43 009 JOURNALOFXI ANJIAOTONG UNIVERSITY Vol.43 Jul.009 1,, 1, FG 1,"#$ 1,,HI 1 (1.JK.; /LMJK N/O,610054, ;. / 345 689:; 4,400050, ) :!"#$%&'()*+,,-./) 01 "#$%&' 01, )"#$%&'.34( 56 89:;, <=>?@ABCDE F,! ()GH F.IJ"#$%&KLM,!NO ( ),, < F, PQRSTUV"# $%& ' ST OW@A.!"#: ; <; ;$%& $% &':O346;TB114.3 :A (':053?98X(009)0?0110?05 犉狌狕狕狔犉犪狌犾狋犜狉犲犲犃犪犾狔狊犻狊犳狅狉犃狌狋狅犇狉犻狏犲犃狓犾犲犛狔狊狋犲犿 LIYanfeng 1,,DULi 1,XIAONingcong 1,HUANG Hong zhong 1,,MIAOQiang 1 (1.SchoolofMechatronicsEngineering,UniversityofElectronicScienceandTechnologyofChina,Chengdu610054,China;.KeyLaboratoryofManufactureandTestTechniquesforAutomobileParts(ChongqingUniversityofTechnology), MinistryofEducation,Chongqing400050,China) 犃犫狊狋狉犪犮狋 :Anfuzzyfaulttreeanalysisforautomobiledriveaxlesystemwasproposed.Thetheory offuzzyfaulttreewasintroducedaswelasthestructureofautomobiledriveaxle,thefaulttree oftheautomobiledriveaxlesystemwasestablished.theascendingmethodwasusedtofindmin imalcutingsets.thefuzzynumberswereemployedtodescribethefaultprobability.further more,theintervalrepresentationandcalculationstrategywerepresentedwhenbothtriangular fuzzynumberandnormalfuzzynumberwerechosentodescribethefaultprobability.anexample ofaautomobiledriveaxlesystemshowsthatthediferencebetweenfuzzyfaulttreewithtriangu larfuzzynumberandnormalfuzzynumberisnotsignificantandbaringwearisthekeyfailuree ventinthisautomobiledriveaxle. 犓犲狔狑狅狉犱狊 :faulttree;fuzzynumber;fuzzyfaulttree;driveaxle PQRS PTU&VWXY E, Z \]^_`abc &V P c, N @>. c P Z QR! ab 1], N, (&V )` (34 5 )! ab LY` Y,@ _/ P ]. &V, @ _/ &VP, 345P,3 45. :008?10?1. : (1981-),,!;"#$(%&'),,,!. (): *+,-./ 01()(50506); / 345689:; 4 <= 01() (00901);>?@AB CDE 01().
, :&VP 111 1 PQRc 1 1 )* PQR (FaultTreeAnalysis, FTA)S&VWXY P QR, S QR, &V! P), @ QR 5!. @ %&,?P,, 345 &V &. Y P,W5!,&V.? P,W5! ab 8, `ab 3?4]. 1 + @ _5! ab., 345 ab 0.0~0.03,!W" 0.0#$,%&W@_. @ _5! ab,'"!ab, " N; '( `)*_ +, -_, % Q R E. / 0 Y ` Y,4?6].? @1 -_ _ 犃, 犔 犚 _ 1 -_, E 犔 (( 犿 - 狓 )/α) 狓 犿, α>0 μ 犃 ( 狓 )= { 犚 (( 狓 - 犿 )/ β ) 狓 犿 β>0 ( 1) _ 犃 犔 犚 _, 犃 =( 犿,α, β ) 犔犚. : 犿 犃 3 ;α β 4 犃 6> ; μ 犃 ( 狓 ) 犃 +,-_.8α β 0, 犃 S _ S Z 9:_.α β ;, 犃 ; ]. 犔 犚 _ +,-_E, E `, 1` <. 1 +,-_<= 1..1 XY < _ +,- _ μ 犃 ( 狓 )= +,-_<= 烄 0 狓 < 犿 -α 1- (( 犿 - 狓 )/α) 犿 -α 狓 犿烅 () 1- (( 狓 - 犿 )/ β ) 犿 < 狓 犿 +β 烆 0 狓 > 犿 +β _( 犿 -α), 犿,( 犿 +β )] (0 1)> 犃 =( 犿 -α)+α,( 犿 +β ) -β]? _, 犃 犅 _,@A(BCD?8], 0,1],E CDE 犃 + 犅 = 犚犃 ]+ 犔犃 + 犚犃 + 犚犅 ] (3) 犃 - 犅 = 犚犃 ]- 犔犃 - 犚犃 - 犚犅 ] (4) 犃 犅 = 犚犃 ] 犔犃 犚犃犚犅 ] (5) 犃 / 犅 = 犚犃 ]/ 犔犃 / 犚犃 / 犚犅 ] (6) 1.. XY < _ +,- _ 犔 ( 狓 )=e - (( 犿 - 狓 )/α) 烄 狓 < 犿,α>0 μ 犅 ( 狓 )= 烅 1 狓 = 犿 犚 ( 狓 )=e - (( 狓 - 犿 )/ β ) 烆 狓 > 犿, β <0 () > _ 犅 +,-_ 犔 ( 狓 )=e - (( 犿 - 狓 )/α) 烄狓 犿 -α(-ln) 1/, 犿 ] 犚 ( 狓 )=e - (( 狓 - 犿 )/ β ) μ 犅 ( 狓 )= 烅狓 犿, 犿 +β ( -ln) 1/ ] 1 狓 = 犿 0 狓 < 犿 -α(-ln) 1/ 烆 狓 > 犿 +β ( -ln) 1/ >? (8) 犅 = 犿 -α(-ln) 1/, 犿 +β ( -ln) 1/ ] 1 3,-. VP, absf
11? / / 43 @K5! ab E, GH!ab` -_&W I &V!ab. P N, @ _! ab, @ K^J V K,K 5! ab _ 4,9].8@ _L<!ab,@A _>L<Q R,!ab > 犉 1 = ( 犿 1-α1)+α1,( 犿 1+β 1 )-β 1 ] 犉 = ( 犿 -α)+α,( 犿 +β )-β ] 犉 = ( 犿 -α )+α,( 犿 +β )-β ] ` K. and 犉狊 = 犉犻 = 犉 1 犉,, 犉 = (( 犿 1-α1)+α1,( 犿 1+β )-β 1 1 )(( 犿 -α)+ α,( 犿 +β )-β ),, (( 犿 -α )+α,( 犿 +β )-β )= (( 犿犻 -α 犻 )+α ), 犻 (1- ( 犿犻 +β 犻 )-β 犻 ) ] or 犉 狊 =1- (9) (1- 犉犻 )= 1,1]- (1,1]- (( 犿犻 -α 犻 )+α,( 犻犿犻 +β 犻 )+β )) 犻 = 1- (1- ( 犿犻 -α 犻 )-α 犻 ),1- (1- ( 犿犻 +β 犻 )+β 犻 ) ] ( 10) 8@ _L<!ab, ` K. ( 犻 = 1 and 犉狊 = 犉犻 = 犉 1 犉 犉 3,, 犉 = 犿犻 - 犪犻 (-ln) ) 1/, 犿犻 +β 犻 (-ln) ) 1/ or 犉 1- =1- 狊 (1- 犉犻 ) = ( ] (1- ( 犿犻 - 犪犻 (-ln) 1/ )), (11) 1- (1- ( 犿犻 +β 犻 (-ln) 1/ )) ] (1) &V P 1,/01 M &V NO, 3 < 10]. "S:15 L? P QR SQR TU V, WX Q Y@;? P QR V ZQ ;3? SQR \]V SQ,K ^_` a]v Q,. 3 b*< <=,,c, P QR`SQR. % =!, &! ( L1), 4 <. 1 @A 犜 犕 1 犕 犕 3 狓 1 狓 狓 3 狓 4 狓 5 狓 6 狓 狓 8 狓 9 狓 10 P QR P VU SQR VV * ] 3 V M VU P V V K V P V U 狓 11 狓 1 狓 13 狓 14 狓 15 狓 16 狓 1 狓 18 狓 19 狓 0 狓 1 狓 U U U U SQR SQR V V U` TU V TU V TU V 3 SQRU TU V8 TU V TU
, :&VP 113 4 &V 3,3 Y P P&V, &S Y P & V!W"Y, P(!ab ).,S"!,!, 5 &!,% 11]. @ QRS> R` R, @> R. > R R, >, @5 L<, S, S 5, > L<, >,L<, 3F@ E Z 3].,@A @ @,E 犜 = 犕 1+ 犕 + 犕 3 (13) 犕 1 = 狓 1+ 狓 + 狓 3+ + 狓 9 (14) 犕 = 狓 10+ 狓 11+ 狓 1+ 狓 13+ 狓 14 (15) 犕 3 = 狓 15+ 狓 16+ + 狓 (16) 犜 = 狓 1+ 狓 + 狓 3+ + 狓 19+ 狓 0+ 狓 1+ 狓 (1) &V { 狓 1},{ 狓 },{ 狓 3},,{ 狓 0},{ 狓 1},{ 狓 } 4,4 P, 犕 P.@A 0 1], ab 10%. AV 13], U 16%8,36%, 14%,34%. 犕!ab L <,@A>!a b >? L<QR, E 犉 10 = ((0.016-0.005)+0.005, (0.016+0.005)-0.005) (18) 犉 11 = ((0.034-0.01)+0.01, (0.034+0.01)-0.01) (19) 犉 1 = ((0.036-0.01)+0.01, (0.036+0.01)-0.01) (0) 犉 13 = ((0.016-0.005)+0.005, (0.016+0.005)-0.005) (1) 犉 14 = ((0.016-0.005)+0.005, (0.016+0.005)-0.005) () @A 犕 01< 犿 α β 狓 10 U 0.016 0.005 0.005 狓 11 U 0.034. 0.010 0.010 狓 1 U 0.036 0.010 0.010 狓 13 U 0.016 0.005 0.005 狓 14 U 0.016 0.005 0.005 犕 = 狓 10+ 狓 11+ 狓 1+ 狓 13+ 狓 14, (10)`(18)~(),4ME _,! ab >? 犉犕 = 0.066+0.035,0.16-0.0135] (3) 8=1, 8!ab, 犉犕 1=0.1091. 8=0,!ab _, 犉犕? 0.066,0.16], 0 犉犕 0.066, 0.16. 0,8@ +,-_L<,@AL _, (10)`(1), 犉犕 L 犉犕 = 0.0543+0.0585,0.165-0.054] (4) 犉犕?,8=0, 0.0543, 0.165], 犕 0 0.0543, 0.165. 3 ab KWXY,345 &V Y, WX. 5 ab 3] 犐犺 ( 犼 )= 犺 ( 狆 ) 犼 =1,,, (5) : 犺 ( 狆 )= 犺 ( 狆 1, 狆,, 狆 ) - _; 狆犼 犼 狓犼! ab. PQ, _5!ab, P ab.
114? / / 43 4, 犺 ( 狆 )=1- (1- 犉犻 )= 1,1]- (1,1]- (( 犿犻 -α 犻 )+α,( 犻犿犻 +β 犻 )+β )) 犻 = ( 1- (1- ( 犿犻 -α 犻 )-α 犻 ),1- (1- ( 犿犻 +β 犻 )+β 犻 ) ( 6) = (( 犿犼 -α 犼 )+α 犼,( 犿犼 +β 犼 )-β 犼 ) 8 犐犺 ( 犼 )= 犺 ( 狆 ) 1- ( (1- 狆犻 ) = = 犻 犼 8 (1- 狆犻 )= 犻 犼 ((1- ( 犿犻 - 犪犻 )- 犪犻 ), () (1- ( 犿犻 +β 犻 )+β 犻 )) (8) PQ, 犕 狓 9~ 狓 13 P,&V5 QR.@A() (8) (9)8 L, 0, E: 犐犺 (10)=0.841,0.998]; 犐犺 (11)=0.895,0.94]; 犐犺 (1)= 0.890, 0.9441]; 犐犺 (13)=0.841,0.998]; 犐犺 (14)= 0.841,0.998]., 犕 ab 犐犺 (1)> 犐犺 (11)> ( 犐犺 (10)= 犐犺 (13)= 犐犺 (14)) 4 c &V WXY P, PQRc 8 &V, &V, &VY P. 4 @ ` +,-_ & V WXYP, QRS4.,&Vab P, 犕.K W,U S 犕. 9:, ab 9 :,W E&V 9: b. 56 : 1],!.&VWXY N M].:./,198:166?195. ] TANAKA H,FANLT,LAIFS,etal.Fault tree analysisbyfuzzyprobabilityj].ieee Transactions onreliability,1983,3(5):453?45. 3],N.WXY_/ c M].:,006:131?164. 4] SINGERD.Afuzzysetapproachtofaulttreeandreli abilityanalysisj].fuzzysetsandsystems,1990,34 ():145?155. 5] HUANGHZ,TONGX,ZUO MJ.Posbistfaulttree analysisofcoherentsystemsj].reliabilityengineer ingandsystemsafety,004,84():141?148. 6] "#$.LM&VP QR J].LM./ ;,1994,49(1):1?. HUANG Hongzhong.A newfuzzysetapproachto mechanicalsystemfaulttreeanalysisj].mechanical ScienceandTechnology,1994,49(1):1?. ] DUBOISD,PRADEH.fuzzysetsandsystems:theo ryandapplication M].New York,USA:Academic Press,1980:0?4. 8],. _/ 8 @ M]. : /,1996:8 30. 9]!",# $.P8 @ J]. *.//,001,1(6):81?8. ZHAOYanping,GONG Wenwei.Fuzzyfaulttreea nalysisanditsapplication J].ChinaSafetyScience Journal,001,1(6):81?8. 10]%+&. M].:L M ', 006:11?156. 11],,`. P M]. :( ',1990:194?0. 1]) ^* W EB/OL].008?09?01].htp: business.sohu.com/auto/detail/no0004.html. 13]U `+,QREB/OL].008?09?01]. htp: www.sjlbearing.com/gongsi xinwen/jishu zil iao/0804 48.html. (- Z)