1、Designation: E105 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 last rev
2、ision. 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 forthe guidance of ASTM technical committees and others in thepreparation
3、 of a sampling plan for a specific material.2. Referenced Documents2.1 ASTM Standards:E122 Practice for Calculating Sample Size to Estimate, WithSpecified Precision, the Average for a Characteristic of aLot or ProcessE300 Practice for Sampling Industrial ChemicalsE141 Practice for Acceptance of Evid
4、ence Based on theResults 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 E456and Guide E1402.3.1.2 judgment sampling, na procedure whereby enu-merators select a
5、few items of the population, based on visual,positional, or other cues that are believed to be related to thevariable of interest, so that the selected items appear to matchthe population.3.1.3 probability sampling plan, na sampling plan whichmakes use of the theory of probability to combine a suita
6、bleprocedure for selecting sample items with an appropriateprocedure for summarizing the test results so that inferencesmay be drawn and risks calculated from the test results by thetheory of probability.3.1.3.1 DiscussionFor any given set of conditions, therewill usually be several possible plans,
7、all valid, but differing inspeed, simplicity, and cost. Further discussion is provided inPractice E141.4. Significance and Use4.1 The purpose of the sample may be to estimate propertiesof a larger population, such as a lot, pile or shipment, thepercentage of some constituent, the fraction of the ite
8、ms thatfail to meet (or meet) a specified requirement, the averagecharacteristic or quality of an item, the total weight of theshipment, or the probable maximum or minimum content of,say, some chemical.4.2 The purpose may be the rational disposition of a lot orshipment without the intermediate step
9、of the formation of anestimate.4.3 The purpose may be to provide aid toward rationalaction concerning the production process that generated the lot,pile or shipment.4.4 Whatever the purpose of the sample, adhering to theprinciples of probability sampling will allow the uncertainties,such as bias and
10、 variance of estimates or the risks of therational disposition or action, to be calculated objectively andvalidly from the theory of combinatorial probabilities. Thisassumes, of course, that the sampling operations themselveswere carried out properly, as well. For example, that anyrandom numbers req
11、uired were generated properly, the units tobe sampled from were correctly identified, located, and drawn,and the measurements were made with measurement error at alevel not exceeding the required purposes.4.5 Determination of bias and variance and of risks can becalculated when the selection was onl
12、y partially determined byrandom numbers and a frame, but they then require supposi-tions and assumptions which may be more or less mistaken orrequire additional data which may introduce experimentalerror.5. Characteristics of a Probability Sampling Plan5.1 A probability sampling plan will possess ce
13、rtain char-acteristics of importance, as follows:5.1.1 It will possess an objective procedure for the selectionof the sample, with the use of random numbers.5.1.2 It will include a definite formula for the estimate, ifthere is to be an estimate; also for the standard error of anyestimate. If the sam
14、ple is used for decision without theintermediate step of an estimate, the decision process willfollow definite rules. In acceptance sampling, for example,1This practice is under the jurisdiction of ASTM Committee E11 on Quality andStatistics and is the direct responsibility of Subcommittee E11.10 on
15、 Sampling /Statistics.Current edition approved April 1, 2016. Published April 2016. Originallyapproved in 1954. Last previous edition approved in 2010 as E105 10. DOI:10.1520/E0105-16.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1th
16、ese are often based on predetermined risks of taking theundesired action when the true levels of the characteristicconcerned have predetermined values; for example, acceptableand rejectable quality levels may be specified.5.2 The minimum requirements that must be met in order toobtain the characteri
17、stics mentioned in 5.1 appear in Section 6,which also indicates the minimum requirements for the de-scription of a satisfactory sampling plan.6. Minimum Standards for a Probability Sampling Plan6.1 For a sampling plan to have the requirements mentionedin Section 5, it is necessary:6.1.1 That every p
18、art of the pile, lot, or shipment have anonzero chance of selection,6.1.2 That these probabilities of selection be known, at leastfor the parts actually selected, and6.1.3 That, either in measurement or in computation, eachitem be weighted in inverse proportion to its probability ofselection. This l
19、atter criterion should not be departed from; forexample, equal weights should not be used when the probabili-ties of selection are unequal, unless calculations show thatbiases introduced thereby will not impair the usefulness of theresults.6.2 To meet the requirements of 6.1.1 and 6.1.2, thesampling
20、 plan must describe the sampling units and how theyare to be selected. To meet requirements of 5.1.1, the samplingplan must specify that the selection will be made objectively atrandom. To achieve random selection, a table of randomnumbers or a sequence of random numbers generated by arandom number
21、generator may be used. Random numbergeneration is commonly available in commercial software. Fora discussion of sample size related to specified precision, seePractice E122.6.3 In meeting the requirements of 6.1.3, carefully state thepurposes served by sampling, lest a relatively unimportant aimover
22、balance a more important one. For example, estimates ofthe overall average quality of a stock of items may be lessimportant than the rational disposition of subgroups of thestock of inferior quality. In this case the method of usingsubsamples of equal size drawn from each subgroup is moreefficient,
23、although at some expense to the efficiency of theestimate of the overall average quality. Similarly, in acceptanceinspection, samples of equal size drawn from lots that varywidely in size serve primarily to provide consistent judgmentwith respect to each lot, and secondarily to provide an estimateof
24、 the process average. Where the estimate of the overallaverage of a number of lots is the important objective, samplesproportional to the sizes of the subgroups will usually yield anefficient estimate. For other possible criteria, sizes intermediatebetween equal and proportional sampling from the su
25、bgroupswill be appropriate.6.4 It is not easy to describe in a few words the many sortsof plans that will meet the requirements of 6.1.2 (see GuideE1402). Nor is it easy to describe how these plans differ fromthose that do not satisfy the requirement. Many standardtechniques, such as pure random uns
26、tratified sampling, randomstratified sampling, and sampling with probabilities in propor-tion to size, will satisfy the requirement; likewise every planwill do so where the sample is made up of separate identifiablesubsamples that were selected independently and by the use ofrandom numbers.6.5 A pro
27、bability sampling plan for any particular materialmust be workable, and if several alternative plans are possible,each of which will provide the desired level of precision, theplan adopted should be the one that involves the lowest cost.6.6 A probability sampling plan must describe the samplingunits
28、 and how they are to be selected (with or withoutstratification, equal probabilities, etc.). The sampling plan mustalso describe:6.6.1 The formula for calculating an estimate (averageconcentration, minimum concentration, range, total weight,etc.),6.6.2 A formula or procedure by which to calculate th
29、estandard error of any estimate from the results of the sampleitself, and6.6.3 Sources of possible bias in the sampling procedure orin the estimating formulas, together with data pertaining to thepossible magnitudes of the biases and their effects on the usesof the data.6.7 The development of a good
30、 sampling plan will usuallytake place in steps, such as:6.7.1 A statement of the problem for which an estimate isnecessary,6.7.2 Collection of information about relevant properties ofthe material to be sampled (averages, components of variance,etc.),6.7.3 Consideration of a number of possible types
31、of sam-pling plans, with comparisons of overall costs, precisions, anddifficulties,6.7.4 An evaluation of the possible plans, in terms of cost ofsampling and testing, delay, supervisory time, inconvenience,6.7.5 Selection of a plan from among the various possibleplans, and6.7.6 Reconsideration of al
32、l the preceding steps.7. Selection of Sample7.1 Calculation of the margin of error or the risk in the useof the results of samples is possible only if the selection of theitems for test is made at random. This is true whether theprocedure is stratified or unstratified.7.2 For a method of sampling to
33、 be random it must satisfystatistical tests, the most common of which are the “run tests”and “control charts,” and certain other special statistical tests.Randomness is obtained by positive action; a random selectionis not merely a haphazard selection, nor one declared to bewithout bias. Selection b
34、y the proper use of a standard table ofrandom numbers is acceptable as random. It is possible andfeasible to adapt the use of random numbers to the laboratory,to the field, and to the factory.7.3 Mechanical randomizing devices are sometimes used,but no device is acceptable as random in the absence o
35、fthorough tests. The difficulties in attaining randomness aregreater than generally known. Thus, special randomizingdevices intended for the production of random numbers haveE105 162often failed to give satisfactory results until adjusted andretested with perseverance. However, mechanical selection
36、isstill usually preferable to a judgment-selection.7.4 Some other methods of sampling should be mentionedthat do not meet the requirements of randomness. For example,one may declare that a lot of item is “thoroughly mixed,” andhence that any portion, even the top layer, would give everyitem an equal
37、 chance of selection. In the absence of elaboratesteps to mix the product, followed by careful tests forrandomness, such assumptions are risky, as they often lead towrong results.7.5 Again, another common practice is to take a systematicsample consisting of every kth item. Even if the first item iss
38、elected at random, this type of sample, although random, isactually a sample of only one of the k possible sampling unitsthat can be formed with an interval of k. Hence, in the absenceof knowledge concerning the order of the material, such asample does not permit a valid calculation of the standard
39、error.Moreover, it does not yield a comparison of the variancesbetween and within groups of units, statistical information thatmight indicate the direction of change toward a more efficientsampling plan.7.6 However, the use of 10 independent random startsbetween 1 and 10 k, together with every 10 kt
40、h unit thereafter,to form 10 independent systematic subsamples does permit avalid calculation of the standard error, together with someinformation on the variances between and within groups ofunits.7.7 The foregoing paragraphs do not mean that nonrandomand judgment sampling are of no value. A prelim
41、inary judg-ment sample, for example, may provide useful information forthe efficient design of a probability sampling plan.Again, if thematerial being inspected is known to vary but little, a “grab”sample will be helpful in assessing the level of the character-istic concerned.7.8 It also should be n
42、oted that judgment plays an importantrole in the design of a probability sampling plan. For example,it may be used to assess costs, to estimate spreads and likelyvalues of variances; also definitions of strata. In the actualprobability sample, however, judgment is not used in theselection of the ind
43、ividual items of the sample, nor in makingthe inferences, nor in calculating the risks of decisions basedwholly on the sample of succession of samples.8. Sampling of Bulk Materials8.1 Sampling of a bulk material involves some similar andsome different principles from probability sampling of discrete
44、units.8.1.1 A sample from the population consists of increments,not items that can be individually identified. Sample size refersto weight or volume or the number of increments rather thanthe number of items.8.1.2 Forms of systematic or stratified sampling may still beused to subdivide the populatio
45、n, but only in a limited sense.For example, one may stratify an area of land according toground slope and wind direction. Still, once one starts tosample the actual material, groups of items, such as dirtparticles, are obtained in increments.8.1.3 It can be difficult to apply the basic principle tha
46、tevery portion of the population has a specified non-zeroprobability of being in the sample. This principle becomesimpossible to apply when some units are inaccessible, such asin odd-shaped containers or cargo holds. Trying to get materialnear the side or bottom of a container can disturb the matter
47、nearby. Denser or smaller particles might be near the bottom.Similar difficulties of access can affect sampling of discreteunits.8.1.4 Considerations outside the usual sampling spherebecome important. Material may change chemically whenexposed to different pressure, to light, or to the atmosphere.8.
48、2 In general, sampling variation can be reduced by takingsmaller increments, taking more increments, reducing theparticle size of solid material before sampling, and mixing thematerial before sampling. Use a sampling tool that will notunder- or over-represent certain type of particles. Roundedscoops
49、, for example, will under-represent particles near thebottom. Carryover of material can happen when the samplingtools or connectors are not cleaned between sampling events.For discussion of particular methods for sampling differentkinds of bulk materials, see Practice E300.8.3 As experience is acquired, the sample can be increasedor decreased to meet the requirements more exactly and moreeconomically. In any case, a valid estimate can be made of theprecision provided by any probability sample that was selected,based on an examination of the sample itself. In thisconnection, random
