1、 Reference number ISO 24153:2009(E) ISO 2009INTERNATIONAL STANDARD ISO 24153 First edition 2009-12-01 Random sampling and randomization procedures Modes opratoires dchantillonnage et de rpartition alatoires ISO 24153:2009(E) PDF disclaimer This PDF file may contain embedded typefaces. In accordance
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4、very care has been taken to ensure that the file is suitable for use by ISO member bodies. In the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below. COPYRIGHT PROTECTED DOCUMENT ISO 2009 All rights reserved. Unless otherwise speci
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6、se postale 56 CH-1211 Geneva 20 Tel. + 41 22 749 01 11 Fax + 41 22 749 09 47 E-mail copyrightiso.org Web www.iso.org Published in Switzerland ii ISO 2009 All rights reservedISO 24153:2009(E) ISO 2009 All rights reserved iiiContents Page Foreword iv Introduction.v 1 Scope1 2 Normative references1 3 T
7、erms, definitions, and symbols .1 4 General .5 5 Random sampling Mechanical device methods6 6 Pseudo-independent random sampling Table method.7 7 Pseudo-independent random sampling Computer method.7 8 Applications to common sampling situations .11 Annex A (normative) Random number tables18 Annex B (
8、informative) Random number generation algorithm computer code .22 Annex C (informative) Random sampling and randomization computer code 25 Bibliography31 ISO 24153:2009(E) iv ISO 2009 All rights reservedForeword ISO (the International Organization for Standardization) is a worldwide federation of na
9、tional 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 established has the right to be represented on that committee. Intern
10、ational 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 standardization. International Standards are drafted in accordance with the
11、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 voting. Publication as an International Standard requires approval by
12、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 be held responsible for identifying any or all such patent rights. ISO 24153 was prepared by Technical Committee ISO/
13、TC 69, Applications of statistical methods, Subcommittee SC 5, Acceptance sampling. ISO 24153:2009(E) ISO 2009 All rights reserved vIntroduction Random sampling and randomization procedures are the cornerstone to the validity of many statistical methods used in experimentation, whether for industria
14、l quality control and improvement purposes or for designed experiments in the medical, biological, agricultural, or other scientific fields. Many statistical standards address the conduct of such experimentation. In particular, all of the following acceptance-sampling standards have been designed on
15、 the premise that random sampling is employed to select the required sampling units for lot disposition purposes: ISO 2859 (all parts), Sampling procedures for inspection by attributes ISO 3951 (all parts), Sampling procedures for inspection by variables ISO 8422, Sequential sampling plans for inspe
16、ction by attributes ISO 8423, Sequential sampling plans for inspection by variables for percent nonconforming (known standard deviation) ISO 13448 (all parts), Acceptance sampling procedures based on the allocation of priorities principle (APP) ISO 14560, Acceptance sampling procedures by attributes
17、 Specified quality levels in nonconforming items per million ISO 18414, Acceptance sampling procedures by attributes Accept-zero sampling system based on credit principle for controlling outgoing quality ISO 21247, Combined accept-zero sampling systems and process control procedures for product acce
18、ptance In addition, ISO 2859-3 and ISO 21247 include provisions for random sampling to be applied to determine whether a lot should be inspected or not under skip-lot sampling procedures, and to decide which units require inspection from a production process under continuous sampling plans, respecti
19、vely. Consequently, it is of great importance to the valid operation of all of the above standards that sampling be effectively random in its application. Although the principles of this International Standard are universally applicable where random sampling is required and the sampling units can be
20、 clearly defined, preferably on the basis of discrete items, there are many situations in which the material of interest does not lend itself to being quantified on a discrete-item basis, as in the case of a bulk material. In such situations, the user is advised to consult the following ISO Internat
21、ional Standards for appropriate guidance: ISO 11648 (all parts), Statistical aspects of sampling from bulk materials INTERNATIONAL STANDARD ISO 24153:2009(E) ISO 2009 All rights reserved 1Random sampling and randomization procedures 1 Scope This International Standard defines procedures for random s
22、ampling and randomization. Several methods are provided, including approaches based on mechanical devices, tables of random numbers, and portable computer algorithms. This International Standard is applicable whenever a regulation, contract, or other standard requires random sampling or randomizatio
23、n to be used. The methods are applicable to such situations as a) acceptance sampling of discrete units presented for inspection in lots, b) sampling for survey purposes, c) auditing of quality management system results, and d) selecting experimental units, allocating treatments to them, and determi
24、ning evaluation order in the conduct of designed experiments. Information is also included to facilitate auditing or other external review of random sampling or randomization results where this is required by quality management personnel or regulatory bodies. This International Standard does not pro
25、vide guidance as to the appropriate random sampling or randomization procedures to be used for any particular experimental situation or give guidance with respect to possible sampling strategy selection or sample size determination. Other ISO standards (such as those listed in the Introduction) or a
26、uthoritative references should be consulted for guidance in such areas. 2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced
27、 document (including any amendments) applies. ISO 3534-1, Statistics Vocabulary and symbols Part 1: General statistical terms and terms used in probability ISO 3534-2, Statistics Vocabulary and symbols Part 2: Applied statistics ISO 3534-3, Statistics Vocabulary and symbols Part 3: Design of experim
28、ents ISO 80000-2, Quantities and units Part 2: Mathematical signs and symbols to be used in the natural sciences and technology 3 Terms, definitions, and symbols For the purposes of this document, the terms and definitions given in ISO 3534-1, ISO 3534-2, ISO 3534-3, and the following apply. ISO 241
29、53:2009(E) 2 ISO 2009 All rights reserved3.1 Terms and definitions 3.1.1 cluster part of a population (3.1.6) divided into mutually exclusive groups of sampling units (3.1.13) related in a certain manner ISO 3534-2:2006, definition 1.2.28 3.1.2 cluster sampling sampling (3.1.12) in which a random sa
30、mple (3.1.8) of clusters (3.1.1) is selected and all the sampling units (3.1.13) which constitute the clusters are included in the sample (3.1.11) ISO 3534-2:2006, definition 1.3.9 3.1.3 derangement complete permutation permutation of elements where no element remains in its original position in the
31、 set (e.g. 3, 1, 2 is a derangement of 1, 2, 3) 3.1.4 lot definite part of a population (3.1.6) constituted under essentially the same conditions as the population with respect to the sampling (3.1.12) purpose NOTE The sampling purpose can, for example, be to determine lot acceptability, or to estim
32、ate the mean value of a particular characteristic. ISO 3534-2:2006, definition 1.2.4 3.1.5 multistage sampling sampling (3.1.12) in which the sample (3.1.11) is selected by stages, the sampling units (3.1.13) at each stage being sampled from the larger sampling units chosen at the previous stage NOT
33、E Multistage sampling is different from multiple sampling. Multiple sampling is sampling by several criteria at the same time. ISO 3534-2:2006, definition 1.3.10 3.1.6 population reference totality of items under consideration ISO 3534-2:2006, definition 1.2.1 3.1.7 pseudo-independent random samplin
34、g sampling (3.1.12) where a sample (3.1.11) of n sampling units (3.1.13) is taken from a population (3.1.6) in accordance with a table of random numbers or a computer algorithm designed such that each of the possible combinations of n sampling units has a particular probability of being taken (see a
35、lso 4.4) 3.1.8 random sample sample (3.1.11) selected by random sampling (3.1.9) ISO 3534-2:2006, definition 1.2.25 ISO 24153:2009(E) ISO 2009 All rights reserved 33.1.9 random sampling sampling (3.1.12) where a sample (3.1.11) of n sampling units (3.1.13) is taken from a population (3.1.6) in such
36、a way that each of the possible combinations of n sampling units has a particular probability of being taken ISO 3534-2:2006, definition 1.3.5 3.1.10 randomization process by which a set of items are set into a random order NOTE If, from a population (3.1.6) consisting of the natural numbers 1 to n,
37、 numbers are drawn at random (i.e. in such a way that all numbers have the same chance of being drawn), one by one, successively, without replacement, until the population is exhausted, the numbers are said to be drawn “in random order“. If these n numbers have been associated in advance with n dist
38、inct units or n distinct treatments that are then re-arranged in the order in which the numbers are drawn, the order of the units or treatments is said to be randomized. 3.1.11 sample subset of a population (3.1.6) made up of one or more sampling units (3.1.13) ISO 3534-2:2006, definition 1.2.17 3.1
39、.12 sampling act of drawing or constituting a sample (3.1.11) ISO 3534-2:2006, definition 1.3.1 3.1.13 sampling unit unit one of the individual parts into which a population (3.1.6) is divided NOTE 1 A sampling unit can contain one or more items, for example, a box of matches, but one test result wi
40、ll be obtained for it. NOTE 2 A sampling unit can consist of discrete items or a defined amount of bulk material. ISO 3534-2:2006, definition 1.2.14 3.1.14 sampling with replacement sampling (3.1.12) in which each sampling unit (3.1.13) taken and observed is returned to the population (3.1.6) before
41、 the next sampling unit is taken ISO 3534-2:2006, definition 1.3.15 3.1.15 sampling without replacement sampling (3.1.12) in which each sampling unit (3.1.13) is taken from the population (3.1.6) once only without being returned to the population ISO 3534-2:2006, definition 1.3.16 ISO 24153:2009(E)
42、4 ISO 2009 All rights reserved3.1.16 seed numerical value or set of values used to initialize a pseudo-independent random sampling (3.1.7) algorithm or to establish a starting point in a table of random numbers 3.1.17 simple random sample sample (3.1.11) selected by simple random sampling (3.1.18) I
43、SO 3534-2:2006, definition 1.2.24 3.1.18 simple random sampling sampling (3.1.12) where a sample (3.1.11) of n sampling units (3.1.13) is taken from a population (3.1.6) in such a way that all possible combinations of n sampling units have the same probability of being taken ISO 3534-2:2006, definit
44、ion 1.3.4 3.1.19 stratified sampling sampling (3.1.12) such that portions of the sample (3.1.11) are drawn from the different strata (3.1.21) and each stratum is sampled with at least one sampling unit (3.1.13) ISO 3534-2:2006, definition 1.3.6 3.1.20 stratified simple random sampling simple random
45、sampling (3.1.18) from each stratum (3.1.21) ISO 3534-2:2006, definition 1.3.7 3.1.21 stratum mutually exclusive and exhaustive sub-population considered to be more homogeneous with respect to the characteristics investigated than the total population (3.1.6) ISO 3534-2:2006, definition 1.2.29 3.2 S
46、ymbols For the purposes of this document, the mathematical signs and symbols given in ISO 80000-2 and the following apply. d ithe ith (least significant) digit, or face value of a coin or die N lot size n sample size n ithe size of the ith sample U uniformly-distributed random real variable on the o
47、pen range (0, 1) x ithe ith value of the variable x j! factorial j z ceiling function of z (returns the smallest integer greater than or equal to real value z) z floor function of z (returns the integer portion of real value z) ISO 24153:2009(E) ISO 2009 All rights reserved 54 General 4.1 Random sam
48、pling is a prerequisite to the correct application of most sampling plans in industrial use. Similarly, randomization, which uses the principles of random sampling, is indispensable in the conduct of designed experiments, as it increases the internal validity of an experiment, allowing statistical m
49、ethods to be used in the interpretation of an experiments results. The goal of random sampling is to provide a means of applying the results of probability theory to practical problems, while avoiding any form of bias. This goal is not attainable using certain other types of sampling. For example, sampling based on such concepts as personal intuition or judgment, haphazardness, or quota-achievement are inherently biased and consequently can lead to serious errors in the dec
