内部控制系统评价定量分析的数学模型

200588:100026788(2005)0820010208,(,,130012):,,.,,.,,,.:;;;;:F230:AMathematicalModelforQuantitativeAnalysisofInternalControlEvaluationWANGLi2yong,SHIZhu2xian(BusinessSchool,QuantitativeResearchCenterofEconomics,Changchun130012,China)Abstract:Thepapersetsupwithreliabilitytheoryandknowledgeofstatisticsamathematicalmodelofinternalcontrolsystemevaluation,andcomputesimportanceforeachprocessandthewholesystem,withwhichwecanevaluatetheeffectofinternalcontrol.Alsowecangetstructuralimportanceandreliabilityimportancethroughsensitivityanalysis,withwhichwecanestimatetheinfluenceofreliabilityforeachprocessonliabilityforsystem,whichsupportstheimprovementofinternalcontrol.Finally,thepaperanalyzesthefactorofcostinevaluationofinternalcontrolandestimationofparameters,thisispropitioustoimprovingtheintegralityandaccuracyofthemodel.Keywords:internalcontrol;evaluation;reliability;sensitivityanalysis;failurerate:2004206203:(03JB790043);(05JJD790006):(1977-),,,,;(1947-),,,,.1,[16],20027[3][1].,,[1].COSO(theCommitteeofSponsoringOrganizationsoftheTreadwayCommition),,,,.,,.,,.,,,.2[7,8],:©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.1).,.2).,,R(t),R(t)=P(Tt).,t,T.F(t)=P(Tt),R(t)+F(t)=1.f(t)F(t)=t0f(t)dt.3).t,,,(t).4).,.,.5).()(),.,,,:1);2);3)(1).3,,(orderentry),(process).M.[7,8,1012]:1);2);3)();4),.5),.311,.M,7(Process),1:1,,,,118,,.©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,3,123.,Xi,:Xi=1,0,(1),(X),,(),,3:1:1(X)=1-(1-X11)(1-X12);(2)2:2(X)=X21X22;(3)3:3(X)=1-(1-X31X32)(1-X33).(4),3(,),:(X)=3k=1k(X)(5)312,,,.,,(timetofailure),:f(x)=e-x,x00,x0(6),0.,[9],KSFS,FS,.:Sn=ni=1|i|,(7)i=maxin-F(Xi),F(Xi)-i-1n,(8)F(Xi)=1-ex1€x.(9)1FSXi(hours)X(i)F(X(i))i18.111401136011369.231001269011313.0912016090120916.51615018210122111418110184701153S5=01850:X(i),Sn,,.M:1),.(Documents),(),.,Xi.,.1FS.,,,,.2)2120058©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.=5%,1132,S5=018501132,,,,.,R(t)=P(Tt)=1-FT(t).(10),T,.FT(t)T.,T,FT(t)=t0fT(t)dt=t0e-tdt=1-e-t,(11)R(t)=e-t.(12),1P,.[7,8]:,,Rs(t)=f(R1(t),R2(t),R3(t),,Rn(t)).(13)(),.,:Rs(t)=ni=1Ri(t).(14):Rs(t)=1-ni=1(1-Ri(t)).(15),,,.,,,:M,8520,2.115.,X[9],Pk=P(x=k)=ke-Pk!,k=0,1,2,.(16)E(x)=.M,=2.pi,1:1:1(p)=1-(1-p11)(1-p12);(17)2:2(p)=p21p22;(18)3:3(p)=1-(1-p31p32)(1-p33);(19)(p)=3k=1k(p),(20),[1-(p)].(21):R(t)=e-[1-(p)]t.(22)pipi=(ni-ri)Pni,(23),ni,ri.M2.318©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.2Miniripi1130010.99712NA3NA0.9502130010.9972230010.9973116010.99432NANA1.0003325210.996312,,5%.,[1-(p)]01006,,(=2):R(t)=e-01012t(24):2,.,M(40)62%.313,,,,.,(11),5Rs5Ri(i=1,2,,n).,...,,,.1),11()22(),,,1112,22.:n(i)={x|xi=1}[(1i,x)-(0i,x)].(25),(1i,x)i,;(0i,x)i,.,(1i,x)=(x1,x2,,xi-1,1,xi+1,,xn);(0i,x)=(x1,x2,,xi-1,0,xi+1,,xn).,331.,n(31)=1,n(32)=1,n(33)=3.,3,33(,32).,7,26=64,647=448,VC++610.2):Ih(i)=5Rs5Ri=5(p)5pi,(26)Ih(i)=(1i,p)-(0i,p),(27)4120058©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.0Ih(i)1.(28),.322X31=1,3(X31,X32,X33)[(131,x)-(031,x)](1,0,0)0-0=0(1,1,0)1-0=1(1,0,1)1-1=0(1,1,1)1-1=0n(31)=14ipin(i)110.99753120.95053210.997151220.997151310.99434321.00034330.99662314,,22(21,22),,.M,,,22122(2);,,,.3223.22(X)=1-(1-X21X22)(1-X23).(29),Ih(i),:h=ni=1Ih(i)pi.(30),h;pii.,.;,.,,.315,.,2(),,,[1012].,,2.1),,.,,.,,.,,,,,.:,:p;518©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.4p(e),;p(s),;p(c),;p(d),;Cc;Cs,;Ce.,R=pP(s)+p(1-P(s))P(d)+(1-p)P(e)P(c).(31)R=R-p,(32),,Ct=(1-p)Ce,(33)Ct=Cc+(1-R)Ce+[p(1-P(s))+(1-p)Pe]Cs,(34)C=Ct-Ct.(35)..5,,:,,.,,,,,piP(ei)P(si)P(ci)P(di)i.,iRiRi=piP(si)+pi(1-P(si))P(di)+(1-pi)P(ei)P(ci),(36),Rii.R=(R1)(R2)(Rn).(37),p=(p1)(p2)(pn),(38)R=R-p.,Cc,CsCe.Ct=Cc+ni=1(1-Ri)Cei+ni=1[pi(1-P(si))+(1-pi)P(ei)]Csi,(39)Ct=ni=1(1-pi)Cei.(40)C=Ct-Ct.,.,(34),6.,,,(C3,R3).6120058©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.6,:,(pp(e)p(s)p(c)p(d)):;.,(CcCsCe):Cc,,.,,;Cs;Ce,Ce.7,,Ce,0,.2)(),.IRi,Ci,:5RsCi5Ri(i=1,2,,n).(41),CiRi,Ci=Ci(R1,R2,,Rn),Ri,..4,.,,,,,.,.,,,.,,,,.,,,,,...,,.,.:[1].[M].:,2004.WangLiyong.TheAnalysisofInternalControlSystem[M].Beijing:ChineseEconomyPublishingHouse,2004.[2],,.[J].,2003,8:37-43.ZhuRongen,etal.RevelationofdevelopmentofamericaninternalcontroloverfinancialreportingassessmenttoChina[J].AccountingResearch,2003,8:37-43.(43)718©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,:1).,(1),(1);2),.T(wanti,q,b).,(2);3),,,,().,,,.:[1]PasternackB.Optimalpricingandreturnspoliciesforperishablecommodities[J].MarketingScience,1985,4(2):166-176.[2]PadmanabhanV,PngIPL.Returnspolicies:makemaneybymakinggood[J].SloanManagementReview,1995,Fall:65-72.[3]PadmanabhanV,PngIPL.Manufacturersreturnspolicyandretailcompetiton[J].MarketingScience,1997,16(1):81-94.[4]CachonGP.Supplychaincoordinationwithcontracts[R].workingpaper,UniverisityofPennsylvania,Philadelphia,PA.2002.[5]RossSM.StochasticProcesses[M].JohnWiley&Sons,1996.[6]CausenJ,HansenJ,LarsenJ.Disruptionmanagement[J].ORPMSToday,2001,28(5):40-43.[7]ThengvallB,BardJF,YuG,Balancinguserpreferencesfora