1、Designation: E105 10An 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 revi
2、sion. 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,With Specified Precision, the Average for a Characteristicof a Lot or ProcessE141 Practice for Acceptance of Evidence Based on theResults of Probability Sampling
4、E456 Terminology Relating to Quality and StatisticsE1402 Guide for Sampling Design3. Terminology3.1 DefinitionsFor general terminology, refer to Termi-nology E456 and Guide E1402.3.1.1 judgment sampling, na procedure whereby enu-merators select a few items of the population, based on visual,position
5、al or other cues that are believed to berelated to the variable of interest, so that the selected itemsappear to match the population.3.1.2 probability sampling plan, na sampling plan whichmakes use of the theory of probability to combine a suitableprocedure for selecting sample items with an approp
6、riateprocedure for summarizing the test results so that inferencesmay be drawn and risks calculated from the test results by thetheory of probability.3.1.2.1 DiscussionFor any given set of conditions, therewill usually be several possible plans, all valid, but differing inspeed, simplicity, and cost
7、. 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 items thatfail to meet (or meet) a specified requirement,
8、 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 of the formation of anestimate.4.3 The purpose may be
9、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 variance of estimates or the risks of therational dis
10、position 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 required were generated properly, the units tobe sampled
11、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 only partially determined byrandom numbers and a frame, b
12、ut 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 certain char-acteristics of importance, as follows:5.1.1
13、 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 sample is used for decision without theintermediate step
14、of an estimate, the decision process willfollow definite rules. In acceptance sampling, for example,these 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
15、levels may be specified.1This practice is under the jurisdiction of ASTM Committee E11 on Quality andStatistics and is the direct responsibility of Subcommittee E11.10 on Sampling /Statistics.Current edition approved Oct. 1, 2010. Published November 2010. Originallyapproved in 1954. Last previous ed
16、ition approved in 2004 as E105 04. DOI:10.1520/E0105-101Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.5.2 The minimum requirements that must be met in order toobtain the characteristics mentioned in 5.1 appear in Section 6,which als
17、o 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 part of the pile, lot, or shipment have anonzero chanc
18、e 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 latter criterion should not be departed from; forexamp
19、le, 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 plan must describe the sampling units and how theyar
20、e to be selected. It must specify that the selection shall beobjectively at random. To achieve random selection, userandom sampling numbers, since mechanical randomizingdevices usually lead to biases and are not standard tools. Therequirements of 6.1.3 may be met, in nonobvious ways, byvarious speci
21、al methods of computation.6.3 In meeting the requirements of 6.1.3, carefully state thepurposes served by sampling, lest a relatively unimportant aimoverbalance a more important one. For example, estimates ofthe overall average quality of a stock of items may be lessimportant than the rational dispo
22、sition of subgroups of thestock of inferior quality. In this case the method of usingsubsamples of equal size drawn from each subgroup is moreefficient, although at some expense to the efficiency of theestimate of the overall average quality. Similarly, in acceptanceinspection, samples of equal size
23、 drawn from lots that varywidely in size serve primarily to provide consistent judgmentwith respect to each lot, and secondarily to provide an estimateof the process average. Where the estimate of the overallaverage of a number of lots is the important objective, samplesproportional to the sizes of
24、the subgroups will usually yield anefficient estimate. For other possible criteria, sizes intermediatebetween equal and proportional sampling from the subgroupswill 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 Guide
25、E1402). Nor is it easy to describe how these plans differ fromthose that do not satisfy the requirement. Many standardtechniques, such as pure random unstratified sampling, randomstratified sampling, and sampling with probabilities in propor-tion to size, will satisfy the requirement; likewise every
26、 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 probability sampling plan for any particular materialmust be workable, and if several alternative plans are possible,each of which will provide the de
27、sired level of precision, theplan adopted should be the one that involves the lowest cost.6.6 A probability sampling plan must describe the samplingunits and how they are to be selected (with or withoutstratification, equal probabilities, etc.). The sampling plan mustalso describe:6.6.1 The formula
28、for calculating an estimate (averageconcentration, minimum concentration, range, total weight,etc.),6.6.2 A formula or procedure by which to calculate thestandard error of any estimate from the results of the sampleitself, and6.6.3 Sources of possible bias in the sampling procedure orin the estimati
29、ng 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 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 info
30、rmation about relevant properties ofthe material to be sampled (averages, components of variance,etc.),6.7.3 Consideration of a number of possible types of sam-pling plans, with comparisons of overall costs, precisions, anddifficulties,6.7.4 An evaluation of the possible plans, in terms of cost ofsa
31、mpling and testing, delay, supervisory time, inconvenience,6.7.5 Selection of a plan from among the various possibleplans, and6.7.6 Reconsideration of all the preceding steps.7. Some Problems Encountered in the ProbabilitySampling of Bulk Materials7.1 There are two major difficulties that may be enc
32、ounteredin planning and carrying out the probability sampling of a lotof bulk material:7.1.1 Lack of information on the pertinent statistical char-acteristics of the lot of material, and7.1.2 The physical difficulties or the costs of drawing intothe sample the specific ultimate sample units to be sp
33、ecified inthe sampling plan.7.2 There may be little information on the nature of thedistribution of the desired property in any given lot or in theuniverse of such lots, or on the magnitude and stability of thecomponents of variance involved. This circumstance is to beexpected if the manufacturing p
34、rocess has not had the benefitof statistical methods to eliminate assignable causes of vari-ability. It will then be difficult to specify in advance the exactsize of sample for a prescribed degree of precision. For furtherdiscussion of sample size related to specified precision, seePractice E122.7.3
35、 As experience is acquired, however, the sample can beincreased or decreased to meet the requirements more exactlyand more economically. In any case, a valid estimate can bemade of the precision provided by any probability sample thatwas selected, based on an examination of the sample itself. Inthis
36、 connection, random fluctuations that arise from the mea-surement process must be considered and appropriate allow-ance made, if necessary.E105 1027.4 Because of the physical nature, condition, or location ofthe material at the time of intended sampling, selection of theunits specified in a proposed
37、 sampling plan may not befeasible, physically or economically. No matter how sound agiven sampling plan is in a statistical sense, it is not suitable ifthe cost involved is prohibitive or if the work required is sostrenuous that it leads to short cuts or subterfuge by thoseresponsible for the sampli
38、ng.8. Planning for Sampling8.1 Different problems or difficulties are encountered withvarious kinds of materials, and they require specific solutionsfor individual cases. Some general features of solutions tocommon difficulties are as follows:8.1.1 Lack of specific information on the pertinent stati
39、sticalcharacteristics of the class of material to be sampled maysometimes be overcome to a satisfactory degree, withoutexcessive cost or delay, by investigation and utilization ofexisting, apparently unrelated data and general information.8.1.2 The cost of a sampling plan is not confined to thedirec
40、t monetary costs of sampling and testing. Plans that securegreater simplicity, convenience, or speed at the expense ofhigher direct costs sometimes have lower total costs and maythen be appropriately adopted.8.1.3 Random error can sometimes be reduced by properstratification. Where physical difficul
41、ties are encountered instratified sampling, the statistician requires the cooperation ofthe engineer for possible solutions; in any case, the knowledgeand cooperation of the engineer will be helpful in choosing thenature and extent of stratification.8.1.4 Economic reduction in the variance of the ul
42、timatesampling unit is sometimes possible, as by a change in size orshape, or by a choice of units that cut across natural strata.8.1.5 Inability to obtain economically the desired samplingunits from a lot of material in place is frequently a majorstumbling block in the actual sampling of such mater
43、ial. Forsuch units to become accessible, the material must be handledor moved. Since movement (transportation) is usually neces-sary at some stage in the utilization of the material, consider-ation should be given to the possibility of drawing the sampleat this time.8.1.6 Certain forms of transporta
44、tion of some classes of bulkmaterials sometimes effect a mixing of the elementary particlesof the material, and sometimes a segregation. The samplingplan may often be modified to take advantage of this mixing orsegregation. Sometimes a modification in the transportingsystem will emphasize such a cha
45、nge, so that a modifiedsampling plan will permit still more economical sampling.8.1.7 Selection by use of random numbers need not be moreonerous or costly than hit-or-miss methods of sample selection,provided the sampling plan is thoughtfully formulated. Forexample, where the actual use of random nu
46、mber tables isdifficult, random numbers may be selected in advance andprovided in envelopes for use as needed. In the selection ofmaterial from boxes, templates with random cutouts can beused. Units difficult to move in warehouses may be dividedinto rows or stacks or other appropriate subgroups; the
47、 sub-groups, and the units within subgroups, that are to be drawninto the sample can then be determined by the use of randomnumbers. A general rule is that where the use of tables ofrandom numbers appears cumbersome or costly, there canusually be found a reformulation of the sampling plan that willm
48、inimize the cost without sacrificing the probabilistic nature ofthe desired estimate.8.1.8 The sampling devices that are used in any given placecan affect enormously the accessibility of the ultimate sam-pling units specified by the sampling plan, and therefore thepossibility of attaining randomness
49、, and proportionality withinstrata. The expenditure of considerable effort is frequentlywarranted in the development of superior devices.As statisticaland engineering factors are mutually interacting throughout thedesign of an efficient probability sampling plan, close coop-eration is necessary between specialists in the two fields. It ispossible, of course, that adequate specialized knowledge ofboth fields may be combined in one person.APPENDIX(Nonmandatory Information)X1. SELECTION OF SAMPLEX1.1 Calculation of the margin of error or the risk in the useof the results of samples i
