the probability that a lot whose per- product is good enough to warrant the introduction of sam-
centage defective is equal to the LTPD will be accepted by the pling. The economies of sampling will be realized, of course,
plan. only insofar as the percent defective in submitted product is
such that the acceptance criteria of the selected sampling plan
will be met. A statistical analysis of past inspection results
4. Significance and Use
should first be made, therefore, in order to determine existing
4.1 Two general types of tables (Note 1) are given, one
levels and fluctuations in the percent defective for the charac-
based on the concept of lot tolerance, LTPD, and the other on
teristicorthegroupofcharacteristicsunderconsideration.This
AOQL. The broad conditions under which the different types
provides information with respect to the degree of control as
have been found best adapted are indicated below.
well as the usual level of percent defective to be expected
4.1.1 For each of the types, tables are provided both for
under existing conditions. Determine a value from this and
single sampling and for double sampling. Each of the indi-
other information for the process average percent defective
vidual tables constitutes a collection of solutions to the
that should be used in applying the selected sampling table, if
problem of minimizing the over-all amount of inspection.
sampling is to be introduced.
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
5. Procedure
AOQL tables are often conservative.
5.1 Twodistinctmethodsofinspectionareemployed,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 inAnnexA3 andAnnexA4) 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.
screensoutdefectivesintheproductsubmittedtotheinspector.
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 Givenaspecificproblemofreplacinga100 %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 andsecondsamplescombinedexceedsc ,inspectallthepieces
on the type of protection desired, to select the desired limit of in the remainder of the lot.
percent defective lot tolerance (LTPD) orAOQLvalue 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.
E1994–98 (2003)
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-
5.3.3.4 As a manufacturer trying to meet a consumer’s
dure. These steps are shown in the following numbered
stated AQL (Note 2), use for final inspection an AOQL plan
paragraphs.
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
NOTE 2—AQL = Acceptable Quality Level, as used to index certain
single characteristic or selected group of characteristics of like
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.
5.3.4.1 For LTPD, choose the value of percent defective for
5.3.1.5 Include in any group characteristics of essentially
lot acceptance not more than 10 % of the time (that is, reject at
the same degree of seriousness. If two degrees of seriousness
least 90 % of the time).
are involved, say major and minor, keep all majors together in
5.3.4.2 For AOQL, choose the value of average percent
one group and all minors in a second group.
defective in product after inspection that should not be ex-
5.3.1.6 Consider these plans applicable to all basic types of
ceeded.
inspection for manufactured products receiving, process, and
5.3.4.3 In choosing a value of LTPD (or AOQL), consider
final and to the inspection of administrative and clerical
and compare the cost of inspection with the economic loss that
products as in paper-work quality control.
would ensue if quality as bad as the LTPD were accepted often
5.3.2 Decide what is to constitute a lot for purposes of
(or if the average level of percent defective were greater than
sampling inspection.
theAOQL). Even though the evaluation of economic loss may
5.3.2.1 So far as practicable, require that individual lots
be difficult, relative values for different levels of percent
presented for acceptance comprise essentially homogeneous
defective may often be determined.
material from a common source.
5.3.5 Choose between single sampling and double sam-
5.3.2.2 If presented material comes from two or mo
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