Designation: E1994 − 09 (Reapproved 2013) An American National StandardStandard Practice forUse of Process Oriented AOQL and LTPD Sampling Plans1This standard is issued under the fixed designation E1994; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.INTRODUCTIONThis standard is an abbreviated compilation of the sampling plans presented by H.F. Dodge andH.G. Romig in their classic development of sampling plans for use with the process associated witha continuing supply of products. The so calledAOQL plans provide a means for disposition of productwhether or not the process is in control as well as incentives for process improvement in terms ofreduced sample size as the process average percent defective is lowered. In addition, so called LTPDplans are provided for use with individual lots of product, not necessarily associated with a processstream.The sampling plans and parts of the text given here are taken from the Wiley Classics LibraryEdition of the Dodge-Romig tables (copyright 1998). Additional tables and detailed discussion of theplans, OC curves, and their derivation will be found in that text.2The theoretical development of theDodge-Roming plans will be found in Volumes 8 and 20 of the Bell System Technical Journal3,4andan amplification of the plans is given in Acceptance Sampling in Quality Control.51. Scope1.1 This practice is primarily a statement of principals forthe guidance of ASTM technical committees and others in theuse of Average Outgoing Quality Limit, AOQL, and LotTolerance Percent Defective, LTPD, sampling plans for deter-mining acceptable of lots of product.2. Referenced Documents2.1 ASTM Standards:6E178 Practice for Dealing With Outlying ObservationsE456 Terminology Relating to Quality and Statistics3. Terminology3.1 Definitions—Terminology E456 provides a more exten-sive list of terms in E11 standards.3.2 average quality protection—a type of protection inwhich there is prescribed some chosen value of average percentdefective in the product after inspection (average outgoingquality limit (AOQL), that shall not be exceeded in the longrun no matter what may be the level of percent defective in theproduct submitted to the inspector.3.3 average outgoing quality (AOQ)—the average percentdefective of outgoing product including all accepted lots orbatches, after any defective units found in them are replaced byacceptable units, plus all lots or batches which are not acceptedafter such lots or batches have been effectively 100 % in-spected and all defective units replaced by acceptable units.3.4 average outgoing quality limit (AOQL)—the maximumof the AOQs for all possible incoming percentages defectivefor the process, for a given acceptance sampling plan.3.5 lot quality protection—a type of protection in whichthere is prescribed some chosen value of limiting percentdefective in a lot (lot tolerance percent defective, (LTPD)) andalso some chosen value for the probability (called the consum-er’s risk) of accepting a submitted lot that has a percentdefective equal to the lot tolerance percent defective.3.6 lot tolerance percent defective (LTPD)—for purposes ofacceptance sampling, the percentage of defective units in a lotfor which the consumer has a stated low probability ofacceptance of the lot.1This practice is under the jurisdiction of ASTM Committee E11 on Quality andStatistics and is the direct responsibility of Subcommittee E11.30 on StatisticalQuality Control.Current edition approved April 1, 2013. Published April 2013. Originallyapproved in 1998. Last previous edition approved in 2009 as E1994 – 09. DOI:10.1520/E1994-09R13.2Available from John Wiley and Sons, Inc., 605 Third Ave., New York, NY10158.3Dodge, H. F. and Romig, H. G., “A Method of Sampling Inspection,” The BellSystem Technical Journal, Vol 8 , No. 10, 1924, pp. 613–631.4Dodge, H. F. and Romig, H. G., “Single Sampling and Double SamplingInspection Tables,” The Bell System Technical Journal, Vol 20, No. 1, 1941, pp.1–61.5Schilling, E. G., Acceptance Sampling in Quality Control, Marcel Dekker Inc.,NY, 1982, pp. 372–399.6For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.7 Definitions of Terms Specific to This Standard:3.7.1 consumer’s risk—the probability that a lot whosepercentage defective is equal to the LTPD will be accepted bythe plan.4. Significance and Use4.1 Two general types of tables (Note 1) are given, onebased on the concept of lot tolerance, LTPD, and the other onAOQL. The broad conditions under which the different typeshave been found best adapted are indicated below.4.1.1 For each of the types, tables are provided both forsingle sampling and for double sampling. Each of the indi-vidual tables constitutes a collection of solutions to theproblem of minimizing the over-all amount of inspection.Because each line in the tables covers a range of lot sizes, theAOQL values in the LTPD tables and the LTPD values in theAOQL tables are often conservative.NOTE 1—Tables in Annex A1-Annex A4 and parts of the text arereproduced by permission of John R. Wiley and Sons. More extensivetables 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 perhapsbest adapted to conditions where interest centers on each lotseparately, for example, where the individual lot tends to retainits identity either from a shipment or a service standpoint.These tables have been found particularly useful in inspectionsmade by the ultimate consumer or a purchasing agent for lotsor shipments purchased more or less intermittently.4.3 The sampling tables based on average quality protection(AOQL) (the tables in AnnexA3 and AnnexA4) are especiallyadapted for use where interest centers on the average quality ofproduct after inspection rather than on the quality of eachindividual lot and where inspection is, therefore, intended toserve, if necessary, as a partial screen for defective pieces. Thelatter point of view has been found particularly helpful, forexample, in consumer inspections of continuing purchases oflarge quantities of a product and in manufacturing processinspections of parts where the inspection lots tend to lose theiridentity by merger in a common storeroom from whichquantities are withdrawn on order as needed.4.4 The plans based on average quality protection (AOQL)consider the degree to which the entire inspection procedurescreens out defectives in the product submitted to the inspector.Lots accepted by sample undergo a partial screening throughthe elimination of defectives found in samples. Lots that fail tobe accepted by sample are completely cleared of defectives.Obviously, this requires a nondestructive test. The over-allresult is some average percent defective in the product as itleaves the inspector, termed the average outgoing quality,which depends on the level of percent defective for incomingproduct and the proportion of total defectives that are screenedout.4.5 Given a specific problem of replacing a 100 % screeninginspection by a sampling inspection, the first step is to decideon the type of protection desired, to select the desired limit ofpercent defective lot tolerance (LTPD) or AOQL value for thattype of protection, and to choose between single and doublesampling. This results in the selection of one of the appendedtables. The second step is to determine whether the quality ofproduct is good enough to warrant the introduction of sam-pling. The economies of sampling will be realized, of course,only insofar as the percent defective in submitted product issuch that the acceptance criteria of the selected sampling planwill be met. A statistical analysis of past inspection resultsshould first be made, therefore, in order to determine existinglevels and fluctuations in the percent defective for the charac-teristic or the group of characteristics under consideration. Thisprovides information with respect to the degree of control aswell as the usual level of percent defective to be expectedunder existing conditions. Determine a value from this andother information for the process average percent defectivethat should be used in applying the selected sampling table, ifsampling is to be introduced.5. Procedure5.1 Two distinct methods of inspection are employed, singlesampling and double sampling. In single sampling only onesample is permitted before a decision is reached regarding thedisposition of the lot, and the acceptance criterion is expressedas an acceptance number, c. In double sampling, a secondsample is permitted and two acceptance numbers are used; thefirst, c1, applying to the observed number of defectives for thefirst sample alone and the second, c2, applying to the observednumber of defectives for the first and second samples com-bined. The specific procedures assumed in the development ofthe tables are as follows:5.1.1 Single Sampling Inspection Procedure:5.1.1.1 Inspect a sample of n pieces.5.1.1.2 If the number of defectives found in the sample doesnot exceed c, the acceptance number, accept the lot.5.1.1.3 If the number of defectives found in the sampleexceeds c, inspect all the pieces in the remainder of the lot.5.1.1.4 Regardless of whether or not the lot was accepted,correct or replace all defective pieces found in the sample aswell as in any subsequent inspection of the remainder of thelot.5.1.2 Double Sampling Inspection Procedure:5.1.2.1 Inspect a first sample of n1pieces.5.1.2.2 If the number of defectives found in the first sampledoes not exceed c1, the acceptance number for the first sample,accept the lot.5.1.2.3 If the number of defectives found in the first sampleexceeds c2, the acceptance number for the combined first andsecond samples, inspect all the pieces in the remainder of thelot.5.1.2.4 If the number of defectives found in the first sampleexceeds c1, but does not exceed c2, inspect a second sample ofn2pieces.5.1.2.5 If the total number of defectives found in the firstand second samples combined does not exceed c2, accept thelot.5.1.2.6 If the total number of defectives found in the firstand second samples combined exceeds c2, inspect all the piecesin the remainder of the lot.E1994 − 09 (2013)25.1.2.7 Regardless of whether or not the lot was accepted,correct or replace all defective pieces found in either sample aswell as any in subsequent inspection or the remainder of thelot.5.2 In choosing a sampling plan for a particular application,a number of decisions must be made which depend on theconditions under which the plan is to be used. The accompa-nying Sequence of Steps gives an outline of a typical proce-dure. These steps are shown in the following numberedparagraphs.5.3 Sequence of Steps:5.3.1 Decide what characteristics will be included in theinspection.5.3.1.1 If advantageous, use a separate sampling plan for asingle characteristic or selected group of characteristics of likeimportance. Sampling need not wait until all characteristicshave good quality.5.3.1.2 If one or two characteristics give an outstandinglyhigh number of defective units, treat them separately (using100 percent inspection; also, if possible, concentrate on cor-recting the causes of trouble) and include the rest collectivelyin the sampling inspection.5.3.1.3 If all characteristics have satisfactory quality, in-clude all of them collectively in the sampling inspection.5.3.1.4 In general, combine at one inspection station char-acteristics subject to essentially similar inspection operations,for example, all visual inspection items together, all gauging,or all testing. Visual and gauging inspection operations oftencombine well.5.3.1.5 Include in any group characteristics of essentiallythe same degree of seriousness. If two degrees of seriousnessare involved, say major and minor, keep all majors together inone group and all minors in a second group.5.3.1.6 Consider these plans applicable to all basic types ofinspection for manufactured products receiving, process, andfinal and to the inspection of administrative and clericalproducts as in paper-work quality control.5.3.2 Decide what is to constitute a lot for purposes ofsampling inspection.5.3.2.1 So far as practicable, require that individual lotspresented for acceptance comprise essentially homogeneousmaterial from a common source.5.3.2.2 If presented material comes from two or more directsources not under a common system of control, arrange to haveeach presented lot comprise material from only one of thosesources; otherwise have source identification information fur-nished with each lot.5.3.2.3 To minimize the amount of inspection, make the lotsas large as practicable, considering the limitations of availablestorage space, delays in shipment, difficulty in handling largerejected lots, etc.5.3.3 Choose between lot quality (LTPD) and averageoutgoing quality (AOQL) protection.5.3.3.1 ChooseAOQLif interest centers on the general levelof quality of product after inspection. AOQL plans have beenfound generally more useful than LTPD plans in inspections ofa continuing supply of product, especially in consumer’sacceptance inspections and in producer’s receiving, process,and final inspections.5.3.3.2 Choose AOQL for a percent defective that willalmost always be safely met by the running average quality ofproduct after inspection.5.3.3.3 Choose LTPD for a percent defective that willalmost always be met by each lot. (This will be a much morepessimistic figure than the AOQL value of the plan).5.3.3.4 As a manufacturer trying to meet a consumer’sstated AQL (Note 2), use for final inspection an AOQL planwith anAOQL value equal to the specifiedAQL value, in orderto provide good assurance that outgoing quality will be foundacceptable by the consumer (or set the AOQL at one and onethird times the AQL for reasonably good assurance).NOTE 2—AQL = Acceptable Quality Level, as used to index certainsystems of sampling plans, signifying what the consumer feels to be themaximum percent defective that, for sampling purposes, can be consid-ered satisfactory as a process average.5.3.3.5 When producer and consumer of a product are twodepartments of the same company, use AOQL plans with theprovision that the producer perform the 100 percent inspectionof rejected lots. Close interchange of quality findings willexpedite good process control of quality.5.3.3.6 Wherever practicable, make arrangements for theproducer to perform the 100 percent inspection of rejected lot