Designation: E2762 − 10 (Reapproved 2014) An American National StandardStandard Practice forSampling a Stream of Product by Variables Indexed byAQL1This standard is issued under the fixed designation E2762; 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.1. Scope1.1 Purpose—This practice establishes lot or batch sam-pling plans and procedures for inspection by variables usingMIL-STD-414 as a basis for sampling a steady stream of lotsindexed by AQL.1.2 This practice provides the sampling plans of MIL-STD-414 in ASTM format for use by ASTM committees and others.It recognizes the continuing usage of MIL-STD-414 in indus-tries supported by ASTM. Most of the original text in MIL-STD-414 is preserved in Sections 6–9of this practice.1.3 The values stated in inch-pound units are to be regardedas standard. No other units of measurement are included in thisstandard.1.4 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E456 Terminology Relating to Quality and StatisticsE2234 Practice for Sampling a Stream of Product by Attri-butes Indexed by AQLE2586 Practice for Calculating and Using Basic Statistics2.2 Other Standards:3MIL-STD-414 Sampling Procedures and Tables for Inspec-tion by Variables for Percent DefectiveMIL-STD-105E Sampling Procedures and Tables for In-spection by Attributes3. Terminology3.1 Definitions:3.1.1 For a more extensive list of terms in E11 standards,see Terminology E456.3.1.2 acceptance quality limit (AQL), n—quality limit that isthe worst tolerable process average when a continuing series oflots is submitted for acceptance sampling. E22343.1.2.1 Discussion—This definition supersedes that given inMIL-STD-105E and MIL-STD-414.3.1.3 classification of defects, n—the enumeration of pos-sible defects of the unit of product classified according to theirseriousness, that is, critical, major, or minor defect. E22343.1.4 critical defect, n—a defect that judgment and experi-ence indicate would result in hazardous or unsafe conditionsfor individuals using, maintaining, or depending upon theproduct, or a defect that judgment and experience indicate islikely to prevent performance of the function of a major enditem. E22343.1.5 defect, n—any nonconformance of the unit of productwith specified requirements. E22343.1.6 inspection, n—the process of measuring, examining,testing, or otherwise comparing the unit of product with therequirements. E22343.1.7 inspection by variables, n—inspection wherein theunit of product is measured on a continuous scale with respectto a given requirement or set of requirements.3.1.8 inspection lot, n—a collection of units of productproduced under conditions that are considered uniform andfrom which a sample is drawn and inspected. E22343.1.9 major defect, n—a defect, other than critical, that islikely to result in failure, or to reduce materially the usabilityof the unit of product for its intended purpose. E22343.1.10 minor defect, n—a defect that is not likely to reducematerially the usability of the unit of product for its intendedpurpose, or is a departure from established standards havinglittle bearing on the effective use or operation of the unit.E22341This 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, 2014. Published May 2014. Originallyapproved in 2010. Last previous edition approved in 2010 as E2762 – 10. DOI101520/E2762-10.2For 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.3Available from Standardization Documents Order Desk, DODSSP, Bldg. 4,Section D, 700 Robbins Ave., Philadelphia, PA 19111-5098, http://dodssp.daps.dla.mil.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.1.11 operating characteristic, n—probability of accep-tance using a specified acceptance sampling plan, as a functionof parameters describing quality of the lot. E22343.1.12 sample, n—a group of observations, test results,taken from a large collection of observations, test results,which serves to provide information that may be used as a basisfor making a decision concerning the larger collection. E25863.1.12.1 Discussion—A sample consists of one or moreunits of product drawn from an inspection lot, the units of thesample being selected at random without regard to theirquality. The number of units of product in the sample is thesample size.4. Summary of Practice4.1 The main body of this practice is divided into foursections. Section 6 (Section A in MIL-STD-414) describesgeneral procedures of the sampling plans. Sections 7 and 8(Sections B and C in MIL-STD-414) describe specific proce-dures and applications of the sampling plans when variabilityis unknown. In Section 7 (Section B in MIL-STD-414) theestimate of lot standard deviation is used as the basis for anestimate of the unknown variability, and in Section 8 (SectionC in MIL-STD-414) the average range of the sample is used.Section 9 (Section D in MIL-STD-414) describes the planswhen variability is known.4.2 Each of Sections 7, 8, and 9 is divided into three parts:(I) Sampling Plans for the Single Specification Limit Case, (II)Sampling Plans for the Double Specification Limit Case, and(III) Procedures for Estimation of ProcessAverage and Criteriafor Tightened and Reduced Inspection. For the single specifi-cation limit case, the acceptability criterion is given in twoforms: Form 1 and Form 2. Either of the forms may be used,since they are identical as to sample size and decision for lotacceptability or rejectability. In deciding whether to use Form 1or Form 2, the following point should be borne in mind.Form 1 provides the lot acceptability criterion without estimat-ing lot percent defective. The Form 2 lot acceptability criterionrequires estimates of lot percent defective. These estimates alsoare required for estimation of the process average.4.3 Operating Characteristic Curves in Table A-3 (see Fig.A1.3) show the relationship between quality and percent of lotsexpected to be acceptable for the quality characteristic in-spected. As stated, these Operating Characteristic Curves arebased on the assumption that measurements are selected atrandom from a normal distribution.4.4 The corresponding sampling plans in Sections 7, 8, and9 were matched as closely as possible under a system of fixedsample size with respect to their Operating CharacteristicCurves. Operating Characteristic Curves in Table A-3 (see Fig.A1.3) have been computed for the sampling plans based on theestimate of lot standard deviation of unknown variability. Theyare equally applicable for sampling plans based on the averagerange of the sample of unknown variability and those based onknown variability.4.5 Certain characteristics concerning the sampling plans inSections 7 and 8 and those in Section 9 should be noted. Plansbased on the estimate of unknown variability require fewersample units for comparable assurance when the estimate of lotstandard deviation is used than when the average range of thesample is used; on the other hand, plans using the averagerange of the sample require simpler computations. Plans usingknown variability require considerably fewer sample units forcomparable assurance than either of the plans when variabilityis unknown; however, the requirement of variability is astringent one. The user is advised to consult his technicalagency before applying sampling plans using known variabil-ity.4.6 Table B-8 (see Fig. A1.11) provides values of thefactor F to compute the maximum standard deviation MSD.The MSD serves as a guide for the magnitude of the estimateof lot standard deviation when using plans for the doublespecification limit case, based on the estimate of lot standarddeviation of unknown variability. Similarly, Table C-8 (see Fig.A1.19) provides values of the factor f to compute the maxi-mum average range MAR. The MAR serves as a guide for themagnitude of the average range of the sample when using plansfor the double specification limit case, based on the averagerange of the sample of unknown variability. The estimate of lotstandard deviation or average range of the sample, if it is lessthan the MSD or MAR respectively, helps to insure, but doesnot guarantee, lot acceptability.4.7 All symbols and their definitions are given in Annex A1for their applicable section. An illustration of the computationsand procedures used in the sampling plans is given in theexamples of Parts I and II of the applicable section. Thecomputations involve simple arithmetic operations such asaddition, subtraction, multiplication, and division of numbers,or at most, the taking of a square root of a number. The usershould become familiar with the general procedures of Section6, and refer to the applicable section for detailed instructionsregarding specific procedures, computations, and tables for thesampling plans.5. Significance and Use5.1 This practice was prepared to meet a growing need forthe use of standard sampling plans for inspection by variablesin customer procurement, supply and storage, and maintenanceinspection operations. The variables sampling plans apply to asingle quality characteristic which can be measured on acontinuous scale, and for which quality is expressed in terms ofpercent defective. The theory underlying the development ofthe variables sampling plans, including the operating charac-teristic curves, assumes that measurements of the qualitycharacteristic are independent, identically distributed normalrandom variables.5.2 In comparison with attributes sampling plans, variablessampling plans have the advantage of usually resulting inconsiderable savings in sample size for comparable assuranceas to the correctness of decisions in judging a single qualitycharacteristic, or for the same sample size, greater assurance isobtained using variables plans. Attributes sampling plans havethe advantage of greater simplicity, of being applicable toeither single or multiple quality characteristics, and of requir-ing no knowledge about the distribution of the continuousmeasurements of any of the quality characteristics.E2762 − 10 (2014)25.3 It is important to note that variables sampling plans arenot to be used indiscriminately, simply because it is possible toobtain variables measurement data. In considering applicationswhere the normality or independence assumptions may bequestioned, the user is advised to consult his technical agencyto determine the feasibility of application.5.4 Application—Sampling plans designated in this publi-cation are applicable, but not limited, to inspection of thefollowing: (1) end items, (2) components and raw materials, (3)operations or services, (4) materials in process, (5) supplies instorage, (6) maintenance operations, (7) data or records, and(8) administrative procedures.6. General Description of Sampling Plans6.1 Scope:6.1.1 Purpose—This practice establishes sampling plansand procedures for inspection by variables for use in customerprocurement, supply and storage, and maintenance inspectionoperations. When applicable this practice shall be referenced inthe specification, contract, or inspection instructions, and theprovisions set forth herein shall govern.6.1.2 Inspection—Inspection is the process of measuring,examining, testing, gaging, or otherwise comparing the “unit ofproduct” (see 6.1.4) with the applicable requirements.6.1.3 Inspection by Variables—Inspection by variables isinspection wherein a specified quality characteristic (see 6.1.5)on a unit of product is measured on a continuous scale, such aspounds, inches, feet per second, etc., and a measurement isrecorded.6.1.4 Unit of Product—The unit of product is the entity ofproduct inspected in order to determine its measurable qualitycharacteristic. This may be a single article, a pair, a set, acomponent of a product, or the end product itself. The unit ofproduct may or may not be the same as the unit of purchase,supply, production, or shipment.6.1.5 Quality Characteristic—The quality characteristic forvariables inspection is that characteristic of a unit of productthat is actually measured to determine conformance with agiven requirement.6.1.6 Specification Limits—The specification limit(s) is therequirement that a quality characteristic should meet. Thisrequirement may be expressed as an upper specification limit;or a lower specification limit, called herein a single specifica-tion limit; or both upper and lower specification limits, calledherein a double specification limit.6.1.7 Sampling Plans—A sampling plan is a procedurewhich specifies the number of units of product from a lot whichare to be inspected, and the criterion for acceptability of the lot.Sampling plans designated in this practice are applicable to theinspection of a single quality characteristic of a unit of product.These plans may be used whether procurement inspection isperformed at the plant of a prime contractor, subcontractor orvendor, or at destination, and also may be used when appro-priate in supply and storage, and maintenance inspectionoperations.6.2 Classification of Defects:6.2.1 Method of Classifying Defects—A classification ofdefects is the enumeration of defects of the unit of productclassified according to their importance. A defect is a deviationof the unit of product from requirements of the specifications,drawings, purchase descriptions, and any changes thereto in thecontract or order. Defects normally belong to one of thefollowing classes; however, defects may be placed in otherclasses.6.2.1.1 Critical Defects—A critical defect is one that judg-ment and experience indicate could result in hazardous orunsafe conditions for individuals using or maintaining theproduct; or, for major end items units of product, such as ships,aircraft, or tanks, a defect that could prevent performance oftheir tactical function.6.2.1.2 Major Defects—A major defect is a defect, otherthan critical, that could result in failure, or materially reducethe usability of the unit of product for its intended purpose.6.2.1.3 Minor Defects—A minor defect is one that does notmaterially reduce the usability of the unit of product for itsintended purpose, or is a departure from established standardshaving no significant beari