1、 Reference number ISO/TR 8550-3:2007(E) ISO 2007TECHNICAL REPORT ISO/TR 8550-3 First edition 2007-06-01 Guidance on the selection and usage of acceptance sampling systems for inspection of discrete items in lots Part 3: Sampling by variables Lignes directrices pour la slection dun systme, dun progra
2、mme ou dun plan dchantillonnage pour acceptation pour le contrle dunits discrtes en lots Partie 3: chantillonnage par variables ISO/TR 8550-3:2007(E) PDF disclaimer This PDF file may contain embedded typefaces. In accordance with Adobes licensing policy, this file may be printed or viewed but shall
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7、7 E-mail copyrightiso.org Web www.iso.org Published in Switzerland ii ISO 2007 All rights reservedISO/TR 8550-3:2007(E) ISO 2007 All rights reserved iiiContents Page Foreword iv Introduction v 1 Scope . 1 2 Normative references . 1 3 Normality . 2 4 Types of control 12 5 Forms of acceptance criteria
8、 15 6 International Standards for acceptance sampling of lots by variables 29 7 Effect on the selection process of market and production conditions. 31 Annex A (normative) Normal probability paper 38 Bibliography . 39 ISO/TR 8550-3:2007(E) iv ISO 2007 All rights reservedForeword ISO (the Internatio
9、nal 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 subject for which a technical committee has been
10、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 (IEC) on all matters of electrotechnical standar
11、dization. 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 committees are circulated to the member bodies for v
12、oting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote. In exceptional circumstances, when a technical committee has collected data of a different kind from that which is normally published as an International Standard (“state of the ar
13、t”, for example), it may decide by a simple majority vote of its participating members to publish a Technical Report. A Technical Report is entirely informative in nature and does not have to be reviewed until the data it provides are considered to be no longer valid or useful. Attention is drawn to
14、 the possibility that some of the elements of this document may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights. ISO/TR 8550-3 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods, Subcommittee SC 5, Accep
15、tance sampling. This first edition of ISO/TR 8550-3, together with ISO/TR 8550-1 and ISO/TR 8550-2, cancels and replaces ISO/TR 8550:1994. ISO/TR 8550 consists of the following parts, under the general title Guidance on the selection and usage of acceptance sampling systems for inspection of discret
16、e items in lots: Part 1: Acceptance sampling Part 3: Sampling by variables The following part is under preparation: Part 2: Sampling by attributes ISO/TR 8550-3:2007(E) ISO 2007 All rights reserved vIntroduction This part of ISO/TR 8550 gives guidance on the selection of an acceptance sampling syste
17、m for inspection by variables. It does this principally by reviewing the available systems specified by various standards and showing ways in which these can be compared in order to assess their suitability for an intended application. It is assumed that the choice has already been made to use sampl
18、ing by variables in preference to sampling by attributes. A corresponding guidance document on the selection of a generic acceptance sampling system, scheme or plan for inspection by attributes is given in ISO/TR 8550-2. TECHNICAL REPORT ISO/TR 8550-3:2007(E) ISO 2007 All rights reserved 1Guidance o
19、n the selection and usage of acceptance sampling systems for inspection of discrete items in lots Part 3: Sampling by variables 1 Scope The guidance in this part of ISO/TR 8550 is confined to acceptance sampling of products that are supplied in lots and that can be classified as consisting of discre
20、te items (i.e. discrete articles of product). Each item in a lot can be identified and segregated from the other items in the lot and has an equal chance of being included in the sample. Each item of product is countable and has specific characteristics that are measurable on a continuous scale. Eac
21、h characteristic has, at least to a good approximation, a normal distribution or a distribution that can be transformed so that it closely resembles a normal distribution. Standards on acceptance sampling by variables are applicable to a wide variety of inspection situations. These include, but are
22、not limited to, the following: a) end items, such as complete products or sub-assemblies; b) components and raw materials; c) services; d) materials in process; e) supplies in storage; f) maintenance operations; g) data or records; h) administrative procedures. Although this part of ISO/TR 8550 is w
23、ritten principally in terms of manufacture and production, it should be interpreted liberally as it is applicable to the selection of sampling systems, schemes and plans for all types of product and processes as defined in ISO 9000. 2 Normative references The following referenced documents are indis
24、pensable for the application of this document. For dated references, only the edition listed applies. For undated references, the latest edition of the referenced document (including any amendment) applies. ISO/TR 8550-1:2007, Guidance on the selection and usage of acceptance sampling systems for in
25、spection of discrete items in lots Part 1: Acceptance sampling ISO/TR 8550-3:2007(E) 2 ISO 2007 All rights reserved3 Normality 3.1 Relationship between form of distribution of quality characteristic and percent nonconforming A key aspect of sampling by variables is the form of the distributions of t
26、he quality characteristics. Consider a single quality characteristic. If it is normally distributed and if an upper specification limit is located at the mean plus two standard deviations, the percent nonconforming is about 2,5 %. If the specification limit is located at the mean plus three standard
27、 deviations, the percent nonconforming is about 0,1 %. However, if the distribution of the quality characteristic is not normal and has a large positive skewness, i.e. a long tail to the right, an upper specification limit located at the mean plus three standard deviations could conceivably yield a
28、percent nonconforming approaching 10 % instead of about 0,1 % (see Figures 1 and 2). Therefore, whenever a sampling plan for inspection by variables for percent nonconforming is to be employed, it is highly desirable to check any assumptions about the shape of the distribution, especially in the tai
29、ls of the distribution. If the AQL is very small, for example 0,1 %, a study of several thousand items should be made, including a test of distributional form. ISO/TR 8550-3:2007(E) ISO 2007 All rights reserved 3Key 1 upper specification limit 2 0,1 % above specification Figure 1 Normal distribution
30、 Key 1 upper specification limit Figure 2 Distribution with large positive skewness 3.2 Identifying departure from normality 3.2.1 Subjective assessment The degree to which a sample appears to have come from a normal distribution can be subjectively assessed by means of a normal probability plot. Su
31、ch a plot is constructed in the following way. Once the random sample has been selected and the quality characteristic x has been measured for each item, the values x 1 , x 2 , . . ., x nare arranged in ascending order x 1 , x 2 , . . ., x n , such that x 1u x 2u, . . . u x n . The points with ISO/T
32、R 8550-3:2007(E) 4 ISO 2007 All rights reservedcoordinates () () ,/ 3 1 84 i xi n + are then plotted on a sheet of normal probability paper for i = 1, 2, . . ., n. To facilitate this process, an A4 sheet of normal probability paper that can be freely photocopied is provided in Annex A. Figure 3 show
33、s the normal probability plot of a random sample of size 100 from a normal distribution. The graph paper is specially designed so that data from a normal distribution tend to lie close to a straight line. A straight line has been drawn by eye through the data, showing in this case that there are onl
34、y minor departures from linearity. When data originate from a normal distribution, departures of the probability plot from linearity are due solely to sampling fluctuations. Conversely, data from other types of distribution will tend to show departures from linearity of a characteristic type, helpin
35、g in the determination of the family of distributions to which the data belong. Knowledge of this family can indicate the appropriate transformation to make to the data to bring these closer to normality. Figures 4 to 7 show the density functions and examples of normal probability plots based on a r
36、andom sample of size 100 for, respectively, a lognormal, Cauchy, Laplace, and exponential distribution, respectively. On the normal probability plot for Figures 4 to 6, a straight line has been drawn through the data points to aid the eye in identifying the characteristic differences. For the lognor
37、mal distribution, there is a pronounced downward concavity. The Cauchy distribution is almost indistinguishable from the normal distribution towards its centre, but the extra thickness of its tails results in the plot being relatively high for low values of x and relatively low for high values of x,
38、 the extremities of the plot being almost horizontal. The Laplace distribution is similar, except that there is a shorter region in the normal probability plot where the distribution is indistinguishable from the normal distribution, and the extremities of the plot are far from horizontal. The norma
39、l probability plot for the exponential distribution has a very characteristic shape, rising very steeply at the left and becoming almost horizontal towards the right. These are a small selection from the many possible distributions from which data might have arisen. In some cases, e.g. the lognormal
40、 distribution, the distribution can be transformed exactly to normality without knowing its parameters (see 3.3.2 and 3.3.3). In other cases, approximate normality may be achieved, e.g. by using the fourth root transformation on exponentially distributed variables, as shown by Kittlitz 20 . In other
41、 cases, acceptance sampling by variables might not be possible without a method tailored to that family of distributions. If such a method does not exist, acceptance sampling by attributes might have to be used instead, the loss in efficiency being more than compensated for by the increase in integr
42、ity of the acceptance sampling results. Figures 4 to 7 show normal probability plots for samples of size 100. Often there is not the luxury of such large samples. With small samples, it is less clear whether the departures from linearity of the normal probability plot are due to non-normality or mer
43、ely to sampling fluctuations. In case of doubt, subjective assessment of departure from normality should be replaced by objective statistical tests, such as those discussed in 3.2.2. Further information on tests for departure from normality is given in ISO 5479 and ISO 2854:1976, Clause 2. ISO/TR 85
44、50-3:2007(E) ISO 2007 All rights reserved 5Key X quality characteristic, x Y probability density of x a) Normal distribution b) Normal probability plot of a random sample of size 100 from a normal distribution Figure 3 Normal distribution and normal probability plot ISO/TR 8550-3:2007(E) 6 ISO 2007
45、All rights reservedKey X quality characteristic, x Y probability density of x a) Lognormal distribution b) Normal probability plot of a random sample of size 100 from a lognormal distribution Figure 4 Lognormal distribution and normal probability plot ISO/TR 8550-3:2007(E) ISO 2007 All rights reserv
46、ed 7Key X quality characteristic, x Y probability density of x a) Cauchy distribution b) Normal probability plot of a random sample of size 100 from a Cauchy distribution Figure 5 Cauchy distribution and normal probability plot ISO/TR 8550-3:2007(E) 8 ISO 2007 All rights reservedKey X quality charac
47、teristic, x Y probability density of x a) Laplace distribution b) Normal probability plot of a random sample of size 100 from a Laplace distribution Figure 6 Laplace distribution and normal probability plot ISO/TR 8550-3:2007(E) ISO 2007 All rights reserved 9Key X quality characteristic, x Y probabi
48、lity density of x a) Exponential distribution b) Normal probability plot of a random sample of size 100 from an exponential distribution Figure 7 Exponential distribution and normal probability plot ISO/TR 8550-3:2007(E) 10 ISO 2007 All rights reserved3.2.2 Statistical tests for departure from norma
49、lity 3.2.2.1 Directional versus omnibus tests Statistical tests are used to determine the degree to which the available evidence fails to support a given null hypothesis, say H 0 . The power of the test is the probability of rejecting the hypothesis H 0in favour of the alternative hypothesis H 1when the alternative hypothesis is true. When testing for departures from normality, the null hypothesis H 0is that the distribution is normal while the alternative hypothesis H
