1、BRITISH STANDARD BS 6000-3:2005 Guide to the selection and usage of acceptance sampling systems for inspection of discrete items in lots Part 3: Guide to sampling by variables ICS 03.120.30 BS 6000-3:2005 This British Standard was published under the authority of the Standards Policy and Strategy Co
2、mmittee on 25 July 2005 BSI 25 July 2005 First published as BS 6000 March 1972 Second edition May 1996 BS 6000-3 first edition pubished 25 July 2005 The following BSI references relate to the work on this British Standard: Committee reference SS/5 Draft for development 03/102303 DC ISBN 0 580 46417
3、2 Committees responsible for this British Standard The preparation of this British Standard was entrusted to Technical Committee SS/5, Acceptance sampling schemes, upon which the following bodies were represented: Association for Road Traffic and Safety Management British Measurement and Testing Ass
4、ociation City University Clay Pipe Development Association Ltd. Institute of Metal Finishing Institute of Quality Assurance Ministry of Defence UK Defence Standardization Co-opted members Amendments issued since publication Amd. No. Date CommentsBS 6000-3:2005 BSI 25 July 2005 i Contents Page Commit
5、tees responsible Inside front cover Foreword iii 1S c o p e 1 2 Terms and definitions 1 3N o r m a l i t y 1 4 Types of control 15 5 Forms of acceptance criteria 17 6 British Standards for acceptance sampling of lots by variables 31 7 Effect on the selection process of market and production conditio
6、ns 33 Annex A Normal probability paper 40 Bibliography 41 Figure 1 Normal distribution 2 Figure 2 Distribution with large positive skewness 2 Figure 3a) Normal distribution 3 Figure 3b) Normal probability plot of a random sample of size 100 from a normal distribution 4 Figure 4a) Lognormal distribut
7、ion 5 Figure 4b) Normal probability plot of a random sample of size 100 from a lognormal distribution 6 Figure 5a) “Square-root-normal” distribution 7 Figure 5b) Normal probability plot of a random sample of size 100 from a Square-root-normal distribution 7 Figure 6a) Cauchy distribution 8 Figure 6b
8、) Normal probability plot of a random sample of size 100 from a Cauchy distribution 8 Figure 7a) Laplace distribution 9 Figure 7b) Normal probability plot of a random sample of size 100 from a Laplace distribution 10 Figure 8a) Exponential distribution 11 Figure 8b) Normal probability plot of a rand
9、om sample of size 100 from an exponential distribution 12 Figure 9 Acceptance diagram for a single, upper specification limit of 110, sample size code letter G, “s“ method, AQL = 1 %: n = 18, k = 2.770 20 Figure 10 Standardized acceptance diagram for separate control of double specification limits:
10、“s” method, sample size code letter G, AQLs 0.40 % on lower limit and 1.0 % on upper limit 21 Figure 11 Standardized acceptance diagram for combined control of double specification limits: “s“ method, sample size code letter G, AQL = 1 %: n = 18, p* = 0.03323 24 Figure 12 Standardized acceptance dia
11、gram for combined control of double specification limits: sigma method, sample size code letter G, AQL = 1 %: n = 10, p* = 0.03323 25 Figure 13 Standardized acceptance diagrams for complex control of double specification limits: sigma method, sample size code letter M, combined AQL = 1.5 %, AQL 0.4
12、% for upper limit 26 Figure 14 Acceptance diagram for sequential sampling by variables for a single specification limit: sigma method, sample size code letter K, AQL = 1.0 %, h A= 2.764, h R= 3.895, g = 1.900, n t= 27 30 Figure 15 Illustration of the selection procedure for inspection by variables w
13、hen production is continuous and run length exceeds 10 lots on original inspection 37BS 6000-3:2005 ii BSI 25 July 2005 Figure 16 Illustration of the selection procedure for inspection by variables when production is not continuous or run length is 10 lots or fewer on original inspection 38 Table 1
14、Guide for selection of a candidate acceptance sampling system, scheme or plan for inspection by variables, based on the inspection situation 33 Table 2 Guide for the selection of an acceptance sampling system, scheme or plan for sampling by variables, using existing market conditions 34 Table 3 Guid
15、e for the selection of an acceptance sampling system, scheme or plan for sampling by variables, using existing production conditions 35BS 6000-3:2005 BSI 25 July 2005 iii Foreword This part of BS 6000 has been prepared by Technical Committee SS/5. Together with BS 6000-1 and BS 6000-2 it supersedes
16、BS 6000:1996, which is withdrawn. BS 6000:2004, Guide to the selection and usage of acceptance sampling systems for inspection of discrete items in lots is in three parts: Part 1: General guide to acceptance sampling Part 2: Guide to sampling by attributes Part 3: Guide to sampling by variables. Thi
17、s 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 itself confer immunity from legal obligations.Summary of pages This document comprises a front cover, an inside fron
18、t cover, pages i to iii, a blank page, pages 1 to 41 and a back cover. The BSI copyright notice displayed in this document indicates when the document was last issued.blankBS 6000-3:2005 BSI 25 July 2005 1 1 Scope This British Standard gives guidance on the selection of an acceptance sampling system
19、, scheme or plan for inspection by variables. It does this principally by reviewing the available systems specified by various British 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
20、 been made to use sampling by variables in preference to sampling by attributes. The guidance in this British Standard is confined to acceptance sampling of products that are supplied in lots and that can be classified as consisting of discrete items (i.e. discrete articles of product). Each item in
21、 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. Each characteristic has, at least to a good approximation, a
22、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 not limited to, the following: a) end items, such as compl
23、ete 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 British Standard is written principally in terms of manufacture and production, th
24、is 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 BS EN ISO 9000. 2 Terms and definitions For the purposes of this British Standard, the terms and definitions given in BS ISO 3534-1, BS
25、ISO 3534-2 and BS EN ISO 9000 apply. 3 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 the quality characteristics. Consider a single quality characteristic. If it is
26、 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 deviations, the percent nonconforming is about 0.1 %. However, if the distrib
27、ution 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 percent nonconforming approaching 10 % instead of about 0.1 % (see Figure 1 an
28、d Figure 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 tails of the distribution. If the AQL is very small, for example 0.1 %, a s
29、tudy of several thousand items should be made, including a test of distributional form.BS 6000-3:2005 2 BSI 25 July 2005 Key 1 = Upper specification limit 2 = 0.1 % above specification Figure 1 Normal distribution Key 1 = Upper specification limit Figure 2 Distribution with large positive skewness 1
30、 2 1BS 6000-3:2005 BSI 25 July 2005 3 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. Such a plot is constructed in the following way.
31、 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 1k x 2k, . . . k x n . The points with coordinates are then plotted on a sheet of normal p
32、robability paper for i = 1, 2, . . ., n. In order to facilitate this process, an A4 sheet of normal probability paper is provided in Annex A. Figure 3b) shows the normal probability plot of a random sample of size 100 from a normal distribution (Figure 3a) shows the density function). The graph pape
33、r 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 only minor departures from linearity. Figure 3a) Normal distribution xi n i ,/ () + () 3 8 1 4 0 0.05 0.1
34、0.15 0.2 0.25 0.3 0.35 0.4 0.45 01234567891 01 11 2 X Probability density of XBS 6000-3:2005 4 BSI 25 July 2005 Figure 3b) Normal probability plot of a random sample of size 100 from a normal distribution99.9950.0099.900.100.501.0099.0098.002.00 95.005.0090.0010.0080.0020.0070.0030.0099.800.2060.004
35、0.000.01BS 6000-3:2005 BSI 25 July 2005 5 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,
36、 helping 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 in order to bring these closer to normality. Figure 4a) to Figure 8b) show the density functions and examples of normal prob
37、ability plots based on a sample of size 100 for, respectively, a lognormal, “square-root-normal”, Cauchy, Laplace and exponential distribution. (For brevity, the distribution for which the square root of the variable has a normal distribution is referred to as the “square-root-normal” distribution.)
38、 On some of the normal probability plots, a straight line has been drawn through the data points to aid the eye in identifying the characteristic differences. For the lognormal distribution, there is a pronounced downward concavity. The normal probability plot of the square-root-normal distribution
39、is similar to that of the lognormal distribution, except that the concavity is less pronounced. This is only to be expected, as both distributions can be transformed to normality with the Box-Cox transformation (see 3.3.4), but the value of Box-Cox parameter = 0 for the lognormal distribution is twi
40、ce as far away from the null value = 1 as the value = required for the square-root-normal distribution. 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 o
41、f x and relatively low for high values of x, 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
42、 the plot are far from horizontal. The exponential distribution has a very characteristic shape, rising very steeply at the left and becoming almost horizontal towards the right. Figure 4a) Lognormal distribution 0 0.1 0.2 0.3 01234567891 01 11 2 X Probability density of XBS 6000-3:2005 6 BSI 25 Jul
43、y 2005 Figure 4b) Normal probability plot of a random sample of size 100 from a lognormal distribution99.990.0150.0099.90 0.10 0.501.0099.0098.002.00 95.005.0090.0010.0080.0020.0070.0030.0099.80 0.2060.0040.00BS 6000-3:2005 BSI 25 July 2005 7 Figure 5a) “Square-root-normal” distribution Figure 5b) N
44、ormal probability plot of a random sample of size 100 from a Square-root-normal distribution 0 0.05 0.1 0.15 0.2 0.25 01234567891 01 11 2 X Probability density of X 99.990.01 50.00 99.900.100.501.00 99.00 98.002.00 95.005.00 90.00 10.00 80.00 20.00 70.00 30.0099.800.20 60.00 40.00BS 6000-3:2005 8 BS
45、I 25 July 2005 Figure 6a) Cauchy distribution Figure 6b) Normal probability plot of a random sample of size 100 from a Cauchy distribution 0 0.05 0.1 0.15 0.2 0.25 0 1 2 3 4 5 6 7 8 91 0 1 1 1 2 X Probability density of X99.990.0150.0099.900.100.501.0099.0098.002.00 95.005.0090.0010.0080.0020.0070.0
46、030.0099.800.2060.0040.00BS 6000-3:2005 BSI 25 July 2005 9 Figure 7a) Laplace distribution 0 0.1 0.2 0 1 2 3 4 5 6 7 8 9 10 11 12 X Probability density ofXBS 6000-3:2005 10 BSI 25 July 2005 Figure 7b) Normal probability plot of a random sample of size 100 from a Laplace distribution99.990.0150.0099.
47、900.100.501.0099.0098.002.00 95.005.0090.0010.0080.0020.0070.0030.0099.800.2060.0040.00BS 6000-3:2005 BSI 25 July 2005 11 Figure 8a) Exponential distribution 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 X Probability density of XBS 6000-3:2005 12 BSI 25 July 2005 Figure 8b) Normal probability plot of a random
48、sample of size 100 from an exponential distribution99.990.0199.900.100.501.0098.002.00 95.005.0090.0010.0080.0020.0070.0030.000.2099.8099.00 60.00 50.00 40.00BS 6000-3:2005 BSI 25 July 2005 13 These are a small selection from the many possible distributions from which data might have arisen. In some
49、 cases, e.g. the lognormal and the square-root-normal distributions, the distribution can be transformed to normality without knowing its parameters (see 3.3.2 and 3.3.3). In other 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 attribut
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