1、Designation: E105 10E105 16 An American National StandardStandard Practice forProbability Sampling of Materials1This standard is issued under the fixed designation E105; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of l
2、ast revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice is primarily a statement of principles for the guidance of ASTM technical committees and others in thepre
3、paration of a sampling plan for a specific material.2. Referenced Documents2.1 ASTM Standards:E122 Practice for Calculating Sample Size to Estimate, With Specified Precision, the Average for a Characteristic of a Lot orProcessE300 Practice for Sampling Industrial ChemicalsE141 Practice for Acceptanc
4、e of Evidence Based on the Results of Probability SamplingE456 Terminology Relating to Quality and StatisticsE1402 Guide for Sampling Design3. Terminology3.1 Definitions:3.1.1 For general terminology, refer to Terminology E456 and Guide E1402.3.1.2 judgment sampling, na procedure whereby enumerators
5、 select a few items of the population, based on visual, positional,or other cues that are believed to be related to the variable of interest, so that the selected items appear to match the population.3.1.3 probability sampling plan, na sampling plan which makes use of the theory of probability to co
6、mbine a suitableprocedure for selecting sample items with an appropriate procedure for summarizing the test results so that inferences may bedrawn and risks calculated from the test results by the theory of probability.3.1.3.1 DiscussionFor any given set of conditions, there will usually be several
7、possible plans, all valid, but differing in speed, simplicity, and cost.Further discussion is provided in Practice E141.4. Significance and Use4.1 The purpose of the sample may be to estimate properties of a larger population, such as a lot, pile or shipment, thepercentage of some constituent, the f
8、raction of the items that fail to meet (or meet) a specified requirement, the averagecharacteristic or quality of an item, the total weight of the shipment, or the probable maximum or minimum content of, say, somechemical.4.2 The purpose may be the rational disposition of a lot or shipment without t
9、he intermediate step of the formation of anestimate.4.3 The purpose may be to provide aid toward rational action concerning the production process that generated the lot, pile orshipment.4.4 Whatever the purpose of the sample, adhering to the principles of probability sampling will allow the uncerta
10、inties, suchas bias and variance of estimates or the risks of the rational disposition or action, to be calculated objectively and validly from thetheory of combinatorial probabilities. This assumes, of course, that the sampling operations themselves were carried out properly,1 This practice is unde
11、r the jurisdiction ofASTM Committee E11 on Quality and Statistics and is the direct responsibility of Subcommittee E11.10 on Sampling / Statistics.Current edition approved Oct. 1, 2010April 1, 2016. Published November 2010April 2016. Originally approved in 1954. Last previous edition approved in 200
12、42010 asE105 04.E105 10. DOI: 10.1520/E0105-10.10.1520/E0105-16.This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Becauseit may not be technically possible to adequately depict all
13、changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current versionof the standard as published by ASTM is to be considered the official document.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959
14、. United States1as well. For example, that any random numbers required were generated properly, the units to be sampled from were correctlyidentified, located, and drawn, and the measurements were made with measurement error at a level not exceeding the requiredpurposes.4.5 Determination of bias and
15、 variance and of risks can be calculated when the selection was only partially determined byrandom numbers and a frame, but they then require suppositions and assumptions which may be more or less mistaken or requireadditional data which may introduce experimental error.5. Characteristics of a Proba
16、bility Sampling Plan5.1 A probability sampling plan will possess certain characteristics of importance, as follows:5.1.1 It will possess an objective procedure for the selection of the sample, with the use of random numbers.5.1.2 It will include a definite formula for the estimate, if there is to be
17、 an estimate; also for the standard error of any estimate.If the sample is used for decision without the intermediate step of an estimate, the decision process will follow definite rules. Inacceptance sampling, for example, these are often based on predetermined risks of taking the undesired action
18、when the true levelsof the characteristic concerned have predetermined values; for example, acceptable and rejectable quality levels may be specified.5.2 The minimum requirements that must be met in order to obtain the characteristics mentioned in 5.1 appear in Section 6,which also indicates the min
19、imum requirements for the description of a satisfactory sampling plan.6. Minimum Standards for a Probability Sampling Plan6.1 For a sampling plan to have the requirements mentioned in Section 5, it is necessary:6.1.1 That every part of the pile, lot, or shipment have a nonzero chance of selection,6.
20、1.2 That these probabilities of selection be known, at least for the parts actually selected, and6.1.3 That, either in measurement or in computation, each item be weighted in inverse proportion to its probability of selection.This latter criterion should not be departed from; for example, equal weig
21、hts should not be used when the probabilities of selectionare unequal, unless calculations show that biases introduced thereby will not impair the usefulness of the results.6.2 To meet the requirements of 6.1.1 and 6.1.2, the sampling plan must describe the sampling units and how they are to beselec
22、ted. It To meet requirements of 5.1.1, the sampling plan must specify that the selection shallwill be made objectively atrandom. To achieve random selection, use random sampling numbers, since mechanical randomizing devices usually lead to biasesand are not standard tools. The requirements of a tabl
23、e of random numbers or a sequence of random numbers generated by arandom number generator 6.1.3may be met, in nonobvious ways, by various special methods of computation.used. Randomnumber generation is commonly available in commercial software. For a discussion of sample size related to specified pr
24、ecision,see Practice E122.6.3 In meeting the requirements of 6.1.3, carefully state the purposes served by sampling, lest a relatively unimportant aimoverbalance a more important one. For example, estimates of the overall average quality of a stock of items may be less importantthan the rational dis
25、position of subgroups of the stock of inferior quality. In this case the method of using subsamples of equal sizedrawn from each subgroup is more efficient, although at some expense to the efficiency of the estimate of the overall averagequality. Similarly, in acceptance inspection, samples of equal
26、 size drawn from lots that vary widely in size serve primarily toprovide consistent judgment with respect to each lot, and secondarily to provide an estimate of the process average. Where theestimate of the overall average of a number of lots is the important objective, samples proportional to the s
27、izes of the subgroupswill usually yield an efficient estimate. For other possible criteria, sizes intermediate between equal and proportional sampling fromthe subgroups will be appropriate.6.4 It is not easy to describe in a few words the many sorts of plans that will meet the requirements of 6.1.2
28、(see Guide E1402).Nor is it easy to describe how these plans differ from those that do not satisfy the requirement. Many standard techniques, suchas pure random unstratified sampling, random stratified sampling, and sampling with probabilities in proportion to size, will satisfythe requirement; like
29、wise every plan will do so where the sample is made up of separate identifiable subsamples that were selectedindependently and by the use of random numbers.6.5 Aprobability sampling plan for any particular material must be workable, and if several alternative plans are possible, eachof which will pr
30、ovide the desired level of precision, the plan adopted should be the one that involves the lowest cost.6.6 Aprobability sampling plan must describe the sampling units and how they are to be selected (with or without stratification,equal probabilities, etc.). The sampling plan must also describe:6.6.
31、1 The formula for calculating an estimate (average concentration, minimum concentration, range, total weight, etc.),6.6.2 A formula or procedure by which to calculate the standard error of any estimate from the results of the sample itself, and6.6.3 Sources of possible bias in the sampling procedure
32、 or in the estimating formulas, together with data pertaining to thepossible magnitudes of the biases and their effects on the uses of the data.6.7 The development of a good sampling plan will usually take place in steps, such as:6.7.1 A statement of the problem for which an estimate is necessary,6.
33、7.2 Collection of information about relevant properties of the material to be sampled (averages, components of variance, etc.),E105 1626.7.3 Consideration of a number of possible types of sampling plans, with comparisons of overall costs, precisions, anddifficulties,6.7.4 An evaluation of the possib
34、le plans, in terms of cost of sampling and testing, delay, supervisory time, inconvenience,6.7.5 Selection of a plan from among the various possible plans, and6.7.6 Reconsideration of all the preceding steps.7. Selection of Sample7.1 Calculation of the margin of error or the risk in the use of the r
35、esults of samples is possible only if the selection of the itemsfor test is made at random. This is true whether the procedure is stratified or unstratified.7.2 For a method of sampling to be random it must satisfy statistical tests, the most common of which are the “run tests” and“control charts,”
36、and certain other special statistical tests. Randomness is obtained by positive action; a random selection is notmerely a haphazard selection, nor one declared to be without bias. Selection by the proper use of a standard table of randomnumbers is acceptable as random. It is possible and feasible to
37、 adapt the use of random numbers to the laboratory, to the field, andto the factory.7.3 Mechanical randomizing devices are sometimes used, but no device is acceptable as random in the absence of thoroughtests. The difficulties in attaining randomness are greater than generally known. Thus, special r
38、andomizing devices intended forthe production of random numbers have often failed to give satisfactory results until adjusted and retested with perseverance.However, mechanical selection is still usually preferable to a judgment-selection.7.4 Some other methods of sampling should be mentioned that d
39、o not meet the requirements of randomness. For example, onemay declare that a lot of item is “thoroughly mixed,” and hence that any portion, even the top layer, would give every item an equalchance of selection. In the absence of elaborate steps to mix the product, followed by careful tests for rand
40、omness, suchassumptions are risky, as they often lead to wrong results.7.5 Again, another common practice is to take a systematic sample consisting of every kth item. Even if the first item is selectedat random, this type of sample, although random, is actually a sample of only one of the k possible
41、 sampling units that can beformed with an interval of k. Hence, in the absence of knowledge concerning the order of the material, such a sample does notpermit a valid calculation of the standard error. Moreover, it does not yield a comparison of the variances between and withingroups of units, stati
42、stical information that might indicate the direction of change toward a more efficient sampling plan.7.6 However, the use of 10 independent random starts between 1 and 10 k, together with every 10 kth unit thereafter, to form10 independent systematic subsamples does permit a valid calculation of the
43、 standard error, together with some information on thevariances between and within groups of units.7.7 The foregoing paragraphs do not mean that nonrandom and judgment sampling are of no value. A preliminary judgmentsample, for example, may provide useful information for the efficient design of a pr
44、obability sampling plan. Again, if the materialbeing inspected is known to vary but little, a “grab” sample will be helpful in assessing the level of the characteristic concerned.7.8 It also should be noted that judgment plays an important role in the design of a probability sampling plan. For examp
45、le, itmay be used to assess costs, to estimate spreads and likely values of variances; also definitions of strata. In the actual probabilitysample, however, judgment is not used in the selection of the individual items of the sample, nor in making the inferences, norin calculating the risks of decis
46、ions based wholly on the sample of succession of samples.8. Some Problems Encountered in the Probability Sampling of Bulk Materials8.1 There are two major difficulties that may be encountered in planning and carrying out the Sampling of a bulk materialinvolves some similar and some different princip
47、les from probability sampling of a lot of bulk material:discrete units.8.1.1 Lack of information on the pertinent statistical characteristics of the lot of material, andA sample from the populationconsists of increments, not items that can be individually identified. Sample size refers to weight or
48、volume or the number ofincrements rather than the number of items.8.1.2 Forms of systematic or stratified sampling may still be used to subdivide the population, but only in a limited sense. Forexample, one may stratify an area of land according to ground slope and wind direction. Still, once one st
49、arts to sample the actualmaterial, groups of items, such as dirt particles, are obtained in increments.8.1.3 It can be difficult to apply the basic principle that every portion of the population has a specified non-zero probability ofbeing in the sample. This principle becomes impossible to apply when some units are inaccessible, such as in odd-shapedcontainers or cargo holds. Trying to get material near the side or bottom of a container can disturb the matter nearby. Denser orsmaller particles might be near the bottom. Similar difficulties of access can affect sampling of disc
