ASTM_D_5124_-_96_2013.pdf

Designation:D512496(Reapproved 2013)Standard Practice forTesting and Use of a Random Number Generator in Lumberand Wood Products Simulation1This standard is issued under the fixed designation D5124;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()indicates an editorial change since the last revision or reapproval.1.Scope1.1 This practice gives a minimum testing procedure ofcomputer generation routines for the standard uniform distri-bution.Random observations from the standard uniformdistribution,RU,range from zero to one with every valuebetween zero and one having an equal chance of occurrence.1.2 The tests described in this practice only support thebasic use of random number generators,not their use incomplex or extremely precise simulations.1.3 Simulationdetailsforthenormal,lognormal,2-parameter Weibull and 3-parameter Weibull probability dis-tributions are presented.1.4 This standard does not purport to address all of thesafety concerns,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.See specificwarning statement in 5.5.3.2.Referenced Documents2.1 ASTM Standards:2E456 Terminology Relating to Quality and Statistics3.Terminology3.1 Definitions:3.1.1 periodthe number of RUdeviates the computergenerates before the sequence is repeated.3.1.2 seed valuea number required to start the computergeneration of random numbers.Depending upon the computersystem,the seed value is internally provided or it must be userspecified.Consult the documentation for the specific randomnumber generator used.3.1.3 serial correlationthe statistical correlation betweenordered observations.See 5.2.2.3.1.4 standard normal deviate,RNa computer generatedrandom observation from the normal probability distributionhaving a mean equal to zero and standard deviation equal toone.3.1.5 standard uniform deviate,RUa random observationfrom the standard uniform distribution.3.1.6 standard uniform distributionthe probability distri-bution defined on the interval 0 to 1,with every value between0 and 1 having an equal chance of occurrence.3.1.7 triala computer experiment,and in this standard thegeneration and statistical test of one set of random numbers.4.Significance and Use4.1 Computer simulation is known to be a very powerfulanalytical tool for both practitioners and researchers in the areaof wood products and their applications in structural engineer-ing.Complex structural systems can be analyzed by computerwith the computer generating the system components,giventhe probability distribution of each component.Frequently thecomponents are single boards for which a compatible set ofstrength and stiffness properties are needed.However,theentire structural simulation process is dependent upon theadequacy of the standard uniform number generator required togenerate random observations from prescribed probabilitydistribution functions.4.2 The technological capabilities and wide availability ofmicrocomputers has encouraged their increased use for simu-lation studies.Tests of random number generators in com-monly available microcomputers have disclosed serious defi-ciencies(1).3Adequacy may be a function of intended end-use.This practice is concerned with generation of sets of randomnumbers,as may be required for simulations of large popula-tions of material properties for simulation of complex struc-tures.For more demanding applications,the use of packagedand pretested random number generators is encouraged.1This practice is under the jurisdiction of ASTM Committee D07 on Wood andis the direct responsibility of Subcommittee D07.05 on Wood Assemblies.Current edition approved April 1,2013.Published April 2013.Originallyapproved in 1991.Last previous edition approved in 2007 as D5124 96(2007).DOI:10.1520/D5124-96R13.2For 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.3The boldface numbers in parentheses refer to the list of references at the end ofthis standard.Copyright ASTM International,100 Barr Harbor Drive,PO Box C700,West Conshohocken,PA 19428-2959.United States1 5.Uniformity of Generated Numbers5.1 Test of the MeanThe mean of the standard uniformdistribution is12.Generate 100 sets of 1000 random uniformnumbers and conduct the following statistical test on each set.Z 5X2 0.500.009129(1)where:Z=test statistic,X=RU/1000,the standard deviation is assumed to be112,andthe summation over 1000 values is implied.If the absolute value of Z exceeds 1.28 for more than 10%and less than 30%of the trials,the random number generatorpasses.If the random nu