1、Designation: E 105 04An American National StandardStandard Practice forProbability Sampling Of Materials1This standard is issued under the fixed designation E 105; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last re
2、vision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) 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 thepreparati
3、on of a sampling plan for a specific material.2. Terminology2.1 Definitions of Terms Specific to This Standard:2.1.1 probability sampling plans make use of the theory ofprobability to combine a suitable procedure for selectingsample items with an appropriate procedure for summarizingthe test results
4、 so that inferences may be drawn and riskscalculated from the test results by the theory of probability. Forany given set of conditions there will usually be severalpossible plans, all valid, but differing in speed, simplicity, andcost.3. Significance and Use3.1 The purpose of the sample may be to e
5、stimate 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, the averagecharacteristic or quality of an item, the total weight of theshipment, or the probable maximum or min
6、imum content of,say, some chemical.3.2 The purpose may be the rational disposition of a lot orshipment without the intermediate step of the formation of anestimate.3.3 The purpose may to provide aid toward rational actionconcerning the production process that generated the lot, pileor shipment.3.4 W
7、hatever 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 disposition or action, to be calculated objectively andvalidly from the theory of combinatorial probabilities. Thisassu
8、mes, of course, that the sampling operations themselvesere carried out properly, as well. For example, that any randomnumbers required were generated properly, the units to besampled from were correctly identified, located, and drawn,and the measurements were made with measurement error at alevel no
9、t exceeding the required purposes.3.5 Determination of bias and variance and of risks can becalculated when the selection was only 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
10、 may introduce experimentalerror.4. Characteristics of a Probability Sampling Plan4.1 A probability sampling plan will possess certain char-acteristics of importance, as follows:4.1.1 It will possess an objective procedure for the selectionof the sample, with the use of random numbers.4.1.2 It will
11、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 of an estimate, the decision process willfollow definite rules. In acceptance sampling, for example,these are often b
12、ased 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.4.2 The minimum requirements that must be met in order toobtain the characteristics mentioned
13、 in 4.1 appear in Section 5,which also indicates the minimum requirements for the de-scription of a satisfactory sampling plan.5. Minimum Standards for a Probability Sampling Plan5.1 For a sampling plan to have the requirements mentionedin Section 4 it is necessary:5.1.1 That every part of the pile,
14、 lot, or shipment have anonzero chance of selection,5.1.2 That these probabilities of selection be known, at leastfor the parts actually selected, and5.1.3 That, either in measurement or in computation, eachitem be weighted in inverse proportion to its probability ofselection. This latter criterion
15、should not be departed from; for1This practice is under the jurisdiction of ASTM Committee E11 on StatisticalMethods and is the direct responsibility of Subcommittee E11.10 on Sampling andData Analysis.Current edition approved June 1, 2004. Published July 2004. Originally approvedin 1954. Last previ
16、ous edition approved in 1996 as E 105 58 (1996).1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.example, equal weights should not be used when the probabili-ties of selection are unequal, unless calculations show thatbiases introduce
17、d thereby will not impair the usefulness of theresults.5.2 To meet the requirements of 5.1.1 and 5.1.2, thesampling plan must describe the sampling units and how theyare to be selected. It must specify that the selection shall beobjectively at random. To achieve random selection, userandom sampling
18、numbers, since mechanical randomizingdevices usually lead to biases and are not standard tools. Therequirements of 5.1.3 may be met, in nonobvious ways, byvarious special methods of computation.5.3 In meeting the requirements of 5.1.3, carefully state thepurposes served by sampling, lest a relativel
19、y unimportant aimoverbalance a more important one. For example, estimates ofthe over-all 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 subgr
20、oup is moreefficient, although at some expense to the efficiency of theestimate of the over-all average quality. Similarly, in accep-tance inspection, samples of equal size drawn from lots thatvary widely in size serve primarily to provide consistentjudgment with respect to each lot, and secondarily
21、 to providean estimate of the process average. Where the estimate of theover-all average of a number of lots is the important objective,samples proportional to the sizes of the subgroups will usuallyyield an efficient estimate. For other possible criteria, sizesintermediate between equal and proport
22、ional sampling fromthe subgroups will be appropriate.5.4 It is not easy to describe in a few words the many sortsof plans that will meet the requirements of 5.1.2. Nor is it easyto describe how these plans differ from those that do not satisfythe requirement. Many standard techniques, such as purera
23、ndom unstratified sampling, random stratified sampling, andsampling with probabilities in proportion to size, will satisfythe requirement; likewise every plan will do so where thesample is made up of separate identifiable subsamples thatwere selected independently and by the use of random num-bers.5
24、.5 A probability 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.5.6 A probability sampling plan must describe the sampl
25、ingunits and how they are to be selected (with or withoutstratification, equal probabilities, etc.). The sampling plan mustalso describe:5.6.1 The formula for calculating an estimate (averageconcentration, minimum concentration, range, total weight,etc.),5.6.2 A formula or procedure by which to calc
26、ulate thestandard error of any estimate from the results of the sampleitself, and5.6.3 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.5.7 The development o
27、f a good sampling plan will usuallytake place in steps, such as:5.7.1 A statement of the problem for which an estimate isnecessary,5.7.2 Collection of information about relevant properties ofthe material to be sampled (averages, components of variance,etc.),5.7.3 Consideration of a number of possibl
28、e types of sam-pling plans, with comparisons of over-all costs, precisions, anddifficulties,5.7.4 An evaluation of the possible plans, in terms of cost ofsampling and testing, delay, supervisory time, inconvenience,5.7.5 Selection of a plan from among the various possibleplans, and5.7.6 Reconsiderat
29、ion of all the preceding steps.6. Some Problems Encountered in the ProbabilitySampling of Bulk Materials6.1 There are two major difficulties that may be encounteredin planning and carrying out the probability sampling of a lotof bulk material:6.1.1 Lack of information on the pertinent statistical ch
30、ar-acteristics of the lot of material, and6.1.2 The physical difficulties or the costs of drawing intothe sample the specific ultimate sample units to be specified inthe sampling plan.6.2 There may be little information on the nature of thedistribution of the desired property in any given lot or in
31、theuniverse of such lots, or on the magnitude and stability of thecomponents of variance involved. This circumstance is to beexpected if the manufacturing process has not had the benefitof statistical methods to eliminate assignable causes of vari-ability. It will then be difficult to specify in adv
32、ance the exactsize of sample for a prescribed degree of precision.6.3 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 t
33、hatwas selected, based on an examination of the sample itself. Inthis connection, random fluctuations that arise from the mea-surement process must be considered and appropriate allow-ance made, if necessary.6.4 Because of the physical nature, condition, or location ofthe material at the time of int
34、ended sampling, selection of theunits specified in a proposed 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 t
35、o short cuts or subterfuge by thoseresponsible for the sampling.7. Planning for Sampling7.1 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 foll
36、ows:7.1.1 Lack of specific information on the pertinent statisticalcharacteristics of the class of material to be sampled maysometimes be overcome to a satisfactory degree, withoutE105042excessive cost or delay, by investigation and utilization ofexisting, apparently unrelated data and general infor
37、mation.7.1.2 The cost of a sampling plan is not confined to thedirect 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.7.1.3 Random error can s
38、ometimes be reduced by properstratification. Where physical difficulties 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
39、of stratification.7.1.4 Economic reduction in the variance of the ultimatesampling unit is sometimes possible, as by a change in size orshape, or by a choice of units that cut across natural strata.7.1.5 Inability to obtain economically the desired samplingunits from a lot of material in place is fr
40、equently a majorstumbling block in the actual sampling of such material. 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
41、 of drawing the sampleat this time.7.1.6 Certain forms of transportation 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. Sometime
42、s a modification in the transportingsystem will emphasize such a change, so that a modifiedsampling plan will permit still more economical sampling.7.1.7 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 th
43、oughtfully formulated. Forexample, where the actual use of random number 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 m
44、ay be dividedinto rows or stacks or other appropriate subgroups; the 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
45、 canusually be found a reformulation of the sampling plan that willminimize the cost without sacrificing the probabilistic nature ofthe desired estimate.7.1.8 The sampling devices that are used in any given placecan affect enormously the accessibility of the ultimate sam-pling units specified by the
46、 sampling plan, and therefore thepossibility of attaining randomness, 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 effi
47、cient 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
48、 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.X1.2 For a method of sampling to be random it must satisfystatistical tests, the most common of which are t
49、he “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 by 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.X1.3 Mechanical randomizing devices are sometimes used,but no device is acceptable as random in the absence ofthorough tests. The difficulties in attaining randomness aregreate
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