(Attachment_03)_ANSI_Z1_4-2008.pdf

ANSI/ASQ Z1.4-2008

AMERICAN SOCIETY FOR QUALITY

600 NORTH PLANKINTON AVENUE

MILWAUKEE, 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 by The Statistics Subcommittee of the Accredited

Standards Committee Z1 on Quality, Environment, Dependability and Statistics

Secretariat American Society for Quality

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Abstract Sampling Procedures and Tables for Inspection by Attributes is an acceptance sampling system to be used with switching rules on a continuing stream of lots for AQL specified. It provides tightened, normal, and reduced plans to be applied for attributes 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, the consumer, 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 are cautioned to obtain the latest editions.

CAUTION NOTICE: This American National Standard may be revised or withdrawn at any time.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

Published by

AMERICAN SOCIETY FOR QUALITY

600 NORTH PLANKINTON

MILWAUKEE, WISCONSIN 53203

© 2008 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 the prior written permission of the publisher.

Printed in the United States of America

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Foreword iii

(This foreword is not a part of the American National Standard—Sampling Procedures and Tables for Inspection by Attributes, Z1.4-2008)

This standard is a reaffirmation of ANSI/ASQC Z1.4-2003, “Sampling Procedures and Tables for Inspection by Attributes.”

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

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Table of Contents Paragraph Page

1. SCOPE

2. DEFINITIONS AND TERMINOLOGY

3. PERCENT NONCONFORMING AND NONCONFORMITIES PER

HUNDRED UNITS

4. ACCEPTANCE QUALITY LIMIT (AQL)

5. SUBMISSION OF PRODUCT

6. ACCEPTANCE AND NON-ACCEPTANCE

7. DRAWING OF SAMPLES

8. NORMAL, TIGHTENED, AND REDUCED INSPECTION

9. SAMPLING PLANS

10. DETERMINATION OF ACCEPTABILITY

11. SUPPLEMENTARY INFORMATION

Tables Table I Sample Size Code Letters Table II-A Single Sampling Plans for Normal Inspection (Master Table) Table II-B Single Sampling Plans for Tightened Inspection (Master Table) Table II-C Single Sampling Plans for Reduced Inspection (Master Table) Table III-A Doubling Sampling Plans for Normal Inspection (Master Table) Table III-B Doubling Sampling Plans for Tightened Inspection (Master Table) Table III-C Doubling Sampling Plans for Reduced Inspection (Master Table) Table IV-A Multiple Sampling Plans for Normal Inspection (Master Table) Table IV-B Multiple Sampling Plans for Tightened Inspection (Master Table) Table IV-C Multiple Sampling Plans for Reduced Inspection (Master Table) Table V-A Factors for Determining Approximate Values for Average Outgoing Quality Limits for Normal

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

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

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

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

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

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

(normal and tightened inspection) Table X-A Sample Size Code Letter A—Individual Plans Table X-B Sample Size Code Letter B—Individual Plans Table X-C Sample Size Code Letter C—Individual Plans

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Table X-D Sample Size Code Letter D—Individual Plans Table X-E Sample Size Code Letter E—Individual Plans Table X-F Sample Size Code Letter F—Individual Plans Table X-G Sample Size Code Letter G—Individual Plans Table X-H Sample Size Code Letter H—Individual Plans Table X-J Sample Size Code Letter J—Individual Plans Table X-K Sample Size Code Letter K—Individual Plans Table X-L Sample Size Code Letter L—Individual Plans Table X-M Sample Size Code Letter M—Individual Plans Table X-N Sample Size Code Letter N—Individual Plans Table X-P Sample Size Code Letter P—Individual Plans Table X-Q Sample Size Code Letter Q—Individual Plans Table X-R Sample Size Code Letter R—Individual Plans Table X-S Sample Size Code Letter S—Individual Plans Table XI Average Outgoing Quality Limit Factors for ANSI-Z1.4 Scheme Performance

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

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

Pa = 5 Percent (Single Sampling) Table XIV Average Sample Size Tables for ANSI-Z1.4 Scheme Performance (Single Sampling) Table XV-A Sample Size Code Letter A—Scheme Performance Table XV-B Sample Size Code Letter B—Scheme Performance Table XV-C Sample Size Code Letter C—Scheme Performance Table XV-D Sample Size Code Letter D—Scheme Performance Table XV-E Sample Size Code Letter E—Scheme Performance Table XV-F Sample Size Code Letter F—Scheme Performance Table XV-G Sample Size Code Letter G—Scheme Performance Table XV-H Sample Size Code Letter H—Scheme Performance Table XV-J Sample Size Code Letter J—Scheme Performance Table XV-K Sample Size Code Letter K—Scheme Performance Table XV-L Sample Size Code Letter L—Scheme Performance Table XV-M Sample Size Code Letter M—Scheme Performance Table XV-N Sample Size Code Letter N—Scheme Performance Table XV-P Sample Size Code Letter P—Scheme Performance Table XV-Q Sample Size Code Letter Q—Scheme Performance Table XV-R Sample Size Code Letter R—Scheme Performance

INDEX OF TERMSWITH SPECIAL MEANINGS

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1. SCOPE

1.1 PURPOSE. This publication establishes sampling

plans and procedures for inspection by attributes. When specified by the responsible authority, this publication shall be referenced in the specification, contract, inspection instructions, or other documents and the provisions set forth herein shall govern. The “responsible authority” shall be designated in one of the above documents, as agreed to by the purchaser and seller or producer and user.

1.2 APPLICATION. Sampling plans designated in this

publication are applicable, but not limited, to inspection of the 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 for the inspection of isolated lots or batches, but, in this latter case, 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 of product (see 1.5) with the requirements.

1.4 INSPECTION BY ATTRIBUTES. Inspection by

attributes is inspection whereby either the unit of product is classified simply as conforming or nonconforming, or the number of nonconformities in the unit of products is counted, with respect to a given requirement or set of requirements.

1.5 UNIT OF PRODUCT. The unit of product is the unit

inspected 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 end product, or the end product itself. The unit of product may or may not be the same as the unit of purchase, supply, pro-duction, or shipment.

2. DEFINITIONSAND TERMINOLOGY

The definitions and terminology employed in this standard are in accord with ANSI/ASQ A3534-2-2006 (Terms, Symbols, and Definitions for Acceptance Sampling). The following two definitions are particularly important in applying the standard.

DEFECT: A departure of a quality characteristic from its intended level or state that occurs with a sever-ity sufficient to cause an associated product or service 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 occurs with severity sufficient to cause an associated product or service not to meet a specification requirement.

These acceptance sampling plans for attributes are given in terms of the percent or proportion of product in a lot or batch that 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 widely used criteria for acceptance sampling.

In the use of this standard it is helpful to distinguish between:

a. an individual sampling plan—a specific plan that states the sample size or sizes to be used, and the associated acceptance criteria.

SAMPLING PROCEDURESAND TABLES

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b. a sampling scheme—a combination of sampling plans with switching rules and possibly a provision for discontinuance of inspection. In this standard the terms “sampling scheme” and “scheme per-formance” will be used in the restricted sense described in Sec. 11.1.

c. a sampling system—a collection of sampling schemes. This standard is a sampling system indexed by lot-size ranges, inspection levels, and AQLs.

3. PERCENT NONCONFORMINGAND

NONCONFORMITIES PER HUNDRED UNITS

3.1 EXPRESSION OF NONCONFORMANCE. The

extent of nonconformance of product shall be expressed either 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 one hundred times the number of nonconforming units divided by the total number of units of product, i.e.:

3.3 NONCONFORMITIES PER HUNDRED UNITS.

The number of nonconformities per hundred units of any given quantity of units of product is one hundred times the number of nonconformities contained therein (one or more nonconformities 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 with statistical independence within and between units.

4. ACCEPTANCE QUALITY LIMIT (AQL)

4.1 USE. The AQL together with the Sample Size Code

Letter, is used for indexing the sampling plans provided herein.

4.2 DEFINITION. The AQL is the quality level that is the

worst tolerable process average when a continuing series of lots is submitted for acceptance sampling.

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

4.3 NOTE ON THE MEANING OF AQL. The concept

of AQL only applies when an acceptance sampling scheme with rules for switching between normal, tightened and reduced inspection and discontinuance of sampling inspec-tion is used. These rules are designed to encourage suppliers to have process averages consistently better than the AQL. If suppliers fail to do so, there is a high probability of being switched from normal inspection to tightened inspection where lot acceptance becomes more difficult. Once on tight-ened inspection, unless corrective action is taken to improve product 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 can be accepted with fairly high probability, the designation of an AQL does not suggest that this is necessarily a desirable quality level. The AQL is a parameter of the sampling scheme and should not be confused with a process average which describes the operating level of a manufacturing process. It is expected that the product quality level will be less than the AQL to avoid excessive non-accepted lots.

The sampling plans in this standard are so arranged that the probability of lot acceptance at the designated AQL depends upon sample size, being generally higher for large samples than for small samples for a given AQL. To determine the specific protection to the consumer at a given AQL, it is nec-essary to refer to the operating characteristic curves (which are provided in this standard) of the corresponding scheme and its constituent plans.

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

4.4 LIMITATION. The designation of an AQL shall not

imply that the supplier has the right to knowingly supply any nonconforming unit of product.

4.5 SPECIFYINGAQLs. TheAQL 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 nonconformities of a type felt to be of the highest concern for the product or service and therefore be assigned a small AQL value; Group B may include nonconformities of the next higher degree of concern and therefore be assigned a larger AQL value than for 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 × 100 hundred units Number of units inspected

Number nonconforming Percent nonconforming =

Number of units inspected × 100

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4.6 PREFERRED AQLs. The values of AQLs given in

these tables are known as preferred AQLs. If, for any prod-uct, an AQL be designated other than a preferred AQL, these tables are not applicable.

5. SUBMISSION OF PRODUCT

5.1 LOT OR BATCH. The term lot or batch shall mean

“inspection lot” or “inspection batch,” i.e., a collection of units of product from which a sample is to be drawn and inspected to determine conformance with the acceptability criteria, and may differ from a collection of units designated as a lot or batch 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). Each lot or batch shall, as far as is practicable, consist of units of product of a single type, grade, class, size, and composition, manufactured under essentially the same conditions, and at essentially the same time.

5.3 LOT OR BATCH SIZE. The lot or batch size is the

number of units of product in a lot or batch.

5.4 PRESENTATION OF LOTS OR BATCHES. The

formation of the lots or batches, lot or batch size, and the manner in which each lot or batch is to be presented and identified by the supplier shall be designated or approved by the responsible authority. As necessary, the supplier shall provide adequate and suitable storage space for each lot or batch, equipment needed for proper identification and pres-entation, and personnel for all handling of product required for drawing of samples.

6. ACCEPTANCEAND NON-ACCEPTANCE

6.1 ACCEPTABILITY OF LOTS OR BATCHES.

Acceptability of a lot or batch will be determined by the use of a sampling plan or plans associated with the designated AQL or AQLs.

In the use of this standard a statement that a lot is acceptable means simply that sample results satisfy the standard’s acceptance criteria. The acceptance of a lot is not intended to provide information about lot quality. If a stream of lots from a given process is inspected under an acceptance sampling scheme such as provided in this standard, some lots will be accepted and others will not. If all incoming lots are assumed to be at the same process average and if the nonconforming items that are discovered and replaced by conforming items during sample inspection are ignored, it will be found that both the set of accepted lots and the set of non-accepted lots will have the same long run average quality as the original set of lots submitted for inspection. Inspection of incoming lots whose quality levels vary around a fixed long run aver-age quality level will divide the lots into a set of accepted lots and a set of non-accepted lots, but it will be found that the long run average quality of the accepted lots is only slightly better than the long run average quality of the non-accepted lots. Replacement of the nonconforming items that are dis-covered during sample inspection does not alter this finding because the samples are a small fraction of the lots.

The purpose of this standard is, through the economic and psychological pressure of lot non-acceptance, to induce a supplier to maintain a process average at least as good as the specified AQL while at the same time providing an upper limit on the consideration of the consumer’s risk of accept-ing occasional poor lots. The standard is not intended as a procedure for estimating lot quality or for segregating lots.

In acceptance sampling, when sample data do not meet the acceptance criteria, it is often stated that the lot is to be “rejected.” In this connection, the words “to reject” generally are used. Rejection in an acceptance sampling sense means to decide that a batch, lot or quantity of product, material, or service has not been shown to satisfy the acceptance criteria based on the information obtained from the sample(s).

In acceptance sampling, the words “to reject” generally are used to mean “to not accept” without direct implication of product usability. Lots which are “rejected” may be scrapped, sorted (with or without nonconforming units being replaced), reworked, re-evaluated against more spe-cific usability criteria, held for additional information, etc.

Since the common language usage of “reject” often results in an inference of unsafe or unusable product, it is recom-mended that “not accept” be understood rather than “reject” in the use of this standard.

The word “non-acceptance” is used here for “rejection” when it refers to the result of following the procedure.

Forms of the word “reject” are retained when they refer to actions the customer may take, as in “rejection number.”

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6.2 NONCONFORMING UNITS. The right is reserved

to reject any unit of product found nonconforming during inspection whether that unit of product forms a part of a sample or not, and whether the lot or batch as a whole is accepted 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 DESIGNATED

NONCONFORMITIES. Since most acceptance sampling involves evaluation of more than one quality characteristic, and since these may differ in importance in terms of quality and/or economic effects, it is often desirable to classify the types of nonconformity according to agreed upon groupings.

Specific assignment of types of nonconformities to each class is a function of agreement on specific sampling appli-cations. In general, the function of such classification is to permit the use of a set of sampling plans having a common sample size, but different acceptance numbers for each class having 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 for designated classes of nonconformities. The right is reserved to inspect every unit submitted by the supplier for specified nonconformities, and to reject the lot or batch immediately, when a nonconformity of this class is found. The right is reserved also to sample, for specified classes of nonconfor-mities, lots or batches submitted by the supplier and to reject any 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 or

batches found unacceptable shall be resubmitted for rein-spection only after all units are re-examined or re-tested and all nonconforming units are removed or nonconformities corrected. The responsible authority shall determine whether normal or tightened inspection shall be used on reinspection and whether reinspection shall include all types or classes of nonconformities or only the particular types or classes of nonconformities which caused initial rejection.

7. DRAWING OF SAMPLES

7.1 SAMPLE. A sample consists of one or more units of

product drawn from a lot or batch, the units of the sample being selected at random without regard to their quality. The number of units of product in the sample is the sample size.

7.2 SAMPLING. When appropriate, the number of units

in the sample shall be selected in proportion to the size of sublots or subbatches, or parts of the lot or batch, identified by some rational criterion. In so doing, the units from each part of the lot or batch shall be selected at random, as defined in ANSI/ASQ A3534-2-2006.

7.3 TIMEOFSAMPLING.Samples may be drawn after all

the units comprising the lot or batch have been produced, or samples may be drawn during production of the lot or batch.

7.4 DOUBLEORMULTIPLE SAMPLING.Where dou-

ble or multiple sampling is to be used, each sample shall be selected over the entire lot or batch.

8. NORMAL, TIGHTENEDAND REDUCED

INSPECTION

8.1 INITIATION OF INSPECTION. Normal inspection

will be used at the start of inspection unless otherwise directed by the responsible authority.

8.2 CONTINUATION OF INSPECTION. Normal, tight-

ened or reduced inspection shall continue unchanged on successive lots or batches except where the switching pro-cedures given below require change.

8.3 SWITCHING PROCEDURES.

8.3.1 NORMAL TO TIGHTENED. When normal

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

8.3.2 TIGHTENED TO NORMAL. When tightened

inspection is in effect, normal inspection shall be instituted when 5 consecutive lots or batches have been considered acceptable on original inspection.

8.3.3 NORMALTOREDUCED.When normal inspection

is in effect, reduced inspection shall be instituted providing that 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 on original inspection; and

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b. The total number of nonconforming units (or non-conformities) in the samples from the preceding 10 lots or batches (or such other number as was used for condition “a” above) is equal to or less than the applicable limit number given in Table VIII (see 8.5). If double or multiple sampling is in use, all samples inspected should be included, not “first” samples only; and

c. Production is at a steady rate; and

d. Reduced inspection is considered desirable by the responsible authority.

8.3.4 REDUCED TO NORMAL. When reduced inspec-

tion is in effect, normal inspection shall be instituted if any of the following occur on original inspection:

a. A lot or batch is rejected; or

b. A lot or batch is considered acceptable under the procedures for reduced inspection given in 10.1.4; or

c. Production becomes irregular or delayed; or

d. Other conditions warrant that normal inspection shall be instituted.

8.4 DISCONTINUATION OF INSPECTION. If the

cumulative 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 be resumed until corrective action has been taken. Tightened inspection 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 parties to the inspection, that is, the supplier and the end item cus-tomer, the requirements of 8.3.3b may be dropped. This action will have little effect on the operating properties of the scheme.

8.6 SWITCHING SEQUENCE. A schematic diagram

describing the sequence of application of the switching rules is shown in Figure 1.

9. SAMPLING PLANS

9.1 SAMPLING PLAN. A sampling plan indicates the

number of units of product from each lot or batch which are to be inspected (sample size or series of sample sizes) and the criteria for determining the acceptability of the lot or batch (acceptance and rejection numbers).

9.2 INSPECTION LEVEL. The inspection level deter-

mines the relationship between the lot or batch size and the sample size. The inspection level to be used for any partic-ular requirement will be prescribed by the responsible authority. Three inspection levels: I, II and III are given in Table I for general use. Unless otherwise specified, Inspection Level II will be used. However, Inspection Level I may be specified when less discrimination is needed, or Level III may be specified for greater discrimination. Four additional special levels: S-1, S-2, S-3, and S-4, are given in the same table and may be used where relatively small sample sizes are necessary and large sampling risks can or must be tolerated.

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

9.3 CODE LETTERS. Sample sizes are designated by

code letters. Table I shall be used to find the applicable code letter for the particular lot or batch size and the prescribed inspection level.

9.4 OBTAINING SAMPLING PLAN. The AQL and the

code letter shall be used to obtain the sampling plan from Tables II, III, or IV.When no sampling plan is available for a given combination of AQL and code letter, the tables direct the user to a different letter. The sample size to be used is given by the new code letter, not by the original letter. If this procedure leads to different sample sizes for different classes of nonconformities, the code letter corresponding to the largest sample size derived may be used for all classes of nonconformities when designated or approved by the respon-sible authority. As an alternative to a single sampling plan with an acceptance number of 0, the plan with an acceptance number of 1 with its correspondingly larger sample size for a designated AQL (where available), may be used when des-ignated or approved by the responsible authority.

9.5 TYPESOF SAMPLINGPLANS. Three types of sam-

pling plans: Single, Double and Multiple, are given in Tables II, III, and IV, respectively. When several types of plans are available for a given AQL and code letter, any one may be used. A decision as to type of plan, either single, double, or multiple, when available for a given AQL and code letter, will usually be based upon the comparison between the

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10. DETERMINATION OFACCEPTABILITY

10.1 PERCENT NONCONFORMING INSPECTION.

To determine acceptability of a lot or batch under percent non-conforming inspection, the applicable sampling plan shall be used 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 by the plan. If the number of nonconforming units found in the sample is equal to or less than the acceptance number, the lot or batch shall be considered acceptable. If the number of nonconforming units is equal to or greater than the rejection number, the lot or batch shall be considered not acceptable.

10.1.2 DOUBLE SAMPLE PLAN. The number of sample

units first inspected shall be equal to the first sample size given by the plan. If the number of nonconforming units found in the first sample is equal to or less than the first acceptable number, the lot or batch shall be considered acceptable. If the number of nonconforming units found in the first sample is equal to or greater than the first rejection number, 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, a second sample of the size given by the plan shall be inspected. The number of nonconforming units found in the first and second samples shall be accumulated. If the cumu-lative number of nonconforming units is equal to or less than the 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 rejection number, the lot or batch shall be considered not acceptable.

10.1.3 MULTIPLE SAMPLE PLAN. Under multiple

sampling, the procedure shall be similar to that specified in 10.1.2, except that the number of successive samples required to reach a decision might be more than two.

10.1.4 SPECIAL PROCEDURE FOR REDUCED

INSPECTION. Under reduced inspection, the sampling procedure may terminate without making a decision. In these circumstances, the lot or batch will be considered acceptable, but normal inspection will be reinstated starting with the next lot or batch (see 8.3.4(b)).

10.2 NONCONFORMITIES PER HUNDRED UNITS

INSPECTION. To determine the acceptability of a lot or batch 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. Those for the individual plans that represent the elements of the schemes 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 in Tables XI, XII, XIII, XIV, and XV. Scheme performance is defined as the composite proportion of lots accepted at a stated percent nonconforming when the switching rules are applied. The term scheme performance is used here in a very restrictive sense. It refers to how the ANSI Z1.4 scheme of switching rules would operate at a given process level under the assumption that the process stays at that level even after switching to tightened inspection or discontinuation of inspection. This gives a conservative “worst case” description of the performance of the scheme for use as a baseline in the sense that if the psychological and economic pressures asso-ciated with the switching rules are considered, the protection of the scheme may be somewhat better than that shown.

Operating characteristic curves are given in Table X for individual sampling plans for normal and tightened inspec-tion. The operating characteristic curve for unqualified acceptance under reduced inspection can be found by using the AQL index of the normal plan with the sample size(s) and acceptance number(s) of the reduced plan. The curves shown 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 the Poisson distribution and apply for nonconformities per hun-dred units inspection; those for AQLs of 10.0 or less and sample 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 than 80 are based on the Poisson distribution and apply either for nonconformities per hundred units inspection, or for percent

ANSI/ASQ Z1.4-2008

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Not for Resale, 03/18/2010 08:46:20 MDTNo reproduction or networking permitted without license from IHS nonconforming inspection (the Poisson distribution being an adequate approximation to the binomial distribution under these conditions). Tabulated values corresponding to selected values of probabilities of acceptance (Pa in percent) are given for each of the curves shown, and, in addition, are indexed for tightened inspection, and also show values for nonconformities per hundred units for AQLs of 10.0 or less and sample sizes of 80 or less.

The operating characteristic curves for scheme performance shown in Table XV indicate the percentage of lots or batches which may be expected to be accepted under use of the switching rules with the various sampling plans for a given process quality subject to the restrictions stated above. The operating characteristic curves of scheme performance are based on the use of limit numbers in switching to reduced inspection and are approximately correct when the limit numbers for reduced inspection are not used under Option

8.5. The curves also assume a return to tightened inspection

when inspection is resumed after discontinuation has been imposed. This is also true of average outgoing quality limit and 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 low levels of percent nonconforming and that the tightened plan for high levels of percent nonconforming. Use of the reduced plan increases scheme probability of acceptance only for extremely low levels of percent nonconforming.

11.2 PROCESS AVERAGE. The process average is the

average percent nonconforming or average number of non-conformities per hundred units (whichever is applicable) of product submitted by the supplier for original inspection.

Original inspection is the first inspection of a particular quantity of product as distinguished from the inspection of product which has been resubmitted after prior rejection.

When double or multiple sampling is used, only first sample results shall be included in the process average calculation.

11.3 AVERAGE OUTGOING QUALITY (AOQ). The

AOQ is the average quality of outgoing product including all accepted lots or batches, plus all lots or batches which are not accepted after such lots or batches have been effectively 100 percent inspected and all nonconforming units replaced by conforming units.

11.4 AVERAGE OUTGOING QUALITY LIMIT

(AOQL). The AOQL is the maximum of the AOQs for all possible incoming qualities for a given acceptance sampling plan. AOQL values are given in Table V-A for each of the single sampling plans for normal inspection and in TableV-B for each of the single sampling plans for tightened inspec-tions. AOQL values for ANSI Z1.4 scheme performance are given in Table XI subject to the restrictions of 11.1. They show the average outgoing quality limits for scheme per-formance when using single sampling. AOQL will be slightly higher when the limit numbers for reduced inspec-tion are not used under Option 8.5.

11.5 AVERAGE SAMPLE SIZE CURVES. Average

sample size curves for double and multiple sampling as compared to the single sampling plan for each acceptance number are in Table IX. These show the average sample sizes which may be expected to occur under the various sampling plans for a given process quality level. The curves assume no curtailment of inspection and are approximate to the 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. Average sample size tables for ANSI Z1.4 scheme performance are given in Table XIV. They show the average sample size for scheme performance when using single sampling.

11.6 LIMITING QUALITY PROTECTION.

11.6.1 USE OF INDIVIDUAL PLANS. This standard is

intended to be used as a system employing tightened, nor-mal, and reduced inspection on a continuing series of lots to achieve consumer protection while assuring the producer that 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 the standard and used without the switching rules. This is not the intended application of the ANSI Z1.4 system and its use in this way should not be referred to as inspection under ANSI Z1.4.When employed in this way, this document sim-ply represents a repository for a collection of individual plans indexed by AQL. The operating characteristics and other 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 or

batch is of an isolated nature, it is desirable to limit the selection of sampling plans to those, associated with a des-ignated AQL value, that provide not less than a specified limiting quality protection. Sampling plans for this purpose

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Not for Resale, 03/18/2010 08:46:20 MDTNo reproduction or networking permitted without license from IHS can be selected by choosing a Limiting Quality (LQ) and a consumer’s risk to be associated with it. Limiting Quality is the 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 to be 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 are 10 percent and 5 percent respectively. If a different value of consumer’s risk is required, the O.C. curves and their tabu-lated values may be used. For individual lots with percents nonconforming or nonconformities per 100 units equal to the specified Limiting Quality (LQ) values, the probabilities of lot acceptance are less than 10 percent in the case of plans listed in Table VI and less than 5 percent in the case of plans listed in Table VII. When there is reason for avoiding more than a limiting percentage of nonconforming units (or nonconformities) in a lot or batch, TablesVI andVII may be useful 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 of 5 percent is desired for individual lots with an associated Pa of 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 VI indicates that the minimum sample size must be that given by Code Letter M.

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

In the case of an isolated lot, it is preferable for the customer to adapt a sampling plan with a small consumer’s risk. The ideal method of calculating the sample size and risk is by use of the hypergeometric probability function. ASQC Q3-1988 contains sampling plans that have been calculated on this basis and therefore provide a more accurate set of tables for these situations.

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II

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