ansi+asq+z1[1].4-2003

ANSI/ASQ Z1.4-2003

AMERICAN SOCIETY FOR QUALITY600 NORTH PLANKINTON AVENUEMILWAUKEE, WISCONSIN 53203

AMERICAN NATIONAL STANDARD

SAMPLING PROCEDURES AND TABLES FOR INSPECTION BY ATTRIBUTES

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AMERICAN NATIONAL STANDARD

Sampling Procedures and Tables for Inspection by Attributes

Prepared byThe Statistics Subcommittee of the Accredited

Standards Committee Z1 on Quality, Environment,Dependability and Statistics

SecretariatAmerican Society for Quality

ANSI/ASQ Z1.4-2003


AbstractSampling Procedures and Tables for Inspection by Attributes is an acceptance sampling system to be used with switchingrules on a continuing stream of lots for AQL specified. It provides tightened, normal, and reduced plans to be applied forattributes inspection for percent nonconforming or nonconformities per 100 units.

AMERICAN NATIONAL STANDARD: An American national Standard implies a consensus of those substantially con-cerned with its scope and provisions. An American National Standard is intended as a guide to aid the manufacturer, theconsumer, and the general public. The existence of an American National Standard does not in any respect preclude any-one, whether he has approved the standard or not, from manufacturing, marketing, purchasing, or using products, processes,or procedures not conforming to the standard. American National Standards are subject to periodic review and users arecautioned to obtain the latest editions.

CAUTION NOTICE: This American National Standard may be revised or withdrawn at any time. The procedures of theAmerican National Standards Institute require that action be taken to reaffirm, revise, or withdraw this standard no laterthan five years from the date of publication. Purchasers of American National Standards may receive current informationon all standards by calling or writing the American National Standards Institute.

Published byAMERICAN SOCIETY FOR QUALITY600 NORTH PLANKINTONMILWAUKEE, WISCONSIN 53203

2003 by the AMERICAN SOCIETY FOR QUALITY

No part of this publication may be reproduced in any form, in an electronic retrieval system or otherwise, without theprior written permission of the publisher.

Printed in the United States of America


Foreword

iii

(This foreword is not a part of the American NationalStandardSampling Procedures and Tables for Inspectionby Attributes, Z1.4-2003)

This standard is a revision of ANSI/ASQC Z1.4-1993,Sampling Procedures and Tables for Inspection byAttributes. Beyond editorial refinements, only the follow-ing eight changes have been made:

1) Acceptable Quality Level (AQL) has been changed toAcceptance Quality Limit (AQL). See Clause 4.

2) The definition and explanation of AQL have beenchanged. See Clauses 4.2 and 4.3.

3) The Discontinuation of Inspection rule has been changed.See Clause 8.4.

4) ANSI/ASQC A2-1987 has been changed to ANSI/ASQA3534-2-1993. See Clauses 2 and 7.2.

5) ANSI/ASQC Q3 has been changed to ASQC Q3-1988.See Clause 11.6.3.

6) The connected arrows in Table II-A, III-A, III-C, IV-A,and IV-C have been separated.

7) In Tables III-A, III-B, and III-C and for clarification ofinstructions, the * footnote has changed and the + footnoteadded.

8) In Tables IV-A, IV-B, and IV-C and for clarification ofinstructions, the footnotes * and ++ have changed and thefootnote ## added.

Note 1: Other than 3), 7), and 8) above, all tables, tablenumbers and procedures used in MIL-STD-105E (whichwas cancelled in 1995) have been retained.

Note 2: A compatible and interchangeable standard forvariables inspection is ANSI/ASQC Z1.9-2003.

Suggestions for improvement of this standard are wel-comed. Send your comments to the sponsor, ASQ, 600North Plankinton Avenue, Milwaukee, WI 53203.


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Table of ContentsParagraph Page

1. SCOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12. DEFINITIONS AND TERMINOLOGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13. PERCENT NONCONFORMING AND NONCONFORMITIES PER

HUNDRED UNITS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24. ACCEPTANCE QUALITY LIMIT (AQL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25. SUBMISSION OF PRODUCT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36. ACCEPTANCE AND NON-ACCEPTANCE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37. DRAWING OF SAMPLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48. NORMAL, TIGHTENED, AND REDUCED INSPECTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49. SAMPLING PLANS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

10. DETERMINATION OF ACCEPTABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611. SUPPLEMENTARY INFORMATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

TablesTable I Sample Size Code Letters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Table II-A Single Sampling Plans for Normal Inspection (Master Table) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Table II-B Single Sampling Plans for Tightened Inspection (Master Table) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Table II-C Single Sampling Plans for Reduced Inspection (Master Table) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Table III-A Doubling Sampling Plans for Normal Inspection (Master Table) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Table III-B Doubling Sampling Plans for Tightened Inspection (Master Table) . . . . . . . . . . . . . . . . . . . . . . . . . . 15Table III-C Doubling Sampling Plans for Reduced Inspection (Master Table). . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Table IV-A Multiple Sampling Plans for Normal Inspection (Master Table) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Table IV-B Multiple Sampling Plans for Tightened Inspection (Master Table) . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Table IV-C Multiple Sampling Plans for Reduced Inspection (Master Table) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Table V-A Factors for Determining Approximate Values for Average Outgoing Quality Limits for Normal

Inspection (Single Sampling) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Table V-B Factors for Determining Approximate Values for Average Outgoing Quality Limits for Tightened

Inspection (Single Sampling) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Table VI-A Limiting Quality (in percent nonconforming) for Which Pa = 10 Percent

(for Normal Inspection, Single Sampling) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Table VI-B Limiting Quality (in nonconformities per hundred units) for Which Pa = 10 Percent

(for Normal Inspection, Single Sampling) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Table VII-A Limiting Quality (in percent nonconforming) for Which Pa = 5 Percent

(for Normal Inspection, Single Sampling) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Table VII-B Limiting Quality (in nonconformities per hundred units) for Which Pa = 5 Percent

(for Normal Inspection, Single Sampling) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Table VIII Limit Numbers for Reduced Inspection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29Table IX Average Sample Size Curves for Double and Multiple Sampling Plans

(normal and tightened inspection). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Table X-A Sample Size Code Letter AIndividual Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Table X-B Sample Size Code Letter BIndividual Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Table X-C Sample Size Code Letter CIndividual Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

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Table X-D Sample Size Code Letter DIndividual Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Table X-E Sample Size Code Letter EIndividual Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Table X-F Sample Size Code Letter FIndividual Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Table X-G Sample Size Code Letter GIndividual Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Table X-H Sample Size Code Letter HIndividual Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Table X-J Sample Size Code Letter JIndividual Plans. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Table X-K Sample Size Code Letter KIndividual Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Table X-L Sample Size Code Letter LIndividual Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Table X-M Sample Size Code Letter MIndividual Plans. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Table X-N Sample Size Code Letter NIndividual Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Table X-P Sample Size Code Letter PIndividual Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Table X-Q Sample Size Code Letter QIndividual Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59Table X-R Sample Size Code Letter RIndividual Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61Table X-S Sample Size Code Letter SIndividual Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Table XI Average Outgoing Quality Limit Factors for ANSI-Z1.4 Scheme Performance

(Single Sampling) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64Table XII Limiting Quality for ANSI-Z1.4 Scheme Performance for Which

Pa = 10 Percent (Single Sampling) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65Table XIII Limiting Quality for ANSI-Z1.4 Scheme Performance for Which

Pa = 5 Percent (Single Sampling) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Table XIV Average Sample Size Tables for ANSI-Z1.4 Scheme Performance (Single Sampling) . . . . . . . . . . . . . 67Table XV-A Sample Size Code Letter AScheme Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Table XV-B Sample Size Code Letter BScheme Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Table XV-C Sample Size Code Letter CScheme Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Table XV-D Sample Size Code Letter DScheme Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Table XV-E Sample Size Code Letter EScheme Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75Table XV-F Sample Size Code Letter FScheme Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Table XV-G Sample Size Code Letter GScheme Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Table XV-H Sample Size Code Letter HScheme Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Table XV-J Sample Size Code Letter JScheme Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Table XV-K Sample Size Code Letter KScheme Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80Table XV-L Sample Size Code Letter LScheme Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Table XV-M Sample Size Code Letter MScheme Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82Table XV-N Sample Size Code Letter NScheme Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Table XV-P Sample Size Code Letter PScheme Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Table XV-Q Sample Size Code Letter QScheme Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Table XV-R Sample Size Code Letter RScheme Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86INDEX OF TERMS WITH SPECIAL MEANINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

ANSI/ASQ Z1.4-2003


1. SCOPE

1.1 PURPOSE. This publication establishes samplingplans and procedures for inspection by attributes. Whenspecified by the responsible authority, this publication shallbe referenced in the specification, contract, inspectioninstructions, or other documents and the provisions set forthherein shall govern. The responsible authority shall bedesignated in one of the above documents, as agreed to bythe purchaser and seller or producer and user.

1.2 APPLICATION. Sampling plans designated in thispublication are applicable, but not limited, to inspection ofthe following:

a. End items.

b. Components and raw materials.

c. Operations.

d. Materials in process.

e. Supplies in storage.

f. Maintenance operations.

g. Data or records.

h. Administrative procedures.

These plans are intended primarily to be used for a continu-ing series of lots or batches. The plans may also be used forthe inspection of isolated lots or batches, but, in this lattercase, the user is cautioned to consult the operating charac-teristic curves to find a plan which will yield the desired pro-tection (see 11.6).

1.3 INSPECTION. Inspection is the process of measur-ing, examining, testing, or otherwise comparing the unit ofproduct (see 1.5) with the requirements.

1.4 INSPECTION BY ATTRIBUTES. Inspection byattributes is inspection whereby either the unit of productis classified simply as conforming or nonconforming, or

the number of nonconformities in the unit of products iscounted, with respect to a given requirement or set ofrequirements.

1.5 UNIT OF PRODUCT. The unit of product is the unitinspected in order to determine its classification as con-forming or nonconforming or to count the number of non-conformities. It may be a single article, a pair, a set, a length,an area, an operation, a volume, a component of an endproduct, or the end product itself. The unit of product mayor may not be the same as the unit of purchase, supply, pro-duction, or shipment.

2. DEFINITIONS AND TERMINOLOGY

The definitions and terminology employed in this standardare in accord with ANSI/ASQ A3534-2-1993 (Terms,Symbols, and Definitions for Acceptance Sampling). Thefollowing two definitions are particularly important inapplying the standard.

DEFECT: A departure of a quality characteristic fromits intended level or state that occurs with a sever-ity sufficient to cause an associated product orservice not to satisfy intended normal, or foresee-able, usage requirements.

NONCONFORMITY: A departure of a quality charac-teristic from its intended level or state that occurswith severity sufficient to cause an associatedproduct or service not to meet a specificationrequirement.

These acceptance sampling plans for attributes are given interms of the percent or proportion of product in a lot or batchthat depart from some requirement. The general terminol-ogy used within the document will be given in terms of per-cent of nonconforming units or number of nonconformities,since these terms are likely to constitute the most widelyused criteria for acceptance sampling.

In the use of this standard it is helpful to distinguishbetween:

a. an individual sampling plana specific plan thatstates the sample size or sizes to be used, and theassociated acceptance criteria.

1

SAMPLING PROCEDURES AND TABLES FOR INSPECTION BY ATTRIBUTES


b. a sampling schemea combination of samplingplans with switching rules and possibly a provisionfor discontinuance of inspection. In this standardthe terms sampling scheme and scheme per-formance will be used in the restricted sensedescribed in Sec. 11.1.

c. a sampling systema collection of samplingschemes. This standard is a sampling system indexedby lot-size ranges, inspection levels, and AQLs.

3. PERCENT NONCONFORMING AND NONCONFORMITIES PER HUNDRED UNITS

3.1 EXPRESSION OF NONCONFORMANCE. Theextent of nonconformance of product shall be expressedeither in terms of percent nonconforming or in terms of non-conformities per hundred units.

3.2 PERCENT NONCONFORMING. The percent non-conforming of any given quantity of units of product is onehundred times the number of nonconforming units dividedby the total number of units of product, i.e.:

3.3 NONCONFORMITIES PER HUNDRED UNITS.The number of nonconformities per hundred units of anygiven quantity of units of product is one hundred times thenumber of nonconformities contained therein (one or morenonconformities being possible in any unit of product)divided by the total number of units of product, i.e.:

It is assumed that nonconformities occur randomly and withstatistical independence within and between units.

4. ACCEPTANCE QUALITY LIMIT (AQL)

4.1 USE. The AQL together with the Sample Size CodeLetter, is used for indexing the sampling plans provided herein.

4.2 DEFINITION. The AQL is the quality level that is theworst tolerable process average when a continuing series oflots is submitted for acceptance sampling.

Note: The use of the abbreviation AQL to mean AcceptableQuality Level is no longer recommended.

4.3 NOTE ON THE MEANING OF AQL. The conceptof AQL only applies when an acceptance sampling schemewith rules for switching between normal, tightened andreduced inspection and discontinuance of sampling inspec-tion is used. These rules are designed to encourage suppliersto have process averages consistently better than the AQL. Ifsuppliers fail to do so, there is a high probability of beingswitched from normal inspection to tightened inspectionwhere lot acceptance becomes more difficult. Once on tight-ened inspection, unless corrective action is taken to improveproduct quality, it is very likely that the rule requiring dis-continuance of sampling inspection will be invoked.

Although individual lots with quality as bad as the AQL canbe accepted with fairly high probability, the designation of anAQL does not suggest that this is necessarily a desirablequality level. The AQL is a parameter of the samplingscheme and should not be confused with a process averagewhich describes the operating level of a manufacturingprocess. It is expected that the product quality level will beless than the AQL to avoid excessive non-accepted lots.

The sampling plans in this standard are so arranged that theprobability of lot acceptance at the designated AQL dependsupon sample size, being generally higher for large samplesthan for small samples for a given AQL. To determine thespecific protection to the consumer at a given AQL, it is nec-essary to refer to the operating characteristic curves (whichare provided in this standard) of the corresponding schemeand its constituent plans.

The AQL alone does not describe the protection to the con-sumer for individual lots or batches, but more directly relatesto what is expected from a series of lots or batches providedthe provisions of this standard are satisfied.

4.4 LIMITATION. The designation of an AQL shall notimply that the supplier has the right to knowingly supplyany nonconforming unit of product.

4.5 SPECIFYING AQLs. The AQL to be used will be des-ignated in the contract or by the responsible authority.Different AQLs may be designated for groups of nonconfor-mities considered collectively, or for individual nonconfor-mities. For example, Group A may include nonconformitiesof a type felt to be of the highest concern for the product orservice and therefore be assigned a small AQL value; GroupB may include nonconformities of the next higher degree ofconcern and therefore be assigned a larger AQL value thanfor Group A and smaller than that of Group C, etc. The clas-sification into groups should be appropriate to the quality

Nonconformities per=

Number of nonconformities 100hundred units Number of units inspected

Number nonconformingPercent nonconforming = Number of units inspected 100

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requirements of the specific situation. An AQL for a groupof nonconformities may be designated in addition to AQLsfor individual nonconformities, or subgroups, within thatgroup. AQL values of 10.0 or less may be expressed eitherin percent nonconforming or in nonconformities per hun-dred units; those over 10.0 shall be expressed in nonconfor-mities per hundred units only.

4.6 PREFERRED AQLs. The values of AQLs given inthese tables are known as preferred AQLs. If, for any prod-uct, an AQL be designated other than a preferred AQL, thesetables are not applicable.

5. SUBMISSION OF PRODUCT

5.1 LOT OR BATCH. The term lot or batch shall meaninspection lot or inspection batch, i.e., a collection of unitsof product from which a sample is to be drawn and inspectedto determine conformance with the acceptability criteria, andmay differ from a collection of units designated as a lot orbatch for other purposes (e.g., production, shipment, etc.).

5.2 FORMATION OF LOTS OR BATCHES. The prod-uct shall be assembled into identifiable lots, sublots, batches,or in such other manner as may be prescribed (see 5.4). Eachlot or batch shall, as far as is practicable, consist of units ofproduct of a single type, grade, class, size, and composition,manufactured under essentially the same conditions, and atessentially the same time.

5.3 LOT OR BATCH SIZE. The lot or batch size is thenumber of units of product in a lot or batch.

5.4 PRESENTATION OF LOTS OR BATCHES. Theformation of the lots or batches, lot or batch size, and themanner in which each lot or batch is to be presented andidentified by the supplier shall be designated or approved bythe responsible authority. As necessary, the supplier shallprovide adequate and suitable storage space for each lot orbatch, equipment needed for proper identification and pres-entation, and personnel for all handling of product requiredfor drawing of samples.

6. ACCEPTANCE AND NON-ACCEPTANCE

6.1 ACCEPTABILITY OF LOTS OR BATCHES.Acceptability of a lot or batch will be determined by the useof a sampling plan or plans associated with the designatedAQL or AQLs.

In the use of this standard a statement that a lot is acceptablemeans simply that sample results satisfy the standards

acceptance criteria. The acceptance of a lot is not intended toprovide information about lot quality. If a stream of lots froma given process is inspected under an acceptance samplingscheme such as provided in this standard, some lots will beaccepted and others will not. If all incoming lots are assumedto be at the same process average and if the nonconformingitems that are discovered and replaced by conforming itemsduring sample inspection are ignored, it will be found thatboth the set of accepted lots and the set of non-accepted lotswill have the same long run average quality as the originalset of lots submitted for inspection. Inspection of incominglots whose quality levels vary around a fixed long run aver-age quality level will divide the lots into a set of accepted lotsand a set of non-accepted lots, but it will be found that thelong run average quality of the accepted lots is only slightlybetter than the long run average quality of the non-acceptedlots. Replacement of the nonconforming items that are dis-covered during sample inspection does not alter this findingbecause the samples are a small fraction of the lots.

The purpose of this standard is, through the economic andpsychological pressure of lot non-acceptance, to induce asupplier to maintain a process average at least as good as thespecified AQL while at the same time providing an upperlimit on the consideration of the consumers risk of accept-ing occasional poor lots. The standard is not intended as aprocedure for estimating lot quality or for segregating lots.

In acceptance sampling, when sample data do not meet theacceptance criteria, it is often stated that the lot is to berejected. In this connection, the words to reject generallyare used. Rejection in an acceptance sampling sense means todecide that a batch, lot or quantity of product, material, orservice has not been shown to satisfy the acceptance criteriabased on the information obtained from the sample(s).

In acceptance sampling, the words to reject generally areused to mean to not accept without direct implication ofproduct usability. Lots which are rejected may bescrapped, sorted (with or without nonconforming unitsbeing replaced), reworked, re-evaluated against more spe-cific usability criteria, held for additional information, etc.Since the common language usage of reject often resultsin an inference of unsafe or unusable product, it is recom-mended that not accept be understood rather than rejectin the use of this standard.

The word non-acceptance is used here for rejectionwhen it refers to the result of following the procedure.Forms of the word reject are retained when they refer toactions the customer may take, as in rejection number.

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6.2 NONCONFORMING UNITS. The right is reservedto reject any unit of product found nonconforming duringinspection whether that unit of product forms a part of asample or not, and whether the lot or batch as a whole isaccepted or rejected. Rejected units may be repaired or cor-rected and resubmitted for inspection with the approval of,and in the manner specified by, the responsible authority.

6.3 SPECIAL RESERVATION FOR DESIGNATEDNONCONFORMITIES. Since most acceptance samplinginvolves evaluation of more than one quality characteristic,and since these may differ in importance in terms of qualityand/or economic effects, it is often desirable to classify thetypes of nonconformity according to agreed upon groupings.Specific assignment of types of nonconformities to eachclass is a function of agreement on specific sampling appli-cations. In general, the function of such classification is topermit the use of a set of sampling plans having a commonsample size, but different acceptance numbers for each classhaving a different AQL, such as in Tables II, III, and IV.

The supplier may be required at the discretion of the respon-sible authority to inspect every unit of the lot or batch fordesignated classes of nonconformities. The right is reservedto inspect every unit submitted by the supplier for specifiednonconformities, and to reject the lot or batch immediately,when a nonconformity of this class is found. The right isreserved also to sample, for specified classes of nonconfor-mities, lots or batches submitted by the supplier and to rejectany lot or batch if a sample drawn therefrom is found to con-tain one or more of these nonconformities.

6.4 RESUBMITTED LOTS OR BATCHES. Lots orbatches found unacceptable shall be resubmitted for rein-spection only after all units are re-examined or re-tested andall nonconforming units are removed or nonconformitiescorrected. The responsible authority shall determinewhether normal or tightened inspection shall be used onreinspection and whether reinspection shall include all typesor classes of nonconformities or only the particular types orclasses of nonconformities which caused initial rejection.

7. DRAWING OF SAMPLES

7.1 SAMPLE. A sample consists of one or more units ofproduct drawn from a lot or batch, the units of the samplebeing selected at random without regard to their quality. Thenumber of units of product in the sample is the sample size.

7.2 SAMPLING. When appropriate, the number of unitsin the sample shall be selected in proportion to the size ofsublots or subbatches, or parts of the lot or batch, identifiedby some rational criterion. In so doing, the units from eachpart of the lot or batch shall be selected at random, asdefined in ANSI/ASQ A3534-2-1993.

7.3 TIME OF SAMPLING. Samples may be drawn after allthe units comprising the lot or batch have been produced, orsamples may be drawn during production of the lot or batch.

7.4 DOUBLE OR MULTIPLE SAMPLING. Where dou-ble or multiple sampling is to be used, each sample shall beselected over the entire lot or batch.

8. NORMAL, TIGHTENED AND REDUCED INSPECTION

8.1 INITIATION OF INSPECTION. Normal inspectionwill be used at the start of inspection unless otherwisedirected by the responsible authority.

8.2 CONTINUATION OF INSPECTION. Normal, tight-ened or reduced inspection shall continue unchanged onsuccessive lots or batches except where the switching pro-cedures given below require change.

8.3 SWITCHING PROCEDURES.

8.3.1 NORMAL TO TIGHTENED. When normalinspection is in effect, tightened inspection shall be insti-tuted when 2 out of 5 or fewer consecutive lots or batcheshave been non-acceptable on original inspection (i.e., ignor-ing resubmitted lots or batches for this procedure).

8.3.2 TIGHTENED TO NORMAL. When tightenedinspection is in effect, normal inspection shall be institutedwhen 5 consecutive lots or batches have been consideredacceptable on original inspection.

8.3.3 NORMAL TO REDUCED. When normal inspectionis in effect, reduced inspection shall be instituted providingthat all of the following conditions are satisfied.

a. The preceding 10 lots or batches (or more, as indi-cated by the note to Table VIII) have been on nor-mal inspection and all have been accepted onoriginal inspection; and

ANSI/ASQ Z1.4-2003

4


b. The total number of nonconforming units (or non-conformities) in the samples from the preceding 10lots or batches (or such other number as was usedfor condition a above) is equal to or less than theapplicable limit number given in Table VIII (see8.5). If double or multiple sampling is in use, allsamples inspected should be included, not firstsamples only; and

c. Production is at a steady rate; and

d. Reduced inspection is considered desirable by theresponsible authority.

8.3.4 REDUCED TO NORMAL. When reduced inspec-tion is in effect, normal inspection shall be instituted if anyof the following occur on original inspection:

a. A lot or batch is rejected; orb. A lot or batch is considered acceptable under the

procedures for reduced inspection given in10.1.4; or

c. Production becomes irregular or delayed; or

d. Other conditions warrant that normal inspectionshall be instituted.

8.4 DISCONTINUATION OF INSPECTION. If thecumulative number of lots not accepted in a sequence of con-secutive lots on tightened inspection reaches 5, the accept-ance procedures of this standard shall be discontinued.Inspection under the provisions of this standard shall not beresumed until corrective action has been taken. Tightenedinspection shall then be used as if 8.3.1 had been invoked.

8.5 LIMIT NUMBERS FOR REDUCED INSPECTION.When agreed upon by responsible authority for both partiesto the inspection, that is, the supplier and the end item cus-tomer, the requirements of 8.3.3b may be dropped. Thisaction will have little effect on the operating properties ofthe scheme.

8.6 SWITCHING SEQUENCE. A schematic diagramdescribing the sequence of application of the switching rulesis shown in Figure 1.

9. SAMPLING PLANS

9.1 SAMPLING PLAN. A sampling plan indicates thenumber of units of product from each lot or batch which are

to be inspected (sample size or series of sample sizes) andthe criteria for determining the acceptability of the lot orbatch (acceptance and rejection numbers).

9.2 INSPECTION LEVEL. The inspection level deter-mines the relationship between the lot or batch size and thesample size. The inspection level to be used for any partic-ular requirement will be prescribed by the responsibleauthority. Three inspection levels: I, II and III are given inTable I for general use. Unless otherwise specified,Inspection Level II will be used. However, Inspection LevelI may be specified when less discrimination is needed, orLevel III may be specified for greater discrimination. Fouradditional special levels: S-1, S-2, S-3, and S-4, are givenin the same table and may be used where relatively smallsample sizes are necessary and large sampling risks can ormust be tolerated.

NOTE: In the designation of inspection levels S-1 to S-4,care must be exercised to avoid AQLs inconsistent withthese inspection levels.

9.3 CODE LETTERS. Sample sizes are designated bycode letters. Table I shall be used to find the applicable codeletter for the particular lot or batch size and the prescribedinspection level.

9.4 OBTAINING SAMPLING PLAN. The AQL and thecode letter shall be used to obtain the sampling plan fromTables II, III, or IV. When no sampling plan is available for agiven combination of AQL and code letter, the tables directthe user to a different letter. The sample size to be used isgiven by the new code letter, not by the original letter. If thisprocedure leads to different sample sizes for different classesof nonconformities, the code letter corresponding to thelargest sample size derived may be used for all classes ofnonconformities when designated or approved by the respon-sible authority. As an alternative to a single sampling planwith an acceptance number of 0, the plan with an acceptancenumber of 1 with its correspondingly larger sample size fora designated AQL (where available), may be used when des-ignated or approved by the responsible authority.

9.5 TYPES OF SAMPLING PLANS. Three types of sam-pling plans: Single, Double and Multiple, are given in TablesII, III, and IV, respectively. When several types of plans areavailable for a given AQL and code letter, any one may beused. A decision as to type of plan, either single, double, ormultiple, when available for a given AQL and code letter,will usually be based upon the comparison between the

ANSI/ASQ Z1.4-2003

5


administrative difficulty and the average sample sizes of theavailable plans. The average sample size of multiple plans isless than for double (except in the case corresponding to sin-gle acceptance number 1) and both of these are always lessthan a single sample size (see Table IX). Usually the admin-istrative difficulty for single sampling and the cost per unit ofthe sample are less than for double or multiple.

10. DETERMINATION OF ACCEPTABILITY

10.1 PERCENT NONCONFORMING INSPECTION.To determine acceptability of a lot or batch under percent non-conforming inspection, the applicable sampling plan shall beused in accordance with 10.1.1, 10.1.2, 10.1.3 and 10.1.4.

10.1.1 SINGLE SAMPLING PLAN. The number of sam-ple units inspected shall be equal to the sample size given bythe plan. If the number of nonconforming units found in thesample is equal to or less than the acceptance number, the lotor batch shall be considered acceptable. If the number ofnonconforming units is equal to or greater than the rejectionnumber, the lot or batch shall be considered not acceptable.

10.1.2 DOUBLE SAMPLE PLAN. The number of sampleunits first inspected shall be equal to the first sample sizegiven by the plan. If the number of nonconforming unitsfound in the first sample is equal to or less than the firstacceptable number, the lot or batch shall be consideredacceptable. If the number of nonconforming units found inthe first sample is equal to or greater than the first rejectionnumber, the lot or batch shall be considered not acceptable.If the number of nonconforming units found in the first sam-ple is between the first acceptance and rejection numbers, asecond sample of the size given by the plan shall beinspected. The number of nonconforming units found in thefirst and second samples shall be accumulated. If the cumu-lative number of nonconforming units is equal to or less thanthe second acceptance number, the lot or batch shall be con-sidered acceptable. If the cumulative number of noncon-forming units is equal to or greater than the second rejectionnumber, the lot or batch shall be considered not acceptable.

10.1.3 MULTIPLE SAMPLE PLAN. Under multiplesampling, the procedure shall be similar to that specified in10.1.2, except that the number of successive samplesrequired to reach a decision might be more than two.

10.1.4 SPECIAL PROCEDURE FOR REDUCEDINSPECTION. Under reduced inspection, the samplingprocedure may terminate without making a decision. In

these circumstances, the lot or batch will be consideredacceptable, but normal inspection will be reinstated startingwith the next lot or batch (see 8.3.4(b)).

10.2 NONCONFORMITIES PER HUNDRED UNITSINSPECTION. To determine the acceptability of a lot orbatch under Nonconformities per Hundred Units inspection,the procedure specified for Percent Nonconforming inspec-tion above shall be used, except that the word nonconfor-mities shall be substituted for nonconforming units.

11. SUPPLEMENTARY INFORMATION

11.1 OPERATING CHARACTERISTIC CURVES.Operating characteristic curves and other measures of per-formance presented in this standard are of two types. Thosefor the individual plans that represent the elements of theschemes are presented in Tables V, VI, VII, IX, and X.Analogous curves and other measures of overall scheme per-formance when the switching rules are used are given inTables XI, XII, XIII, XIV, and XV. Scheme performance isdefined as the composite proportion of lots accepted at astated percent nonconforming when the switching rules areapplied. The term scheme performance is used here in a veryrestrictive sense. It refers to how the ANSI Z1.4 scheme ofswitching rules would operate at a given process level underthe assumption that the process stays at that level even afterswitching to tightened inspection or discontinuation ofinspection. This gives a conservative worst case descriptionof the performance of the scheme for use as a baseline in thesense that if the psychological and economic pressures asso-ciated with the switching rules are considered, the protectionof the scheme may be somewhat better than that shown.

Operating characteristic curves are given in Table X forindividual sampling plans for normal and tightened inspec-tion. The operating characteristic curve for unqualifiedacceptance under reduced inspection can be found by usingthe AQL index of the normal plan with the sample size(s)and acceptance number(s) of the reduced plan. The curvesshown are for single sampling; curves for double and multi-ple sampling are matched as closely as practicable. The O.C.curves shown for AQLs greater than 10.0 are based on thePoisson distribution and apply for nonconformities per hun-dred units inspection; those for AQLs of 10.0 or less andsample sizes of 80 or less are based on the binomial distri-bution and apply for percent nonconforming inspection;those for AQLs of 10.0 or less and sample sizes larger than80 are based on the Poisson distribution and apply either fornonconformities per hundred units inspection, or for percent

ANSI/ASQ Z1.4-2003

6


nonconforming inspection (the Poisson distribution being anadequate approximation to the binomial distribution underthese conditions). Tabulated values corresponding toselected values of probabilities of acceptance (Pa in percent)are given for each of the curves shown, and, in addition, areindexed for tightened inspection, and also show values fornonconformities per hundred units for AQLs of 10.0 or lessand sample sizes of 80 or less.

The operating characteristic curves for scheme performanceshown in Table XV indicate the percentage of lots or batcheswhich may be expected to be accepted under use of theswitching rules with the various sampling plans for a givenprocess quality subject to the restrictions stated above. Theoperating characteristic curves of scheme performance arebased on the use of limit numbers in switching to reducedinspection and are approximately correct when the limitnumbers for reduced inspection are not used under Option8.5. The curves also assume a return to tightened inspectionwhen inspection is resumed after discontinuation has beenimposed. This is also true of average outgoing quality limitand average sample size for ANSI Z1.4 scheme performance.

Note that the operating characteristic curve for scheme per-formance is approximately that of the normal plan for lowlevels of percent nonconforming and that the tightened planfor high levels of percent nonconforming. Use of thereduced plan increases scheme probability of acceptanceonly for extremely low levels of percent nonconforming.

11.2 PROCESS AVERAGE. The process average is theaverage percent nonconforming or average number of non-conformities per hundred units (whichever is applicable) ofproduct submitted by the supplier for original inspection.Original inspection is the first inspection of a particularquantity of product as distinguished from the inspection ofproduct which has been resubmitted after prior rejection.When double or multiple sampling is used, only first sampleresults shall be included in the process average calculation.

11.3 AVERAGE OUTGOING QUALITY (AOQ). TheAOQ is the average quality of outgoing product includingall accepted lots or batches, plus all lots or batches which arenot accepted after such lots or batches have been effectively100 percent inspected and all nonconforming units replacedby conforming units.

11.4 AVERAGE OUTGOING QUALITY LIMIT(AOQL). The AOQL is the maximum of the AOQs for allpossible incoming qualities for a given acceptance sampling

plan. AOQL values are given in Table V-A for each of thesingle sampling plans for normal inspection and in Table V-Bfor each of the single sampling plans for tightened inspec-tions. AOQL values for ANSI Z1.4 scheme performance aregiven in Table XI subject to the restrictions of 11.1. Theyshow the average outgoing quality limits for scheme per-formance when using single sampling. AOQL will beslightly higher when the limit numbers for reduced inspec-tion are not used under Option 8.5.

11.5 AVERAGE SAMPLE SIZE CURVES. Averagesample size curves for double and multiple sampling ascompared to the single sampling plan for each acceptancenumber are in Table IX. These show the average samplesizes which may be expected to occur under the varioussampling plans for a given process quality level. The curvesassume no curtailment of inspection and are approximate tothe extent that they are based upon the Poisson distribution,and that the sample sizes at each stage for double and mul-tiple sampling are assumed to be 0.631n and 0.25n respec-tively, where n is the equivalent single sample size. Averagesample size tables for ANSI Z1.4 scheme performance aregiven in Table XIV. They show the average sample size forscheme performance when using single sampling.

11.6 LIMITING QUALITY PROTECTION.

11.6.1 USE OF INDIVIDUAL PLANS. This standard isintended to be used as a system employing tightened, nor-mal, and reduced inspection on a continuing series of lots toachieve consumer protection while assuring the producerthat acceptance will occur most of the time if quality is bet-ter than the AQL.

11.6.2 IMPORTANCE OF SWITCHING RULES.Occasionally specific individual plans are selected from thestandard and used without the switching rules. This is notthe intended application of the ANSI Z1.4 system and its usein this way should not be referred to as inspection underANSI Z1.4. When employed in this way, this document sim-ply represents a repository for a collection of individualplans indexed by AQL. The operating characteristics andother measures of a plan so chosen must be assessed indi-vidually for that plan from the tables provided.

11.6.3 LIMITING QUALITY TABLES. If the lot orbatch is of an isolated nature, it is desirable to limit theselection of sampling plans to those, associated with a des-ignated AQL value, that provide not less than a specifiedlimiting quality protection. Sampling plans for this purpose

ANSI/ASQ Z1.4-2003

7


can be selected by choosing a Limiting Quality (LQ) and aconsumers risk to be associated with it. Limiting Quality isthe percentage of nonconforming units (or nonconformities)in a batch or lot for which for purposes of acceptance sam-pling, the consumer wishes the probability of acceptance tobe restricted to a specified low value.

Tables VI and VII give process levels for which the proba-bilities of lot acceptance under various sampling plans are10 percent and 5 percent respectively. If a different value ofconsumers risk is required, the O.C. curves and their tabu-lated values may be used. For individual lots with percentsnonconforming or nonconformities per 100 units equal to thespecified Limiting Quality (LQ) values, the probabilities oflot acceptance are less than 10 percent in the case of planslisted in Table VI and less than 5 percent in the case ofplans listed in Table VII. When there is reason for avoidingmore than a limiting percentage of nonconforming units (ornonconformities) in a lot or batch, Tables VI and VII may beuseful for fixing minimum sample sizes to be associated

with the AQL and Inspection Level specified for the inspec-tion of a series of lots or batches. For example, if an LQ of5 percent is desired for individual lots with an associated Paof 10 percent or less, then if an AQL of 1.5 percent is desig-nated for inspection of a series of lots or batches. Table VIindicates that the minimum sample size must be that givenby Code Letter M.

Where there is interest in a limiting process level, Tables XIIand XIII, which give LQ values and ANSI Z1.4 scheme per-formance may be used in a similar way to fix minimumsample sizes.

In the case of an isolated lot, it is preferable for the customerto adapt a sampling plan with a small consumers risk. Theideal method of calculating the sample size and risk is by useof the hypergeometric probability function. ASQC Q3-1988contains sampling plans that have been calculated on thisbasis and therefore provide a more accurate set of tables forthese situations.

ANSI/ASQ Z1.4-2003

8


9Switc

hing

Rul

es fo

r A

NSI

Z1.

4 Sy

stem

RED

UCE

DN

ORM

AL

STA

RT

TIG

HTE

NED

Pr

eced

ing

10 L

ots

Acc

epte

d, w

ith

Tota

l Non

conf

orm

ing

less

than

Lim

it N

umbe

r(O

ption

al), a

nd

Prod

uctio

n St

eady

,

and

A

ppro

ved

by

Res

pons

ible

Aut

horit

y

2

of 5

or f

ewer

Cons

ecut

ive

Lots

are

Not

Acc

epte

d

5

Cons

ecut

ive

Lots

Acc

epte

d

Lo

t not

Acc

epte

d, o

r

Lot A

ccep

ted

but

Non

conf

orm

ities

foun

d lie

bet

wee

n A

can

d Re

of P

lan,

or

Pr

oduc

tion

Irreg

ular

,

or

O

ther

Con

ditio

ns W

arra

nt

5

Lots

not

Acc

epte

d w

hile

on

Tigh

tene

d In

spec

tion

D

iscon

tinue

Insp

ectio

nU

nder

Z1.

4

SWITCHINGRULES

FIG

URE

1


10

Tabl

e I

Sam

ple

size

code

lette

rs

Lot o

r bat

ch si

ze

2 9 16 26 51 91 151

281

501

1201

3201

1000

1

3500

115

0001

5000

01

to to to to to to to to to to to to to to and

8 15 25 50 90 150

280

500

1200

3200

1000

035

000

1500

0050

0000

over

A A A A B B B B C C C C D D DS-1

A A A B B B C C C D D D E E ES-2

A A B B C C D D E E F F G G HS-3

A A B C C D E E F G G H J J KS-4

A A B C C D E F G H J K L M NI

A B C D E F G H J K L M N P QII

Spec

ial i

nspe

ctio

n le

vel

sG

ener

al in

spec

tion

level

s

(See 9

.2 an

d 9.3)

B C D E F G H J K L M N P Q RIII

CODELETTERS


11

Tabl

e II-

ASi

ngle

sam

plin

g pl

ans f

or

norm

al i

nspe

ctio

n (M

aster

table

)

Sam

ple

size

code

lette

r

Sam

ple

size

Acc

epta

nce

Quali

ty Li

mits,

AQLs

, in P

erce

nt N

onco

nfor

min

g Ite

ms a

nd N

onco

nfor

miti

es p

er 1

00 It

ems (

Norm

al Ins

pecti

on)

A B C D E F G H J K L M N P Q R

2 3 5 8 13 20 32 50 80 125

200

315

500

800

1250

2000

11

1 2

1 2 3

1 2 3 4

1 2 3 4 6

1 2 3 4 6 8

1 2 3 4 6 8 11

1 2 3 4 6 8 11 15

1 2 3 4 6 8 11 15 22

1 2 3 4 6 8 11 15 22

1 2 3 4 6 8 11 15 22

1 2 3 4 6 8 11 15 22

1 2 3 4 6 8 11 15 22

1 2 3 4 6 8 11 15 22

2 3 4 6 8 11 15 22

2 3 4 6 8 11 15 22

2 3 4 6 8 11 15 22

3 4 6 8 11 15 22

4 6 8 11 15 22

6 8 11 15 22

8 11 15 22 31

11 15 22 31 45

15 22 31 45

22 31 45

31 45

00

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

0.01

50.

025

0.04

00.

065

0.10

0.15

0.25

0.40

0.65

1.0

1.5

2.5

4.0

6.5

1015

2540

6510

015

025

040

065

010

000.

010

0 1

0 1 2

0 1 2 3

0 1 2 3 5

0 1 2 3 5 7

0 1 2 3 5 7 10

0 1 2 3 5 7 10 14

0 1 2 3 5 7 10 14 21

0 1 2 3 5 7 10 14 21

0 1 2 3 5 7 10 14 21

0 1 2 3 5 7 10 14 21

0 1 2 3 5 7 10 14 21

0 1 2 3 5 7 10 14 21

1 2 3 5 7 10 14 21

1 2 3 5 7 10 14 21

1 2 3 5 7 10 14 21

2 3 5 7 10 14 21

3 5 7 10 14 21

5 7 10 14 21

7 10 14 21 30

10 14 21 30 44

14 21 30 44

21 30 44

30 44

= U

se th

e fir

st sa

mpl

ing

plan

bel

ow th

e ar

row

. If

sam

ple

size

equa

ls, o

r exce

eds,

lot s

ize,

car

ry o

ut 1

00 p

erce

nt in

spec

tion.

= U

se th

e fir

st sa

mpl

ing

plan

abo

ve

the

arro

w.

= A

ccep

tanc

e nu

mbe

r.=

R

ejecti

on nu

mber.

Ac

Re

(See 9

.4 an

d 9.5)

SINGLENORMAL

PLANS


12

Tabl

e II-

BSi

ngle

sam

plin

g pl

ans f

or

tight

ened

insp

ectio

n (M

aster

table

)

Sam

ple

size

code

lette

r

Sam

ple

size

Acc

epta

nce

Quali

ty Li

mits

(tigh

tened

insp

ectio

n)

A B C D E F G H J K L M N P Q R S

2 3 5 8 13 20 32 50 80 125

200

315

500

800

1250

2000

3150

11 2

1 2

1 2 3

1 2 3 4

1 2 3 4 6

1 2 3 4 6 9

1 2 3 4 6 9 13

1 2 3 4 6 9 13

1 2 3 4 6 9 13 19

1 2 3 4 6 9 13 19

1 2 3 4 6 9 13

1 2 3 4 6 9 13 19

1 2 3 4 6 9 13 19

2 3 4 6 9 13 19

2 3 4 6 9 13 19

2 3 4 6 9 13 19

2 3 4 6 9 13 19

3 4 6 9 13 19

4 6 9 13 19

6 9 13 19 28

9 13 19 28 42

13 19 28 42

19 28 42

28 42

10

0

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

0.01

50.

025

0.04

00.

065

0.10

0.15

0.25

0.40

0.65

1.0

1.5

2.5

4.0

6.5

1015

2540

6510

015

025

040

065

010

000.

010

0 1

0 1

0 1 2

0 1 2 3

0 1 2 3 5

0 1 2 3 5 8

0 1 2 3 5 8 12

0 1 2 3 5 8 12

1918

0 1 2 3 5 8 12 18

0 1 2 3 5 8 12 18

0 1 2 3 5 8 12

1918

0 1 2 3 5 8 12 18

0 1 2 3 5 8 12 18

1 2 3 5 8 12 18

1 2 3 5 8 12 18

1 2 3 5 8 12 18

1 2 3 5 8 12 18

2 3 5 8 12 18

3 5 8 12 18

5 8 12 18 27

8 12 18 27 41

12 18 27 41

18 27 41

27 41

= U

se fi

rst s

ampl

ing

plan

bel

ow a

rrow

. If

sam

ple

size

equa

ls or

exce

eds l

ot o

r bat

ch si

ze, d

o 10

0 pe

rcen

t ins

pect

ion.

= U

se fi

rst s

ampl

ing

plan

abo

ve

arro

w.

= A

ccep

tanc

e nu

mbe

r.=

R

ejecti

on nu

mber.

Ac

Re

(See 9

.4 an

d 9.5)

SINGLETIGHTENEDPLANS


13

Tabl

e II-

CSi

ngle

sam

plin

g pl

ans f

or

redu

ced

insp

ectio

n (M

aster

table

)

Sam

ple

size

code

lette

r

Sam

ple

size

Acc

epta

nce

Quali

ty Li

mits

(redu

ced i

nspe

ction

)


2 2 2 3 5 8 13 20 32 50 80 125

200

315

500

800

11

1 2

1 2 3

1 2 3 4

1 2 3 4 5

1 2 3 4 5 6

1 2 3 4 5 6 8

1 2 3 4 5 6 8 10

1 2 3 4 5 6 8 10 13

1 2 3 4 5 6 8 10 13

1 2 3 4 5 6 8 10 13

1 2 3 4 5 6 8 10 13

1 2 3 4 5 6 8 10 13

1 2 3 4 5 6 8 10 13

2 3 4 5 6 8 10 13

2 3 4 5 6 8 10 13

2 3 4 5 6 8 10 13

3 4 5 6 8 10 13

4 5 6 8 10 13

6 6 8 10 13

8 8 10 13 17

11 11 13 17 24

15 15 17 24

22 22 24

31 31

00

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

0.01

50.

025

0.04

00.

065

0.10

0.15

0.25

0.40

0.65

1.0

1.5

2.5

4.0

6.5

1015

2540

6510

015

025

040

065

010

000.

010

0 0

0 0 1

0 0 1 1

0 0 1 1 2

0 0 1 1 2 3

0 0 1 1 2 3 5

0 0 1 1 2 3 5 7

0 0 1 1 2 3 5 7 10

0 0 1 1 2 3 5 7 10

0 0 1 1 2 3 5 7 10

0 0 1 1 2 3 5 7 10

0 0 1 1 2 3 5 7 10

0 0 1 1 2 3 5 7 10

0 1 1 2 3 5 7 10

0 1 1 2 3 5 7 10

1 1 1 2 3 5 7 10

2 2 2 3 5 7 10

3 3 3 5 7 10

5 5 5 7 10

7 7 7 10 14

10 10 10 14 21

14 14 14 21

21 21 21

30 30

= U

se fi

rst s

ampl

ing

plan

bel

ow a

rrow

. If

sam

ple

size

equa

ls or

exce

eds l

ot o

r bat

ch si

ze, d

o 10

0 pe

rcen

t ins

pect

ion.

= U

se fi

rst s

ampl

ing

plan

abo

ve

arro

w.

= A

ccep

tanc

e nu

mbe

r.=

R

ejecti

on nu

mber.

= If

the

acce

ptan

ce n

umbe

r has

bee

n ex

ceed

ed, b

ut t

he re

jectio

n num

ber h

as no

t been

reach

ed, a

ccept

the lo

t, but r

eins

tate

nor

mal

insp

ectio

n (se

e 10.1

.4).

Ac

Re

(See 9

.4 an

d 9.5)

SINGLEREDUCED

PLANS


14

Tabl

e III

-A

Dou

ble

sam

plin

g pl

ans f

or

norm

al i

nspe

ctio

n (M

aster

table

)Sample size

code letter

Sample

Sample size

Cumulative

sample size

Acc

epta

nce

Quali

ty Li

mits

(redu

ced i

nspe

ction

)


Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

2 2 3 3 5 5 8 8 13 13 20 20 32 32 50 50 80 80 125

125

200

200

315

315

500

500

800

800

1250

1250

2 4 3 6 5 10 8 16 13 26 20 40 32 64 50 100 80 160

125

250

200

400

315

630

500

1000 800

1600

1250

2500

0 12 2

0 1 0 3

2 2 3 4

0 1 0 3 1 4

2 2 3 4 4 5

0 1 0 3 1 4 2 6

2 2 3 4 4 5 5 7

0 1 0 3 1 4 2 6 3 8

2 2 3 4 4 5 5 7 7 9

0 1 0 3 1 4 2 6 3 8 5 12

2 2 3 4 4 5 5 7 7 9 9 13

0 1 0 3 1 4 2 6 3 8 5 12 7 18

2 2 3 4 4 5 5 7 7 9 9 13 11 19

0 1 0 3 1 4 2 6 3 8 5 12 7 18 11 26

2 2 3 4 4 5 5 7 7 9 9 13 11 19 16 27

0 1 0 3 1 4 2 6 3 8 5 12 7 18 11 26

2 2 3 4 4 5 5 7 7 9 9 13 11 19 16 27

0 1 0 3 1 4 2 6 3 8 5 12 7 18 11 26

2 2 3 4 4 5 5 7 7 9 9 13 11 19 16 27

0 1 0 3 1 4 2 6 3 8 5 12 7 18 11 26

2 2 3 4 4 5 5 7 7 9 9 13 11 19 16 27

0 1 0 3 1 4 2 6 3 8 5 12 7 18 11 26

2 2 3 4 4 5 5 7 7 9 9 13 11 19 16 27

0 1 0 3 1 4 2 6 3 8 5 12 7 18 11 26

2 2 3 4 4 5 5 7 7 9 9 13 11 19 16 27

0 1 0 3 1 4 2 6 3 8 5 12 7 18 11 26

2 2 3 4 4 5 5 7 7 9 9 13 11 19 16 27

0 1 0 3 1 4 2 6 3 8 5 12 7 18 11 26

2 2 3 4 4 5 5 7 7 9 9 13 11 19 16 27

0 3 1 4 2 6 3 8 5 12 7 18 11 26

3 4 4 5 5 7 7 9 9 13 11 19 16 27

1 4 2 6 3 8 5 12 7 18 11 26

4 5 5 7 7 9 9 13 11 19 16 27

2 6 3 8 5 12 7 18 11 26

5 7 7 9 9 13 11 19 16 27

3 8 5 12 7 18 11 26

7 9 9 13 11 19 16 27

5 12 7 18 11 26 17 37

9 13 11 19 16 27 22 38

7 18 11 26 17 37 25 56

11 19 16 27 22 38 31 57

11 26 17 37 25 56

16 27 22 38 31 57

17 37 25 56

22 38 31 57

25 5631 57

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

0.01

50.

025

0.04

00.

065

0.10

0.15

0.25

0.40

0.65

1.0

1.5

2.5

4.0

6.5

1015

2540

6510

015

025

040

065

010

000.

010

= U

se fi

rst s

ampl

ing

plan

bel

ow a

rrow

. If

sam

ple

size

equa

ls or

exce

eds l

ot o

r bat

ch si

ze, d

o 10

0 pe

rcen

t ins

pect

ion.

= U

se fi

rst s

ampl

ing

plan

abo

ve

arro

w.

= A

ccep

tanc

e nu

mbe

r.=

R

ejecti

on nu

mber.

= U

se c

orre

spon

ding

sing

le sa

mpl

ing

plan

.

Ac

Re

= U

se c

orre

spon

ding

sing

le sa

mpl

ing

plan

or d

oubl

e sa

mpl

ing

plan

for c

ode

lette

r B b

elow

.+

(See 9

.4 an

d 9.5)

+

++

++

++

++

DOUBLENORMALPLANS


15

Sample size

code letter

Sample

Sample size

Cumulative

sample size

Acc

epta

nce

Quali

ty Li

mits

(tigh

tened

insp

ectio

n)


Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

2 2 3 3 5 5 8 8 13 13 20 20 32 32 50 50 80 80 125

125

200

200

315

315

500

500

800

800

1250

1250

2 4 3 6 5 10 8 16 13 26 20 40 32 64 50 100 80 160

125

250

200

400

315

630

500

1000 800

1600

1250

2500

0 12 2

0 1 0 3

2 2 3 4

0 1 0 3 1 4

2 2 3 4 4 5

0 1 0 3 1 4 2 6

2 2 3 4 4 5 5 7

0 1 0 3 1 4 2 6 3 11

2 2 3 4 4 5 5 7 7 12

0 1 0 3 1 4 2 6 3 11 6 15

2 2 3 4 4 5 5 7 7 12 10 16

0 1 0 3 1 4 2 6 3 11 6 15 9 23

2 2 3 4 4 5 5 7 7 12 10 16 14 24

0 1 0 3 1 4 2 6 3 11 6 15 9 23

2 2 3 4 4 5 5 7 7 12 10 16 14 24

0 1 0 3 1 4 2 6 3 11 6 15 9 23

2 2 3 4 4 5 5 7 7 12 10 16 14 24

0 1 0 3 1 4 2 6 3 11 6 15 9 23

2 2 3 4 4 5 5 7 7 12 10 16 14 24

0 1 0 3 1 4 2 6 3 11 6 15 9 23

2 2 3 4 4 5 5 7 7 12 10 16 14 24

0 1 0 3 1 4 2 6 3 11 6 15 9 23

2 2 3 4 4 5 5 7 7 12 10 16 14 24

0 1 0 3 1 4 2 6 3 11 6 15 9 23

2 2 3 4 4 5 5 7 7 12 10 16 14 24

0 1 0 3 1 4 2 6 3 11 6 15 9 23

2 2 3 4 4 5 5 7 7 12 10 16 14 24

0 1 0 3 1 4 2 6 3 11 6 15 9 23

2 2 3 4 4 5 5 7 7 12 10 16 14 24

0 3 1 4 2 6 3 11 6 15 9 23

3 4 4 5 5 7 7 12 10 16 14 24

1 4 2 6 3 11 6 15 9 23

4 5 5 7 7 12 10 16 14 24

2 6 3 11 6 15 9 23

5 7 7 12 10 16 14 24

3 11 6 15 9 23 15 34

7 12 10 16 14 24 20 35

6 15 9 23 15 34 23 52

10 16 14 24 20 35 29 53

9 23 15 34 23 52

14 24 20 35 29 53

15 34 23 52

20 35 29 53

23 5229 53

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

0.01

50.

025

0.04

00.

065

0.10

0.15

0.25

0.40

0.65

1.0

1.5

2.5

4.0

6.5

1015

2540

6510

015

025

040

065

010

000.

010

(See 9

.4 an

d 9.5)

SFi

rst

Seco

nd20

0020

0020

0040

000 1

2 2

= U

se fi

rst s

ampl

ing

plan

bel

ow a

rrow

. If

sam

ple

size

equa

ls or

exce

eds l

ot o

r bat

ch si

ze, d

o 10

0 pe

rcen

t ins

pect

ion.

= U

se fi

rst s

ampl

ing

plan

abo

ve

arro

w.

= A

ccep

tanc

e nu

mbe

r.=

R

ejecti

on nu

mber.

= U

se c

orre

spon

ding

sing

le sa

mpl

ing

plan

.

Ac

Re

= U

se c

orre

spon

ding

sing

le sa

mpl

ing

plan

or d

oubl

e sa

mpl

ing

plan

for c

ode

lette

r B b

elow

.+

++

++

++

++

DOUBLETIGHTENED

PLANS

Tabl

e III

-B

Dou

ble

sam

plin

g pl

ans f

or

tight

ened

insp

ectio

n (M

aster

table

)


16

Tabl

e III

-C

Dou

ble

sam

plin

g pl

ans f

or

redu

ced

insp

ectio

n (M

aster

table

)Sample size

code letter

Sample

Sample size

Cumulative

sample size

Acc

epta

nce

Quali

ty Li

mits

(redu

ced i

nspe

ction

)


Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

Firs

tSe

cond

2 2 3 3 5 5 8 8 13 13 20 20 32 32 50 50 80 80 125

125

200

200

315

315

500

500

2 4 3 6 5 10 8 16 13 26 20 40 32 64 50 100 80 160

125

250

200

400

315

630

500

1000

0 02 2

0 0 0 0

2 2 3 4

0 0 0 0 0 1

2 2 3 4 4 5

0 0 0 0 0 1 0 3

2 2 3 4 4 5 4 6

0 0 0 0 0 1 0 3 1 4

2 2 3 4 4 5 4 6 5 7

0 0 0 0 0 1 0 3 1 4 2 6

2 2 3 4 4 5 4 6 5 7 7 9

0 0 0 0 0 1 0 3 1 4 2 6 3 8

2 2 3 4 4 5 4 6 5 7 7 9 8 12

0 0 0 0 0 1 0 3 1 4 2 6 3 8 5 12

2 2 3 4 4 5 4 6 5 7 7 9 8 12 10 16

0 0 0 0 0 1 0 3 1 4 2 6 3 8 5 12

2 2 3 4 4 5 4 6 5 7 7 9 8 12 10 16

0 0 0 0 0 1 0 3 1 4 2 6 3 8 5 12

2 2 3 4 4 5 4 6 5 7 7 9 8 12 10 16

0 0 0 0 0 1 0 3 1 4 2 6 3 8 5 12

2 2 3 4 4 5 4 6 5 7 7 9 8 12 10 16

0 0 0 0 0 1 0 3 1 4 2 6 3 8 5 12

2 2 3 4 4 5 4 6 5 7 7 9 8 12 10 16

0 0 0 0 0 1 0 3 1 4 2 6 3 8 5 12

2 2 3 4 4 5 4 6 5 7 7 9 8 12 10 16

0 0 0 1 0 3 1 4 2 6 3 8 5 12

3 4 4 5 4 6 5 7 7 9 8 12 10 16

0 1 0 3 1 4 2 6 3 8 5 12

4 5 4 6 5 7 7 9 8 12 10 16

0 3 1 4 2 6 3 8 5 12

4 6 5 7 7 9 8 12 10 16

1 4 2 6 3 8 5 12

5 7 7 9 8 12 10 16

2 6 3 8 5 12

7 9 8 12 10 16

3 8 5 12

8 12 10 16

5 12 7 18

10 16 12 22

7 18 11 26

12 22 17 30

11 2617 30

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

0.01

50.

025

0.04

00.

065

0.10

0.15

0.25

0.40

0.65

1.0

1.5

2.5

4.0

6.5

1015

2540

6510

015

025

040

065

010

000.

010

= U

se fi

rst s

ampl

ing

plan

bel

ow a

rrow

. If

sam

ple

size

equa

ls or

exce

eds l

ot o

r bat

ch si

ze, d

o 10

0 pe

rcen

t ins

pect

ion.

= U

se fi

rst s

ampl

ing

plan

abo

ve

arro

w.

= A

ccep

tanc

e nu

mbe

r.=

R

ejecti

on nu

mber.

= U

se c

orre

spon

ding

sing

le sa

mpl

ing

plan

.=

If,

afte

r the

seco

nd sa

mpl

e, th

e ac

cept

ance

num

ber h

as b

een

exce

eded

, but t

he re

jectio

n num

ber h

as no

t been

reach

ed,

ac

cept

the

lot,

but r

eins

tate

nor

mal

insp

ectio

n (se

e 10.1

.4).

Ac

Re

= U

se c

orre

spon

ding

sing

le sa

mpl

ing

plan

or d

oubl

e sa

mpl

ing

plan

for c

ode

lette

r D b

elow

.+

(See 9

.4 an

d 9.5)

+

++

++

++

++

++

++

+

+

+ ++

++

++

++

DOUBLEREDUCEDPLANS


17

Tabl

e IV

-A

Mul

tiple

sam

plin

g pl

ans f

or

norm

al i

nspe

ctio

n (M

aster

table

)Sample size

code letter

Sample

Sample size

Cumulative

sample size

Acc

epta

nce

Quali

ty Li

mits

(norm

al ins

pecti

on)

A CB D E F G H

Firs

tSe

cond

Third

Fourt

hFi

fthSi

xth

Seven

thFi

rst

Seco

ndTh

irdFo

urt

hFi

fthSi

xth

Seven

thFi

rst

Seco

ndTh

irdFo

urt

hFi

fthSi

xth

Seven

thFi

rst

Seco

ndTh

irdFo

urt

hFi

fthSi

xth

Seven

thFi

rst

Seco

ndTh

irdFo

urt

hFi

fthSi

xth

Seven

th

2 2 2 2 2 2 2 3 3 3 3 3 3 3 5 5 5 5 5 5 5 8 8 8 8 8 8 8 13 13 13 13 13 13 13

2 4 6 8 10 12 14

2 2 2 3 3 3 3

# # 0 0 1 1 2

2 3 3 4 4 5 5

# 0 0 1 2 3 4

3 3 4 5 6 6 7

# 0 1 2 3 4 6

4 5 6 7 8 9 10

# 1 2 3 5 7 9

4 6 8 10 11 12 14

0 1 3 5 7 10 13

5 8 10 13 15 17 19

0 3 6 8 11 14 18

7 10 13 17 20 23 26

1 4 8 12 17 21 25

9 14 19 25 29 33 38

2 7 13 19 25 31 37

12 19 27 34 40 47 54

4 11 19 27 36 45 53

16 27 39 49 58 68 78

6 17 29 40 53 65 772 2 2 3 3 3 3

# # 0 0 1 1 2

2 3 3 4 4 5 5

# 0 0 1 2 3 4

3 3 4 5 6 6 7

# 0 1 2 3 4 6

4 5 6 7 8 9 10

# 1 2 3 5 7 9

4 6 8 10 11 12 14

0 1 3 5 7 10 13

5 8 10 13 15 17 19

0 3 6 8 11 14 18

7 10 13 17 20 23 26

1 4 8 12 17 21 25

9 14 19 25 29 33 38

2 7 13 19 25 31 37

12 19 27 34 40 47 54

4 11 19 27 36 45 53

16 27 39 49 58 68 78

6 17 29 40 53 65 772 2 2 3 3 3 3

# # 0 0 1 1 2

2 3 3 4 4 5 5

# 0 0 1 2 3 4

3 3 4 5 6 6 7

# 0 1 2 3 4 6

4 5 6 7 8 9 10

# 1 2 3 5 7 9

4 6 8 10 11 12 14

0 1 3 5 7 10 13

5 8 10 13 15 17 19

0 3 6 8 11 14 18

7 10 13 17 20 23 26

1 4 8 12 17 21 25

9 14 19 25 29 33 38

2 7 13 19 25 31 372 2 2 3 3 3 3

# # 0 0 1 1 2

2 3 3 4 4 5 5

# 0 0 1 2 3 4

3 3 4 5 6 6 7

# 0 1 2 3 4 6

4 5 6 7 8 9 10

# 1 2 3 5 7 9

4 6 8 10 11 12 14

0 1 3 5 7 10 13

5 8 10 13 15 17 19

0 3 6 8 11 14 18

7 10 13 17 20 23 26

1 4 8 12 17 21 25

9 14 19 25 29 33 38

2 7 13 19 25 31 372 2 2 3 3 3 3

# # 0 0 1 1 2

2 3 3 4 4 5 5

# 0 0 1 2 3 4

3 3 4 5 6 6 7

# 0 1 2 3 4 6

4 5 6 7 8 9 10

# 1 2 3 5 7 9

4 6 8 10 11 12 14

0 1 3 5 7 10 13

5 8 10 13 15 17 19

0 3 6 8 11 14 18

7 10 13 17 20 23 26

1 4 8 12 17 21 25

9 14 19 25 29 33 38

2 7 13 19 25 31 372 2 2 3 3 3 3

# # 0 0 1 1 2

2 3 3 4 4 5 5

# 0 0 1 2 3 4

3 3 4 5 6 6 7

# 0 1 2 3 4 6

4 5 6 7 8 9 10

# 1 2 3 5 7 9

4 6 8 10 11 12 14

0 1 3 5 7 10 13

5 8 10 13 15 17 19

0 3 6 8 11 14 18

7 10 13 17 20 23 26

1 4 8 12 17 21 25

9 14 19 25 29 33 38

2 7 13 19 25 31 37

3 6 9 12 15 18 21 5 10 15 20 25 30 35 8 16 24 32 40 48 56 13 26 39 52 65 78 91

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

Re

Ac

0.01

50.

025

0.04

00.

065

0.10

0.15

0.25

0.40

0.65

1.0

1.5

2.5

4.0

6.5

1015

2540

6510

015

025

040

065

010

000.

010

= U

se fi

rst s

ampl

ing

plan

bel

ow a

rrow

(refe

r to c

ontin

uatio

n of t

able

on fo

llow

ing

page

, w

hen

nece

ssar

y). If

samp

le siz

e equ

als or

exce

eds l

ot o

r bat

ch si

ze, d

o 10

0 pe

rcen

t ins

pect

ion.

= U

se fi

rst s

ampl

ing

plan

abo

ve

arro

w.

= U

se c

orre

spon

ding

sing

le sa

mpl

ing

plan

.=

U

se c

orre

spon

ding

dou

ble

sam

plin

g pl

an o

r mul

tiple

sam

plin

g pl

an fo

r cod

e le

tter D

bel

ow.

++

= A

ccep

tanc

e nu

mbe

r.=

R

ejecti

on nu

mber.

= A

ccep

tanc

e no

t per

mitt

ed a

t thi

s sam

ple

size.

= U

se c

orre

spon

ding

dou

ble

sam

plin

g pl

an.

Ac

Re # ##

(See 9

.4 an

d 9.5)

JFi

rst

Seco

ndTh

irdFo

urt

hFi

fthSi

xth

Seven

th

20 20 20 20 20 20 20

20 40 60 80 100

120

140

++

++

++

++

++

++

++

++

++

++

++

++

++

++

++

++

++

######

MULTIPLENORMAL

PLANS


18

Sample size

code letter

Sample

Sample size

Cumulative

sample size

Acc

epta

nce

Quali

ty Li

mits

(norm

al ins

pecti

on)

K L M N P Q

Firs

tSe

cond

Third

Fourt

hFi

fthSi

xth

Seven

thFi

rst

Seco

ndTh

irdFo

urt

hFi

fthSi

xth

Seven

thFi

rst

Seco

ndTh

irdFo

urt

hFi

fthSi

xth

Seven

thFi

rst

Seco

ndTh

irdFo

urt

hFi

fthSi

xth

Seven

thFi

rst

Seco

ndTh

irdFo

urt

hFi

fthSi

xth

Seven

th

50 50 50 50 50 50 50 80 80 80 80 80 80 80 125

125

125

125

125

125

125

200

200

200

200

200

200

200

315

315

315

315

315

315

315

50 100

150

200

250

300

350

Firs

tSe

cond

Third

Fourt

hFi

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MULTIPLENORMALPLANS

Tabl

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19

Tabl

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spec

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Sample size

code letter

Sample

Sample size

Cumulative

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Acc

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Quali

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A CB D E F G H

Firs

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ansi+asq+z1[1].4-2003

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