National foreword

This British Standard is the UK implementation of ISO 3951‑6:2023.

The UK participation in its preparation was entrusted to Technical Committee SS/5, Acceptance sampling schemes.

A list of organizations represented on this committee can be obtained on request to its committee manager.

Contractual and legal considerations

This publication has been prepared in good faith, however no representation, warranty, assurance or undertaking (express or implied) is or will be made, and no responsibility or liability is or will be accepted by BSI in relation to the adequacy, accuracy, completeness or reasonableness of this publication. All and any such responsibility and liability is expressly disclaimed to the full extent permitted by the law.

This publication is provided as is, and is to be used at the recipient’s own risk.

The recipient is advised to consider seeking professional guidance with respect to its use of this publication.

This publication is not intended to constitute a contract. Users are responsible for its correct application.

Compliance with a British Standard cannot confer immunity from legal obligations.

This British Standard was published under the authority of the Standards Policy and Strategy Committee on 31 December 2023.

Foreword

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This document was prepared by Technical Committee ISO/TC 69, Applications of statistical methods, Subcommittee SC 5, Acceptance sampling.

A list of all parts in the ISO 3951 series can be found on the ISO website.

Any feedback or questions on this document should be directed to the user’s national standards body. A complete listing of these bodies can be found at www.iso.org/members.html.

Introduction

This document specifies an acceptance sampling system of single sampling plans for inspection by variables. It is indexed in terms of the limiting quality (LQ) for the inspection of lots where switching rules as used in ISO 3951‑1 are not applicable. These switching rules provide protection to the consumer (by the prospect of switching to tightened inspection and discontinuation) and also provide an incentive to the supplier to improve the quality level. However, there are various cases where the switching rules of ISO 3951‑1 are not applicable, such as isolated lots or a short series of lots.

This document is designed for the inspection of a single quality characteristic that is measurable on a continuous scale and is normally distributed, under conditions where ISO 3951‑1 is not applicable, and is complementary to the attributes standard ISO 2859‑2. The operating characteristic curves (OC curves) of the variables plans in this document are similar but not identical to those of the corresponding attributes plans in ISO 2859‑2. The OC curves have been matched by minimizing the difference of the OC curves on condition of getting a comprehensible sample size structure (see Clause 9).

In this document, the acceptance of a lot is implicitly determined from an estimate of the fraction of nonconforming items in the process, based on a random sample of items from the lot. The objectives of the methods laid down in this document are to ensure that lots of limiting quality have a probability of acceptance about 10 % and that the probability of accepting lots with good quality is as high as practicable.

It is assumed in the main body of this document that measurement error is negligible. For information on accommodating measurement error, see Annex B, which was derived from References [24], [29] and [30].

CAUTION — The procedures in this document are not suitable for application to lots that have been screened for nonconforming items.

Inspection by variables for nonconforming items, as described in this document, includes several possible modes, the combination of which leads to a presentation that can appear quite complex to the user:

unknown standard deviation, or known since the start of inspection;
a single specification limit, or combined control of double specification limits.

The choice of the most suitable variables plan, if one exists, requires experience, judgement, and some knowledge of both statistics and the product to be inspected. Clause 5 is intended to help those responsible for specifying sampling plans in making this choice. It suggests the considerations that should be borne in mind when deciding whether a variables plan would be suitable and the choices to be made when selecting an appropriate standard plan.

The basic definitions and notations are provided by Clauses 3 and 4. The basic operational rules are contained in Clauses 5 through 8. Clause 9 informs about the relations between this document and the attributes sampling standard ISO 2859‑2. Clauses 10 and 11 provide background on accounting for measurement uncertainty and the underlying normality assumption. All tables needed for the sampling procedure can be found in Clause 12, and examples for the s–method and the σ–method for both single and double specification limits can be found in Clause 13.

Nine annexes are provided. Annex A indicates how the sample standard deviation, s, and the presumed known value of the process standard deviation, σ, should be determined. Annex B provides procedures for accommodating measurement uncertainty. Annex C shows five different sampling strategies. Annex D gives the general formula for the operating characteristics of the s–method. Annex E gives the general formula for the operating characteristics of the σ–method. Annex F gives the theory underlying the calculation of consumer’s risks. Annex G gives the theory underlying the calculation of producer’s risk quality. Annex H gives details of how acceptance diagrams for double specification limits are constructed. Annex I gives a description of the use of the underlying software, R package ISO 3951, to support implementation of this document.

1 Scope

This document specifies an acceptance sampling system of single sampling plans for inspection by variables, primarily designed for use under the following conditions:

where the inspection procedure is applied to an isolated lot of discrete products all supplied by one producer using one production process;
where only a single quality characteristic, x, of this process is taken into consideration, which is measurable on a continuous scale;
where the quality characteristic, x, is distributed according to a normal distribution or a close approximation to a normal distribution;
where the quality characteristic can be measured without error or with moderate measurement error;
where a contract or standard defines a lower specification limit, L, an upper specification limit, U, or both; an item is qualified as conforming if and only if its measured quality characteristic, x, satisfies the appropriate one of the following inequalities:
1. x ≥ L (i.e. the lower specification limit is not violated);
2. x ≤ U (i.e. the upper specification limit is not violated);
3. x ≥ L and x ≤ U (i.e. neither the lower nor the upper specification limit is violated).

Inequalities 1) and 2) are cases with a single specification limit, whereas inequality 3) is a case with double specification limits.

Where double specification limits apply, it is assumed in this document that conformance to both specification limits is equally important to the integrity of the product. In such cases, it is appropriate to apply a single LQ to the combined fraction of a product outside the two specification limits. This is referred to as combined control.

2 Normative references

3 Terms and definitions

4 Symbols

5 Choice of a sampling plan

5.1 Choice between variables and attributes

5.2 General

5.3 Choice between the s-method and the σ-method

5.4 Choice of the limiting quality (LQ)

6 Standard procedures for the s-method

6.1 General

6.2 Single specification limits

6.3 Double specification limits

7 Standard procedures for the σ-method

7.1 General

7.2 Single specification limits

7.3 Double specification limits

8 The p*-method

9 Relation to ISO 2859‑2

9.1 Similarities

9.2 Differences

10 Allowing for measurement uncertainty

11 Normality, data transformations and outliers

11.1 Normality

11.2 Data transformations

11.3 Outliers

12 Tables

12.1 Information about the tables

13 Examples

13.1 General

13.2 Examples for the s-method

13.3 Examples for the σ-method

13.4 Examples for the p*-method

Bibliography

BS ISO 3951-6:2023

Sampling procedures for inspection by variables - Specification for single sampling plans for isolated lot inspection indexed by limiting quality (LQ)

Current

Published:

31 Dec 2023