ඣ ০ ࿐ Б 2001୍4ᄅSHUILI XUEBAOֻ4௹໓ᅣщݼ:0559 9350(2001)04 0001 06ڄགٳ༅֥ߧ-ෛࠏڄགੱٚم࣮胡国华1,夏 军2(1 ଲഽٓն࿐ݓ࿐ჽ,ଲӉ೬ 410081;2 ݱն࿐ඣሧჷაފੀ۽ӱ༢,Кݱ 430072)ᅋ ေ:Ч໓ࠎႿۀੱંބߧ༢ંٚم,קၬਔߧۀੱaߧۀੱٳ҃aߧۀੱૡ؇aߧ௹ຬࠣߧٚҵ֩ࠎЧۀ,ᆌؓ༢֥ෛࠏ҂ಒקྟބߧ҂ಒקྟ,ࡹ৫ਔڄགٳ༅֥ߧ-ෛࠏڄགੱٚم.ᄝھٚمᇏ,ቔᆀࡼڄགੱ֥҂ಒקྟ݂ၹႿ༢֥ߧ҂ಒקྟ,ࡼ༢ྟିݦඔэਈ֥ٳ҃ԩӮߧۀੱٳ҃,ѩႨߧ-ෛࠏڄགੱটਈ߄༢ാི֥ڄགྟ.ቋު,ࡼߧ-ෛࠏڄགੱሇߐӮ၂Ϯ֥ෛࠏڄགੱ,ࣉطႨڿࣉ၂ࢨؽइمࣉྛ࠹ෘ.ቔູෘ২໓ᇏ۳ԛਔھٚمႋႨႿࡁਲ਼ࡾқ༗؍Ⴕࠏಙڄགੱ֥ܙෘ.ܱՍ:ڄགٳ༅;ߧ҂ಒקྟ;ߧۀੱ;ߧۀੱٳ҃;ߧ-ෛࠏڄགੱᇏٳোݼ:X820 4 ໓ངѓ്:Aᄝඣ໓ඣߌ༢ڄགٳ༅ᇏ,൮༵ླေॉ੮֥൞༢֥҂ಒקྟ໙.ี༢֥҂ಒק,ྟ࠻ჷႿ༢֥ଽᄝ҂ಒק,ྟ္ӁളႿଆ֥҂ಒקྟaҕඔ֥҂ಒקྟބࠆ౼֥֞ྐ༏֥҂ቀބ҂ࣚಒྟ[1].ܱႿڄགა҂ಒקྟ໙ี֥࣮,Ⴍః൞ᄝڄགٳ༅ᇏႵܱ҂ಒקྟؓڄག႕ཙ֥ਈ߄໙ี֥࣮,ၘ൳֞ݓଽຓ࿐ᆀ֥ܱᇿބᇗ൪.Tang֩ದ[2]ᄝॖौྟაڄགٳ༅ᇏࡼ҂ಒקྟٳູႮႿܥႵ֥эၳྟջট֥҂ಒקྟބაܙ࠹༂ҵႵܱ֥҂ಒק.ྟૅݓඣሧჷჴ߶[3]ᄝ۳ڄགა҂ಒקྟקၬൈ۳ԛਔਆᆀᆭࡗ֥ҵၳ,ಪູڄག֥౦ঃॖקၬູమᄝ֥ൻԛ֥ෛࠏหᆘ,ط҂ಒקྟᄵ൞টჷႿཌྷؓಌك֥ಪ[4].്Jonᄝԩگᄖ༢֥ڄགࡎᇏࡼ҂ಒקྟٳູෛࠏ҂ಒקྟބᇶܴ҂ಒק,ྟѩಪູభᆀ֥Ӂള൞ჷႿ༢ିၛྸ؟҂ྙൔ෮іགྷ,ၹطࡼఃູ݂༢֥หྟ,طުᆀ֥ӁളᄵჷႿؓ༢ಪ്֥ྐ༏֥ಌك,෮ၛ݂ఃູؓ༢ࣉྛٳ༅֥ห[5.ྟK,6]ennethaH[7]attis֩ದᄝႨႿದಕࠇള֥ߌڄགٳ༅ᇏ,఼טਔჷႿྐ༏ಌك֥҂ಒקྟބ۱ุᆭࡗܥႵ֥э߄.ྟߛԌڞ֩[8]ᄝᄙݝڄགࡎᇏॉ੮ਔڄག࠹ଆ֥ଆ҂ಒקྟ.ቔᆀᄵิԛࡼჷႿؓ༢ಪᆩ֥ಌك෮Ӂള֥ᇶܴ҂ಒקྟ݂ࢲູߧ҂ಒקྟ[9].ᄝڄགٳ༅ᇏ,ؓႿ༢ЧദܥႵ֥ෛࠏ҂ಒקྟ֥ଆ,၂ϮႨ࠹࿐ഈ֥ۀੱ,္ࠧڄགੱটіᆘ.Ֆᇶܴ҂ಒקྟ֥োљބଢభؓఃіᆘ෮Ⴈ֥ඔ࿐ٚمਆٚ૫ሸކট,ुڄགੱ֥ᇶܴ҂ಒקྟॖٳљႨۀੱٚمaଆࠢંٚمၛࠣߧ༢ંٚمࡆၛਈ߄.ۀੱٚم൞ࠎႿڄགੱ֥ᇶܴ҂ಒקྟՖ࠹ၩၬഈ֥ଖ၂ۀੱٳ҃ྙൔ֥ࡌק.ଆࠢંٚم൞Ⴈଆۀੱіղڄགੱ֥ॖିྟۀ.طߧ༢ٚمᄵ൞ᄝෛࠏڄགੱٚمࠎԤഈ,఼טؓڄགੱ֥ߧ҂ಒקྟ֥૭ඍაਈ߄.Ч໓ᆌؓ༢ڄགٳ༅ᇏթᄝ֥ڄགੱ֥ߧ҂ಒקྟ,ᄝקၬߧۀੱaߧۀੱٳ҃aߧۀੱૡ؇aߧ௹ຬࠣߧٚҵ֩ࠎԤഈ,ิԛਔߧ-ෛࠏڄགੱ֥ۀ,ࡹ৫ਔఃіղྙൔა࠹ෘٚم.൬۠ರ௹:2000 03 27ቔᆀࡥࢺ:ޱݓ(1965-),ଳ,ଲྍโದ,Ѱൖ,ڬ࢝൱,ᇶေՖ൙ඣ໓ඣߌࠣڄག࣮. 1
1 ߧۀੱٳ֥҃ࠎЧۀקၬ1(ߧۀੱ[10])ӫ႘ഝPG: P([0,1])ູߧۀੱ,PG൞( , )ഈ֥оࡗࠢᆴҩ؇;1!PG( ).( , ,PG)ӫູߧۀੱॢࡗ.קၬ2(ߧۀੱٳ)҃קၬᄝဢЧॢࡗ ഈ,౼ᆴႿൌඔთ֥ݦඔ ,ӫູ൞ဢЧॢࡗ ഈ֥ෛࠏэਈ,ѩӫFG(x)=PG( ∀x),(-#<x<#)(1)൞ෛࠏэਈ ֥ߧۀੱٳ҃ݦඔ,ࡥӫߧۀੱٳ҃.PGູൌඔთഈෛࠏэਈ ֥ߧۀੱܙ࠹.קၬ3(ߧۀੱૡ؇) ൞ෛࠏэਈ,FG(x)൞֥ߧۀੱٳ,҃ೂݔթᄝݦඔfG(x),ؓႿၩ֥x,ႵxFG(x)=∃fG(y)dy(2)-#ᄵӫfG(x)ູFG(x)֥ߧۀੱૡ؇ݦඔ,ࡥӫߧۀੱૡ؇.ູ۷ᆰֹܴіགྷߧۀੱٳ֥҃%ߧ&ห,ྟൔ(2)ॖіൕೂ༯ൔ֥ྙൔxxFG(x)=[FG*(x),F*G(x)]=∃FG*(y)dy,∃*fG(y)dy(3)-#-# קၬ4(ߧ௹ຬ)( , ,PG)ᇏ, ൞၂۱ෛࠏэਈ,ఃߧۀੱٳ҃ݦඔູFG(x),֒#∃xdFG(x)<#(4)-#ൈ,ӫ ֥ඔ࿐௹ຬ(ࡥӫߧ௹ຬ)թᄝ,##EG( )=EG*( ),E*G( )=∃xdF*G(x),xdFG*(x)(5)-#∃-# קၬ5(ߧٚҵ)( , ,PG)ᇏ, ൞၂۱ෛࠏэਈ,ఃߧۀੱٳ҃ݦඔູFG(x),ӫ ֥ߧٚҵթᄝ,#DG( )=[DG*( ),D*G( )]=∃2( -EG( ))dFG(x)-###2=∃( -E*G( 2))dFG*(x),∃( -EG*( ))dF*G(x)(6)-#-#2 ߧ-ෛࠏڄགੱ֥ۀࠣіղྙൔ༢֥ڄག൞ᆷ༢҂ିᆳྛఃჰקۿି֥ۀੱࠇᆷ༢ຓটڵހնႿ༢Чദቅॆࠇӵᄛି৯֥ۀ.ੱऌՎ,ॖٳၛ༯3ᇕ౦ঃؓߧ-ෛࠏڄགੱࣉྛקၬބіղ.(1)ᄝ༢ڄགੱႮ၂۱༢ቅॆა၂۱༢ຓটڵހܒӮ౦ঃ༯,֒ॉ੮༢ቅॆࠇӵᄛି৯ູ၂۱Ֆଖ၂ׅࣜٳ֥҃ෛࠏэਈ(ႨXіൕ),ط༢ຓটڵހູ၂۱Ֆଖ၂ߧۀੱٳ֥҃ෛࠏэਈ(ႨYGіൕ)ൈ,ᄵ༢ാི֥ڄགੱקၬູRG=PG(X<YG)(7)ൔᇏ,PGູߧۀ,ੱၹطRGӫູߧ-ෛࠏڄགੱ.ି֤X֥ۀੱૡ؇ݦඔfX(x)ބYG֥ߧۀੱٳ҃ݦඔ[FY(y),F*Y(y)]ࠇߧۀੱૡ؇ݦඔ*[fY(y),fY(y)]ൈ,ൔ(7)ॖڿཿູG*GG*G##RG=∃(1-FY(x))fX(x)dx,0G*∃(1-F*Y(x))f0GX(x)dx(8) ാིڄགੱRG֥ᇉ֥ਈ؇ॖႨ1ᇏ౷ཌfX(x)ٳљაfY(y)a*fGY(y)֥ᇗן҆ٳіൕ.*G(2)ॉҳଖ၂༢֥ڄགੱ,༢ቅॆބ༢ຓটڵހູٳљՖଖ၂ߧۀੱٳ҃FG(x)ა 2
FG(y)֥ෛࠏэਈXGaYG,ᄵ༢ാི֥ڄགੱॖіൕູRG=PG(XG<YG)(9)ି֤XGaYG֥ߧۀੱٳ҃[FX(x),F*X(x)]a[Fy),F*G*GY(GY(y)]ࠇߧۀੱૡ؇ݦඔ*G**[fX(x),fX(x)]a[fY(y),fY(y)]ൈ,ᄵೂ2෮ൕ,౷ཌfX(x)a*fX(x)ٳљაfY(y)aG*GG*GG*GG**fY(y)֥ᇗן҆ٳॖіൕാིڄགੱRG֥ᇉ֥ਈ؇.G1 ༢ڵހ֥ߧۀੱૡ؇ა༢ቅॆ֥ۀੱૡ؇ൕၩ2 ༢ڵހა༢ቅॆ֥ߧۀੱૡ؇ݦඔൕၩ ֒ॉ੮RGູ૭ඍാིڄགੱ֥ቋཬაቋնᆴࡗൈ,ൔ(9)ॖ۷ऎֹุіղ:ູRG=[RG*,R*G]=[PG*,P*G]##=min∃(1-FY(x))fX(x)dx,0G*G*∃(1-F*Y(x))fX(x)dx,0GG*##∃**(1-FY(x))f(1-F*GX(x)dx,*G∃Y(x))f(x)dx,00GXG##(10)max∃(1-FY(x))f0GX(x)dx,(1-F*Y(x))f(x)dx,*G*∃0GXG*##∃**(1-FY(x))fX(x)dx,1-F*Y(x))fX(x)dxG∃(0G*0GG##*=∃(1-F*Y(x))fX(x)dx,0G*G∃(1-FY(x))fGX(x)dx0G* (3)၂Ϯ၂۱༢ടࠣྸ؟ၹࠇሑэਈ,ႨཟਈXG=(XG1,XG2,∋,XGn)іൕ.ၹՎ,༢ྟିݦඔ൞ᆃུၹ֥ݦඔg(XG),༢ാི֥ڄགੱקၬູg(XG)<0֥ۀੱ.ႮႿ༢֥ૄ၂ሑэਈXGiՖॖႨߧۀੱٳ҃ݦඔ[FXG*(x),F*X(x)]ࠇߧۀੱૡ؇ݦiGiඔ*[fXG*(x),fX(x)]іᆘ֥ଖ၂ߧۀੱٳ,҃ၹՎॖোරֹ֤ԛೂ༯ۀ:iGi༢֥ਢࢸྟିေॖקၬູg(XG)=0,൞༢֥%ࠞཋሑ&.ၹՎ,ࣼႵ[g(XG)>0]=%νಆሑ&ࠣ[g(XG)<0]=%ാིሑ& ۴ऌࠫޅ࿐ഈ,ࠞཋሑٚӱg(XG)=0,൞၂۱nົ֥і૫,ӫᆭູ%ാི૫&.ཁಖ,ႮႿXG֥ߧห,ྟթᄝn2۱ാི૫.ാི૫֞ჰ֥ׄቋཬएႨཟਈd=(d1,d2,∋,dn2)іൕ,ᄵႮႿാི૫໊֥ᇂॖႨാི૫֞ჰ֥ׄቋཬएটіൕ,طཌྷؓႿჰ֥ׄാི૫໊֥ᇂႻथק༢֥ڄགྟ,ၹՎ,෮Ⴕቋཬए֥ቋཬᆴmin(d)აቋնᆴmax(d)ॖ࣍රֹႨႿڄགྟ֥ਈ؇,ࠧ[min(d),max(d)].ၹՎ,ೂэਈXG1,XG2,∋,XGn֥৳ކۀੱૡ؇ݦඔfູX,∋,X(XG1,∋,XGn),ാིሑ֥ۀੱູG1Gn 3
RG=∃∋∋,∋,X(XG1,∋,XGng1Gn(XG)<0∃fX)dXG1,∋,dXGnGࡥཿӮRG=∃∋fX(XG)dX(11)g(X)<0GGG3 ߧ-ෛࠏڄགੱ֥࠹ෘٚم࠹ෘڄགੱ֥ٚمႵᇗགྷ௹एمaᆰࢤࠒٳمaหवઌمaनᆴ၂ࢨؽइم(MVFOSM)aڿࣉ၂ࢨؽइم(AFOSM)ၛࠣؽࢨم.ॖ܂ൌ࠽Ⴈ֥၂Ϯ൞หवઌمބAFOSMم.ఃᇏႨหवઌمࣉྛڄགੱ࠹ෘႮႿᄝܙ࠹ഈࢠگᄖބݻൈ,෮ၛ၂ϮᄝႵఃࢠࡥֆ֥ٚمൈ,࣐ਈх૧ႨՎم.AFOSMم҂ᆰࢤྟିݦඔ֥ٳ҃ݦඔ,ط༵Ⴎ۲ၹ֥၂aؽࢨइྟିݦඔ֥၂aؽࢨइ,ಖުࡗࢤܙෘڄག.ੱႮႿߧ-ෛࠏڄགੱॖၛٳࢳູn2۱ෛࠏڄགੱ֥ྙൔটіղ,ၹՎ,ॖၛࡼߧ-ෛࠏڄགੱሇߐӮ၂Ϯ֥ෛࠏڄག,ੱࣉطႨڿࣉ၂ࢨؽइمࣉྛ࠹ෘ.ჰᄵഈ,RGႋՖཟਈR=(R1,R2,∋n,R2)ᇏ๙ݖ౼ቋཬᆴaቋնᆴ֤,֞ࠧ*RG=[R*,R]=[min(R),max(R)](12) ᄝൌ࠽ᄎႨᇏ,ႮႿ๙ݖႵܱྐ༏ࠣٳ༅,ಸၞ֤ᆩ۲ၹXGiэ߄ؓRGնཬ֥႕ཙ.ၹՎ,ऌՎିܔܒᄯ۲ၹ၂aؽࢨइ౼ᆴ֥ਆቆቆކ,ѩՖఃᇏ၂ቆ(࠺ູXG*)ᇏॖ֤ቋཬڄགੱᆴ(࠺ູR*),Ֆਸ਼၂ቆ(XG*)ᇏॖ֤ቋնڄགੱᆴ(࠺ູR*),ࠧR*=P{g(XG*)<0}(13)R*=P{g(XG*)<0}(14) ഈඍR*აR*ᄵॖႨڿࣉ၂ࢨؽइمٳљ.֤4 ෘ ২ؓႿފ؍ඣߌ༢ಙڵހ൞ڎӑԛߌӵ൳ಸਈ֥໙,ีႮႿં൞ߌಸਈ,ߎ൞ඣߌڵހݻႨਈေ൳ඣุߌหᆘބಙหᆘ֥႕ཙ.ᄝ၂Ϯ౦ঃ༯,ູ॥ᇅ؎૫ඣᇉղѓط֤֥ఏ؎૫ླ॥ᇅ֥ಙ୩؇,൞۴ऌหᆘҕඔ֥۲नᆴ֤.֥൙ൌഈ,ᆃུหᆘҕඔႻၹ൳֞ྸ؟҂ಒקྟၹ֥ཁᇷ႕ཙطऎႵ၂קٓຶ֥ෛࠏэྟ.ၹՎ,֒หᆘᆴொनᆴၛ,ުᄵႵॖିؓ෮॥ᇅ؎૫֥ඣᇉӁളߊ,ࠧފ؍ඣߌۿିթᄝߊڄག.і1ູࡁਲ਼ࡾқ༗؍ඣߌหᆘᆴ[11],หᆘᆴթᄝሢ၂קٓຶ֥ෛࠏэ,ѯᆴӯᆞٳ҃.ࣉ၂҄ॉ੮ඣߌҕඔႮႿಌكԉቀ֥ܴҩྐ༏طթᄝߧ҂ಒק,ྟᄵႨShaferٚم[12]ॖࡼᆞٳ֥҃नᆴԩӮೂі2෮ൕ֥ߧࡗྙൔ.і1 ࡁਲ਼ࡾқ༗؍ඣߌҕඔหᆘᆴߌҕඔЎބသ (mg L)K1 d-1K2 d-1L0 (mg L)T d౼ᆴٓຶ11 25~11 790 075~0 100 80~1 2070~1101 95~2 45नᆴ11 570 0841 106892 292नٚҵ0 1980 0500 13013 1250 189 4
і2 ࡁਲ਼ࡾқ༗؍ඣߌҕඔ֥ഈa༯௹ຬᆴߌҕඔCSG (mg L)K1G (1 d)K2G (1 d)L0G (mg L)TG d!*11 6250 0981 14292 6782 345!*11 5150 0701 07085 3222 239ႨЧ໓ิԛ֥ߧ-ෛࠏڄགੱٚمؓࡁਲ਼ࡾқ༗؍ඣߌႵࠏಙࣉྛڄགٳ༅,൮༵ॖၛࡹ৫ھފ؍ඣߌᇉਈሑݦඔູ(ၛႵࠏಙሸކᆷѓಷࢳသቔॉҳ):g(XG)=g(CG,K1G,K2G,L0G,TG)K1GL0G-K5)=1GT(1G(CSG-Ct)-Ke2Gൔᇏ:CGູඣߌಸਈ(DO,mg L);CSGູඣุЎބಷࢳသ୩؇(mg L);Ctູ॥ᇅ؎૫॥ᇅଢѓ(mg L)(Ч໓ၛಷࢳသ୩؇4mg Lቔູ॥ᇅѓሙ);K1Gູݻသ༢ඔ(1 d);K2Gູگသ༢ඔ(1 d);L0GູԚ؎૫BOD5୩؇ᆴ(mg L);TGູඣੀՖԚ؎૫֞॥ᇅ؎૫෮ླൈࡗ(d).֒g(XG)>0ൈ,ඣߌᇉਈղ֞ေ.g(XG)<0,ᄵඣᇉӑݖ॥ᇅଢѓ,ӑѓߧ-ෛࠏڄགੱູRG=[R*,R*]=P{g(XG)<0}(16) Ֆൔ(15)ၞᆩ,ඣߌҕඔK1GaL0Gაඣᇉӑѓߧ-ෛࠏڄགੱRGӯᆞཌྷܱ,طCSGaK2GࠣTGᄵაRGӯڵཌྷ.ܱၹՎ,ႨAFOSMمॖၛՖ(C*SG,K1G*,K**2G,L0G*,TG)ܒӮ֥XG*ᇏ֤ڄགੱ֥ቋཬᆴR*ູ*0 1194,Ֆ(CSG*,K*1G,K2G*,L0G,TG*)ܒӮ֥X*Gᇏॖ֤ڄགੱ֥ቋնᆴR*ູ0 3745.ቋ,ު֤֞ࡁਲ਼ࡾқ༗؍॥ᇅ؎૫ಷࢳသ୩؇ࢆ֞4mg Lၛ༯ൈ֥ߧ-ෛࠏڄགੱRGູ[0 1194,0 3745],ఃࢠݺֹุགྷބ؇ਈਔڄགੱ֥҂ಒק.ྟ5 ࢲ ეЧ໓ᆌؓඣ໓ඣߌ༢թᄝ֥ෛࠏ҂ಒקྟބߧ҂ಒקྟ,఼טᄝࣉྛ༢ڄགٳ༅ൈ,ႋ֒ሸކॉ੮ᆃਆো҂ಒקྟؓڄགੱ֥႕ཙ.ູՎ,ᄝႄೆߧۀੱaߧۀੱٳ҃aߧۀੱૡ؇aߧ௹ຬࠣߧٚҵ֩ࠎԤഈ,ิԛਔߧ-ෛࠏڄགੱۀ,ࡹ৫ਔཌྷႋ֥іղྙൔა࠹ෘٚم,۳ԛਔෘ২.Ч໓ิԛ֥ڄགٳ༅ٚمࡼڄགੱ֥҂ಒקྟ݂ࢲູߧ,ྟࡼ༢ྟିݦඔ֥эਈԩӮߧۀੱٳ҃,ቋުႨߧ-ෛࠏڄགੱটਈ߄༢ാི֥ڄགྟ,ᆃॖၛࢠݺֹุགྷބ؇ਈڄགੱ֥҂ಒקྟ.ൈ,ߧ-ෛࠏڄགੱॖၛሇߐӮ၂Ϯڄག,ੱطႨᇭೂAFOSM֩ٚمࣉྛ࠹ෘ,္х૧ਔႨหवઌٚمଆ෮ջট֥گᄖაݻൈ.Ч࣮ࣇ൞ڄགٳ༅҂ಒקྟਈ߄ٚم֥ྍฐ෬.ႮႿ༢ڄགٳ༅ടࠣ֞նਈ֥ҕඔა҂ಒק,ྟཁಖؓૌᇯ၂ࣉྛਈ߄൞ཌྷ֒گᄖ֥໙ี.ၹՎ,ೂޅࡼЧ໓ิԛ֥ٚمࣉ၂҄ປބຉᅚഉླቓࣉ၂࣮҄.ҕ ॉ ໓ ང:[1] AngAH S,.(Vol.(,translatedbySunFang chuietal.)[M].Beijing:Metallurgicalindustrypress,-460(InChinese).[2] TangWH,YucemenMS,AngAH basedshorttermdesignofsoilslopes[J].CanadianGeotechnicalJ.,1976,13:201-215.[3] (levelC)[J]..,1979a,44(102):30194-30258. 5
[4] [J].RiskAnalysis,1994,14(4):483-511.[5] KennethBogenT,[J].RiskAnalysis,1987,7(4):427-436.[6] [J].1995,5(3):411-419.[7] DaleHattis,[J].RiskAnalysis,1994,14(5):713-730.[8] HuangChongfu,[J].JournalofNaturalDisasters,1994,3(1):1-8(InChinese).[9] ladenriver:[C].Wuhan:WuhanUniversityofHydraulicandElectricEngineering,1998(InChinese).[10] HuangWeijun,[A].In:[M].Chengdu:ChengduScience&TechnologyUniversitypress,1994(InChinese).[11] suddenenvironmentalrisk[J].ChinaEnvironmentalScience,1990,10(3):218-223(InChinese).[12] BillCaselton, Shafertheoryanddecisionmaking[A].In:,un certaintyanddecision making[C].Instituteforriskresearch, stochasticriskmethodforriskanalysisHUG1uo hua,XIA2Jun(1 HunanNormalUniversity,Changsha 410081,China;2 WuhanUniversity,Wuhan 430072,China)Abstract:Theconceptsofgreyprobability,greyprobabilitydistribution,greyprobabilitydensity, ,theuncertaintyofsystemriskisattributedtogreyuncertaintyofsystem,thevariablesofsystemperformancefunctionaretreatedwithgreyprobabilitydistributionsandthesystemhazardisquantifiedwithgrey stochasticriskcanbetransformedintoordinarystochasticriskandcomputedusingadvancedfirst ordersecond :riskanalysis;greyuncertainty;greyprobability;greyprobabilitydistribution;grey sto chasticrisk 6
