ISO 2859-2

lnternational Sundard

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TNTERNAl|ONAL ORGANTZATTON FOR STANOAROIZATTON.MEXAyHAPOAXAB OPfAH113ALlt48 nO CfAHAAPTU3AUt4T4.ORGANISATION INTERNATIONALE DE NORMALISATION

Sampling procedu Part 2: Sampling isolated lot ins Rdgles d'Cchantillonnage pour les indexds d'aprCs la qualitd limib (AL)

First edition

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ffi1[ti

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contrilles de lots isol6s,

genter tor Smn0ar0s,llletrolosy 0nil llualittt

1985-0!r-01

UDC 311.213.2 : 60.113.4

lity (LOl for

:

658.562.012.7

Ref. No. ISO 2859/2-1985 (E)

Descriptore : statistical analysis, quality control, inspection by attributes, sampling, sampling tables. acceptability.

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Price based on 2'l pages

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Gontents Page

0 lntroduction,...,. 1

1

Scope and field of application . . . .

.

1

2 DeJinitions

2

3

Choice of sampling plan .

4

Bulesforacceptanceand non-acceptance

.

.

2

,....

3

5 Doubleandmultiplesamplingplans .......

4

6

Examples illustrating how to use this part of ISO

4

7

Compatibility with ISO 2859

Tables

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...

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p pling ppro Dv a ttributes by ures or lnsoecuon Samplinq Part 2: Sampling plans indexed by limiting quality (LOl for isolated lot inspection 0

Consequently, in c€rtain of the above cases consumer protection may need to be attained or measured by other methods" This part of ISO 2859 uses the limiting quality to measure consumer protection, lt should be remembered, however. that prior information on the supplier's quality assurance system and its effectiveness may play a major part in deciding whether or not to accept a single lot.

lntroduction

0.1

General

ISO 2859 comprises four parts: Part

0: General introduction.

Part 1: Sampling plans indexed by acceptable quality level (AOL) for lot-by-lot inspection" Part 2: Sampling plans indexed by limiting quality (LO) for isolated lot inspection. Part

3: Skip lot sampling plan.

ISO 2859/1 sampling plans, indexed in terms of AOL, which is defined as a process average, were primarilv designed for the assessment of a continuing series of lots. This enables switchinq rules to be employed which not only give protection to the consumer (by the switch to tightened inspection and discontinuation where necessary) but also provide an incentive to the producer (by the switch to reduced inspection) with a reduction to test and inspection costs (when consistently good quality is achieved). However, there is little doubt that in many industrial situations today the switching rules are not applied for a variety of reasons or excuses, ilbt all of which may be valid:

a)

individual ISO 2859/1 plans are used alone but "AOL" protection is still claimed or AOL re-defined, to suit "socalled unique products";

b)

"our industry... product is soecial so ISO 2859/l standard plans need not apply to us";

c) d)

production is intermittent (not continuousl;

e)

purchases are from stock-holders

production is from several different sources in varying quantities, i.e. "job lots";

available;

f)

-

no source data

lots are "small" (use of hypergeometric distribution re-

quired);

g)

lots are "isolated";

h)

lots are re-submitted after initial rejection.

0.2

Objectives

ln an attempt to reconcile the somewhat diverse requests for assistance made over the past few years by cornmittees of international standardizing bodies representing various product sectors, this part of ISO 2859 was drawn up in accordance with the following principles:

a)

the new LQ plans can be easily integrated with the existing AOL plans in ISO 285911;

b)

the LO indexing uses a preterred series of values that cannot be confused with the preferred series of AOL values;

c)

the five basic numbers associated with a single sarnpling plan, i.e. lot size, sample size, acceptance number, AOL (or quality accepted with probability 0,951 and LO, appear in the same table, whenever possible"

0.3

Summary

The problems associated with acceptance sampling inspection involve defining unambiguously the criteria used to judge discrete individual items supplied in quantity, the quality level expected from the manufacturing process, the discrimination offered by the plans and the procedure to be followed when a lot is not accepted, Above afl, however, it is necessary to design the sampling scheme so that it may easily be invoked in a purchasing contract. The plans in this part of ISO 2859 make maximum use of the established plans given in ISO 2859/1, so that sub-clause 12.6 of ISO 2859/1 {see 1.1) can be made directly operational, by providing a rationalized series of plans indexed in terms of limiting quality (LO)'

rso 2859/2-198s (El

Scope and field of application

1

3.2

Scope

1.1

This part of ISO 2859 establishes LQ sampling plans and procedures for inspection by attributes compatible with ISO 285g/l

that can be used when the switching rules given in

8N/lare

ISO not applied. for example, when lots are of an isolated

nature.

The plans in this part of ISO 2859 are indexed by a preferred series of limiting qualities (LO with a consumer's risk usually below 10 %, but always below 13 %. This method of indexing perrnits the "ad-hoc" procedurel) mentioned in sub-clause 12.6 of ISO 2859/1 to be implemented as a standard procedure.

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NOTE The plans in ISO 2859/1 are indexed by a preferred series of AOL values and inspection levels. During the inspection of a continuing series of lots the application of switching rules helps to ensure that the process average in that series of lots is kept below the specified AOL. l-imiting quality does not have the same direct relationship with the process average (see 3.5.11.

1.2

Field of application

Alternative procedures are provided in this part of ISO 2859 to cater for two situations often met in practice:

a!

Procedure A, to be used when the supplier and consumer both wish to regard the lot in isolation. The tables are based on random sampling from finite lots for both consumer and producer risks. This orocedure shall be used unless there is a soecific instruction to use orocedure B,

bl

Procedure B, to be used when the supplier regards the lot as one of continuing series but the consumer considers the lot received in isolation. The tables are based on random sampling from a finite lot for consumer's risk at the limiting quality, but random sampling from a process for the pro-

ducer's risk and the tabulated values

maintain consistent procedures for customers whether or not they receive individual lots or a continuing series of lots. This procedure is suitable for inclusion in product standards

or

specifications

Although procedure A is based on the hypergeometric distribution for sampling results, this distribution is well approximated by the binomial distribution for plans with non-zero acceptance numbers in procedure A. Hence the OC curves for these plans are well approximated by the tabulated performance of the same plans in procedure B. However, procedure A uses plans with acceptance number zero and with sample sizes based on the hypergeometric distribution of sampling results while procedure B excludes accept zero plans, replabing them with 100

% inspection.

The choice between the procedures is dominated by the attitude towards accept zero plans. Procedure A uses accept zero plans linking the sample size and the lot size by the hypergeometric distribution until the proposed plan corresponds to the accept zero plan in ISO 2859/1 corresponding to that limiting quality. Thereafter the progression of sampling size and acceptance number with lot size is based on the inspection levels available in ISO 2859/1. The overall effect of procedure A resembles inspection level ll for limiting quality less than 8 % and level I for limiting quality greater than 8 7o with 8 % being intermediate between these levels. Procedure B provides greater flexibility in the choice of inspec-

tion levels. The tabulated OC curves are based on the probability of producing a nonconforming unit so thgy are approximately.correct for small sampling fractions but as the sampling

fraction increases the curves (and tables) underestimate the probability of acceptance for good quality and underestimate the probability of rejection for poor quality. For sufficiently small lots. procedure B requires 100 % inspection.

of the operating

characteristic (OCl curves. Tie plans used are a selection of the plans available in ISO 2859/1 so thai a producer can

that contain sampling clauses"

The

manufacturer will be concerned with all of his production, but the individual consumer onlv with the particular lot received.

2

Choice of sampling proceduro

Both procedures treat the limiting quality (LOl as the actual percent nonconforming units in the submitted lots and the probability of acceptance at this limiting quality can be found in table Dl for procedure A and tables 81 to B10for procedure B. Procedure B is indicated as the appropriate procedure if the manufacturer is concerned with a continuing series of lots; whether or not these go to the same consumer. Procbdure A is indicated as the appropriate procedure when the lot is a single lot and shall be used if accept zero plans are required to be part of the sampling scheme.

Definitions

The definitions given in ISO 2859/1 shall apply.

3

Choice of sampling plan

3.1

Speclfying a sampling ptan

When reference is made to this part of ISO 2959 in a contract or specification, it is necessary to specify the procedure to be used (i.e" either A or B). ln the absence of any reference to either procedure, then procedure A shall be used.

3.3

Procedure A

(use table A)

A plan is identified by the lot size and the limiting quality (LO).

with the specified lot

size and limiting quality as indexing values, the sampling size (nl and acceptance number (Ac) are given in table A.

1l ISO 2859/ 1 sub-clause 12.6.2. states : "lf the lot or batch is of an isolated nature. it may be desirable to limit the selection of sampling plans to those, associated with a designatod AOL value, that provide not less than a specified limiting quality protectioh. Sampling plans for this puipose can be selocted by choosing a limiting quality (LQl and a consume/s risk to be associated *ith it. Tables 6 and 7 give piocess levels for which the probabifities of lot acceptance under various sampling plans are 10 lo and 5 %, respectively." This part of ISO 2859 esiablishes preferred values for the LQ and allows the consumer,s risk to vary as indicated above.

2

tso

Although the primary index to these tables is the limiting quality (LO), the producer/supplier needs guidance on the quality level required if lots are to have a high probability of acceptance. lnformation on the producer's risk point is contained in table Dl. lnformation on the probability of acceptance ol relatively good lots by accept zero plans is given in table D2.

3.4

Procedure B

A plan is identified by the lot size, limiting quality (LO) and the inspection level (unless otherwise specified, level ll shall be used).

The specified limiting quality is used to select the appropriate table from tables Bl to 810. Within each table the specified lot size and inspection level indicate the appropriate sample size (nl and acceptance number (Ac). Although the primary index to the table is the limiting quality (LO), the producer/supplier needs guidance on the quality level required if lots are to have a high probability of acceptance. Each table gives information on

the equivalent AOL and details of the OC curves. The OC curves are indexed by the sample size code letter used in ISO 2859/1 and the acceptance number. The OC curves given under tables 81

to 810 are based on the Poisson/binomial distribution; the actual operating characteristic will be more discriminating than these curves by accepting with greater probability when the indicated probability is > 0,90 and with a smaller probability when the indicated probability is < 0,10.

The limiting quality has previously been set at 3,5 %. This is not a preferred value and the tables shall be entered by 3,15 06, since using the nominal limiting quality LO 3,5 % lies in the range 2,5 % < LO co H gE

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tso 2859/2-1985

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Table C Preferred value of llmlting quality lLOl %

-

Relation between limitlng quality lLOl and'consumer's risk quality (CRO) Correspondlng range of CRO in tables 81 to 810 lat 10 % consumcr's rlskl

Correspondlng range of CRO in tables Bl to 810 (at 5 96 consumers rlskl

0,54

1,25

0,46