1、 g49g50g3g38g50g51g60g44g49g42g3g58g44g55g43g50g56g55g3g37g54g44g3g51g40g53g48g44g54g54g44g50g49g3g40g59g38g40g51g55g3g36g54g3g51g40g53g48g44g55g55g40g39g3g37g60g3g38g50g51g60g53g44g42g43g55g3g47g36g58Part 4: Sequential sampling plans indexed by acceptance quality limit (AQL) for inspection by varia
2、bles (known standard deviation)ICS 03.120.30Sampling procedures for inspection by variables BRITISH STANDARDBS 6002-4:2006ISO 3951-5:2006BS 6002-4:2006This British Standard was published under the authority of the Standards Policy and Strategy Committee on 31 May 2006 BSI 2006ISBN 0 580 48593 5A lis
3、t of organizations represented on this committee can be obtained on request to its secretary.Cross-referencesThe British Standards which implement international publications referred to in this document may be found in the BSI Catalogue under the section entitled “International Standards Corresponde
4、nce Index”, or by using the “Search” facility of the BSI Electronic Catalogue or of British Standards Online.This publication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application.Compliance with a British Standard does not of itsel
5、f confer immunity from legal obligations.UK interests informed; monitor related international and European developments and promulgate them in the UK.Summary of pagesThis document comprises a front cover, an inside front cover, the ISO title page, pages ii to vi, pages 1 to 36, an inside back cover
6、and a back cover.The BSI copyright notice displayed in this document indicates when the document was last issued.Amendments issued since publicationAmd. No. Date CommentsThe UK participation in its preparation was entrusted to Technical Committee SS/5, Acceptance sampling schemes, which has the resp
7、onsibility to: aid enquirers to understand the text; present to the responsible international/European committee any enquiries on the interpretation, or proposals for change, and keep National forewordThis British Standard reproduces verbatim ISO 3951-5:2006 and implements it as the UK national stan
8、dard. Together with BS ISO 8423 (when published) it supersedes BS 6002-4.1:1994.Readers should note that the 1994 edition of BS 6002-4.1 was identical to ISO 8423:1991. However, the acceptance procedures contained in Annex A of ISO 8423:1991 are now published as ISO 3951-5:2006. The revised edition
9、of ISO 8423 will be published separately by BSI as BS ISO 8423.Reference numberISO 3951-5:2006(E)INTERNATIONAL STANDARD ISO3951-5First edition2006-03-01Sampling procedures for inspection by variables Part 5: Sequential sampling plans indexed by acceptance quality limit (AQL) for inspection by variab
10、les (known standard deviation) Rgles dchantillonnage pour les contrles par mesures Partie 5: Plans dchantillonnage squentiels indexs daprs la limite dacceptation de qualit (LAQ) pour linspection par variables (cart-type connu) BS 6002-4:2006ii iiiContents Page Foreword iv Introduction v 1 Scope . 1
11、2 Normative references . 2 3 Terms and definitions. 2 4 Symbols . 6 5 Acceptance quality limit (AQL) 7 6 Switching rules for normal, tightened and reduced inspection 7 7 Planning. 9 8 Choice between variables and attributes. 9 9 Choice of inspection level and AQL . 9 10 Preliminary operations. 10 11
12、 Sampling plans . 10 12 Further information. 21 13 Examples . 22 14 Tables. 24 Annex A (normative) Sampling plans for normal, tightened and reduced inspection 25 Annex B (normative) Critical values for maximum standard deviation 29 Annex C (informative) Statistical characteristics 32 Bibliography .
13、36 BS 6002-4:2006iv Foreword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a s
14、ubject for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission
15、(IEC) on all matters of electrotechnical standardization. International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2. The main task of technical committees is to prepare International Standards. Draft International Standards adopted by the technical comm
16、ittees are circulated to the member bodies for voting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote. Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. ISO shall not
17、be held responsible for identifying any or all such patent rights. ISO 3951-5 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods, Subcommittee SC 5, Acceptance sampling. This edition cancels and replaces Annex A of ISO 8423:1991, which has been technically revised to
18、greatly improve its compatibility with the sampling systems in ISO 3951-1. ISO 3951 consists of the following parts, under the general title Sampling procedures for inspection by variables: Part 1: Specification for single sampling plans indexed by acceptance quality limit (AQL) for lot-by-lot inspe
19、ction for a single quality characteristic and a single AQL Part 5: Sequential sampling plans indexed by acceptance quality limit (AQL) for inspection by variables (known standard deviation) The following parts are under preparation: Part 2: General specification for single sampling plans indexed by
20、acceptance quality limit (AQL) for lot-by-lot inspection of independent quality characteristics Part 3: Double sampling schemes indexed by acceptance quality limit (AQL) for lot-by-lot inspection BS 6002-4:2006vIntroduction In contemporary production processes, quality is often expected to reach suc
21、h high levels that the number of nonconforming items is reported in parts per million. Under such circumstances, popular acceptance sampling plans by attributes, such as those presented in ISO 2859-1, require prohibitively large sample sizes. When it is possible to apply acceptance sampling plans by
22、 variables, such as those presented in ISO 3951-1, the sample sizes are much smaller. However, especially in the case of acceptance of a product of extremely high quality, those sample sizes are still too large. Therefore, there is a need to apply standardized statistical procedures that require the
23、 smallest possible sample sizes. Sequential sampling plans are the only statistical procedures that satisfy that need. It has been mathematically proved that among all possible sampling plans having similar statistical properties, the sequential sampling plan has the smallest average sample size. Th
24、erefore, there is a strong need to present sequential sampling plans which are statistically equivalent to the commonly used acceptance sampling plans from ISO 3951-1, but which require significantly smaller average sample sizes. The principal advantage of sequential sampling plans is the reduction
25、in the average sample size. The average sample number is the average of all the sample sizes that may occur under a sampling plan for a given lot or process quality level. The use of sequential sampling plans leads to a smaller average sample number than single sampling plans having the equivalent o
26、perating characteristic. For the sequential sampling plans in this part of ISO 3951, a curtailment rule has been introduced involving an upper limit of 1,5 n0on the actual number of items to be inspected, where n0is the sample size of the corresponding single sampling plan. Other factors that should
27、 be taken into account are as follows: a) Complexity The rules of a sequential sampling plan are more easily misunderstood by inspectors than the simple rules for a single sampling plan. b) Variability in the amount of inspection As the actual number of items inspected for a particular lot is not kn
28、own in advance, the use of sequential sampling plans brings about various organizational difficulties. For example, scheduling of inspection operations may be difficult. c) Ease of drawing sample items If drawing sample items is at different times rather difficult, the reduction in the average sampl
29、e size by sequential sampling plans may be cancelled out by the increased sampling cost. d) Duration of test If the test of a single item is of long duration and a number of items can be tested simultaneously, sequential sampling plans are much more time-consuming than the corresponding single sampl
30、ing plans. e) Variability of quality within the lot If the lot consists of two or more sublots from different sources and if there is likely to be any substantial difference between the qualities of the sublots, drawing of a random sample under a sequential sampling plan is more awkward than under t
31、he corresponding single sampling plan. The balance between the advantage of a smaller average sample number of the sequential sampling plan and the above disadvantages leads to the conclusion that sequential sampling plans are suitable only when inspection of individual items is costly in comparison
32、 with inspection overheads. BS 6002-4:2006vi The choice between single and sequential sampling plans should be made before the inspection of a lot is started. During inspection of a lot, it is not permitted to switch from one type of plan to another, because the operating characteristics of the plan
33、 may be drastically changed if the actual inspection results influence the choice of acceptability criteria. Although a sequential sampling plan is on average much more economical than the corresponding single sampling plan, it may occur, during inspection of a particular lot, that acceptance and no
34、n-acceptance comes at a very late stage because the cumulative leeway (the statistic used for the determination of lot acceptability) remains between the acceptance value and the rejection value for a long time. With the graphical method, this corresponds to the random progress of the step-wise line
35、ar curve remaining in the indecision zone. In order to alleviate this disadvantage, the sample size curtailment value is set before the inspection of a lot is started, and inspection terminates if the cumulative sample size reaches the curtailment value, nt, without determination of lot acceptabilit
36、y. The acceptance and non-acceptance of the lot is then determined using the curtailment acceptance and rejection values. For sequential sampling plans in common use, curtailment usually represents a deviation from their intended usage, leading to a distortion of their operating characteristics. In
37、this part of ISO 3951, however, the operating characteristics of the sequential sampling plans have been determined with curtailment taken into account, so curtailment is an integral component of the provided plans. BS 6002-4:20061Sampling procedures for inspection by variables Part 5: Sequential sa
38、mpling plans indexed by acceptance quality limit (AQL) for inspection by variables (known standard deviation) 1 Scope This part of ISO 3951 specifies a system of sequential sampling plans (schemes) for lot-by-lot inspection by variables. The schemes are indexed in terms of a preferred series of acce
39、ptance quality limit (AQL) values, ranging from 0,01 to 10, which are defined in terms of percent nonconforming items. The schemes of ISO 3951 are intended to induce a supplier through the economic and psychological pressure of lot non-acceptance to maintain a process average at least as good as the
40、 specified AQL value, while at the same time providing an upper limit for the risk to the consumer of accepting the occasional poor lot. The schemes are designed to be applied to a continuing series of lots, that is, a series long enough to allow the switching rules (Clause 6) to be applied. These s
41、witching rules provide: automatic protection to the consumer (by means of a switch to tightened inspection or discontinuation of sampling inspection) should a deterioration in quality be detected; an incentive (at the discretion of the responsible authority) to reduce inspection costs (by means of a
42、 switch to reduced inspection) should consistently good quality be achieved. This part of ISO 3951 is designed for use under the following conditions: a) where the inspection procedure is to be applied to a continuing series of lots of discrete products all supplied by one producer using one product
43、ion process. If there are different producers or production processes, apply this part of ISO 3951 to each one separately; b) where only a single quality characteristic, x, of these products is taken into consideration, which must be measurable on a continuous scale; c) where the uncertainty of the
44、measurement system is negligible with respect to the production process standard deviation; d) where production is stable (under statistical control) and the quality characteristic, x, is distributed according to a normal distribution (or a close approximation to the normal distribution) or a distri
45、bution which may be mathematically transformed to a normal distribution; e) where the standard deviation of the quality characteristic, x, is known; CAUTION The procedures in this part of ISO 3951 are not suitable for application to lots that have been screened previously for nonconforming items. f)
46、 where a contract or standard defines an upper specification limit, U, a lower specification limit, L, 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: BS 6002-4:20062 1) x u U (i.e. the si
47、ngle upper specification limit is not violated); 2) x W L (i.e. the single lower specification limit is not violated); 3) L u x u U (i.e. the upper and lower double specification limits are not violated). In this part of ISO 3951, it is assumed that, where double specification limits apply, conforma
48、nce to both specification limits is either equally important to the integrity of the product or is considered separately for both specification limits. In the first case, it is appropriate to apply a single AQL to the combined percentage of product outside the two specification limits. This is refer
49、red to as a combined AQL requirement. In the second case, separate AQLs apply to nonconformity beyond each of the limits, and this is referred to as a separate AQL requirement. In this part of ISO 3951, the acceptability of a lot is implicitly determined from an estimate of the percentage of nonconforming items in the process, based on a random sample of items from the lot. As such, it is not applicable for judging the acceptability of isolated lots or short series of lots. Refer to ISO 2859-2 for applicable sampling
