ASTM_C_970_-_87_2006.pdf

Designation:C 970 87(Reapproved 2006)Standard Practice forSampling Special Nuclear Materials in Multi-ContainerLots1This standard is issued under the fixed designation C 970;the number immediately following the designation indicates the year oforiginal adoption or,in the case of revision,the year of last revision.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 provides an aid in designing a samplingand analysis plan for the purpose of minimizing random errorin the measurement of the amount of nuclear material in a lotconsisting of several containers.The problem addressed is theselection of the number of containers to be sampled,thenumber of samples to be taken from each sampled container,and the number of aliquot analyses to be performed on eachsample.1.2 This practice provides examples for application as wellas the necessary development for understanding the statisticsinvolved.The uniqueness of most situations does not allowpresentation of step-by-step procedures for designing samplingplans.It is recommended that a statistician experienced inmaterials sampling be consulted when developing such plans.1.3 The values stated in SI units are to be regarded as thestandard.1.4 This standard does not purport to address all of thesafety problems,if any,associated with its use.It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2.Referenced Documents2.1 ASTM Standards:2E 300 Practice for Sampling Industrial Chemicals2.2Other Standard:NUREG/CR-0087,Considerations for Sampling NuclearMaterials for SNM Accounting Measurements33.Terminology Definitions3.1 analysis of variancethe body of statistical theory,methods,and practice in which the variation in a set ofmeasurements,as measured by the sum of squares of themeasurements,is partitioned into several component sums ofsquares,each attributable to some meaningful cause(source ofvariation).3.2 confidence interval(a)an interval estimator used tobound the value of a population parameter and to which ameasure of confidence can be associated,and(b)the intervalestimate,based on a realization of a sample drawn from thepopulation of interest,that bounds the value of a populationparameter with at least a stated confidence.3.3 Estimation,Estimator,Estimate:3.3.1 Estimation,in statistics,has a specific meaning,con-siderably different from the common interpretation of guess-ing,playing a hunch,or grabbing out of the air.Instead,estimation is the process of following certain statistical prin-ciples to derive an approximation(estimate)to the unknownvalue of a population parameter.This estimate is based on theinformation available in a sample drawn from the population.3.4 estimatora function of a sample(X1,X2,.,Xn)usedto estimate a population parameter.NOTE1An estimator is a random variable;therefore,not everyrealization(x1,x2,.,xn)of the sample(X1,X2,.,Xn)will lead to thesame value(realization)of the estimator.An estimator can be a functionthat,when evaluated,results in a single value or results in an interval orregion of values.In the former case the estimator is called a pointestimator,and in the latter case it is referred to as an interval estimator.3.5 estimate,(a:n)a particular value or values realized byapplying an estimator to a particular realization of a sample,that is,to a particular set of sample values(x1,x2,.,xn).(b:v)to use an estimator.3.6 nested design one of a particular class of experimentaldesigns,characterized by“nesting”of the sources of variation:for each sampled value of a variable A,a given number ofvalues of a second variable B is sampled;for each of these,agiven number of values of the next variable C is sampled,etc.The result is that each line of the“Expected Value of MeanSquare”column in an analysis of variance table contains all butone of the terms of the preceding line.3.7 random variable a variable that takes on any one ofthe values in its range according to a fixed probabilitydistribution.(Synonyms:chance variable,stochastic variable,variate.)1This practice is under the jurisdiction of ASTM Committee C26 on NuclearFuel Cycle and is the direct responsibility of Subcommittee C26.08 on QualityAssurance and Reference Materials.Current edition approved Jan.1,2006.Published February 2006.Originallyapproved in 1982.Last previous edition approved in 1997 as C 970 87(1997).2For referenced ASTM standards,visit the ASTM website,www.astm.org,orcontact ASTM Customer Service at serviceastm.org.For Annual Book of ASTMStandards volume information,refer to the standards Document Summary page onthe ASTM website.3Available from National Technical Information Service,Springfield,VA22161.1Copyright ASTM International,100 Barr Harbor Drive,PO Box C700,West Conshohocken,PA 19428-2959,United States.3.8 standard deviation(s.d