Reliability Analysis of Automatic Transmission Based on T-S Fuzzy Fault Tree

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1 Ope Access Library Joural 208, Volue 5, e4659 ISSN Olie: ISSN Prit: Reliability Aalysis of Autoatic Trasissio Based o T-S zzy Fault Tree Chaokai Lei *, Haitao Ji, Nig Hu Shaghai Uiversity of Egieerig Sciece, Shaghai, Chia How to cite this paper: Lei, C.K., Ji, H.T. ad Hu, N. (208) Reliability Aalysis of Autoatic Trasissio Based o T-S zzy Fault Tree. Ope Access Library Joural, 5: e Received: May 5, 208 Accepted: Jue, 208 Published: Jue 4, 208 Copyright 208 by authors ad Ope Access Library Ic. This work is licesed uder the Creative Coos Attributio Iteratioal Licese (CC BY 4.0). Ope Access Abstract I order to solve the lack of autoatic trasissio slippage fault data, the ucertaity of the lik betwee the source of the fault ad the degree of failure, the lack of applicability of the traditioal Boolea logic gate, the T-S odel ad fuzzy theory ad the revisio of the cofidece ide are proposed. The epert survey ethod was cobied ad the aalysis ethod was itroduced ito the fault tree. The T-S odel is itroduced ito the typical fault aalysis, usig the fuzzy possibility to describe the failure probability of the copoet. The coectio betwee evets is described with the T-S gate. The fault degree of the copoet is described by the fuzzy uber, the odel siulatio is used to siulate the fault aalysis, ad the cotributio or iportace of the top evet to the failure of the copoet is obtaied. The fuzzy possibility ad fault diagosis of the top evet are calculated. Without kowig the fault echais accurately, we ca fid the weak lik of the syste, ad provide referece for autoatic trasissio slip fault diagosis ad aiteace. Subect Areas Autoata Keywords Autoatic Trasissio, T-S Model, zzy Fault Tree, Fault Diagosis, Reliability Cofidece Ide. Itroductio Hydraulic autoatic trasissio is widely used i cars []. The autoatic trasissio is a cople syste that cobies echaical, electroic ad hydraulic copoets. Due to the cople structure ad workig priciple of the DOI: /oalib Ju. 4, 208 Ope Access Library Joural

2 hydraulic autoatic trasissio, the difficulty of fault detectio is icreased. The fault diagosis carried out by a o-board diagostic syste i a oder electroically cotrolled autoatic trasissio is geerally liited to the udget of the electrical syste fault. There is o clear test result for hydraulic faults that play a key role. Because of the copleity of the structure ad copositio of its ow hydraulic syste, the probability of failure is correspodigly higher. Ad hydraulic syste faults also have diversity, ucertaity ad abiguity [2]. Fault Tree Aalysis (FTA) is a ethod for aalyzig syste reliability. It has bee recogized as oe of the siplest, ost effective, ad ost proisig tools for reliability aalysis, predictio, ad desig of cople systes [3]. Fault tree aalysis is a effective tool for aalyzig the reliability ad safety of large-scale cople systes. Traditioal fault tree aalysis ethods based o probability theory ad Boolea algebra have bee widely used i fault diagosis of hydraulic systes. However, the traditioal fault tree aalysis ethod has the followig deficiecies: a) The failure probability of the botto evet ust be kow accurately; b) The coectio betwee the evets eeds to be accurately kow; c) The severity of the failure caot be described. The above three shortages ake it difficult to establish ad quatitatively aalyze the fault tree, thus liitig the applicatio of fault tree aalysis i hydraulic syste fault diagosis. Taaka et al. [4] itroduced the fuzzy theory ito the fault tree aalysis for the first tie i 983, thus solvig the abiguity ad ucertaity of the failure rate of the basic evet i the fault tree (usig fuzzy ultiplicatio istead of the traditioal logic operatio, but still i ad or gates logically). Yao Chegyu et al. [5] [6] put forward the T-S fuzzy fault tree odel ad applied the to equipet diagosis ad cotrol equipet diagosis, itegrated avigatio syste ad so o, ad achieved good results. The fuzzy theory has the advatages of dealig with fuzzy ad iaccurate iforatio, cobiig the fault tree aalysis ethod with the fuzzy theory. It ot oly draws the advatages of the fault tree aalysis, but also takes full accout of the characteristics of the fault occurrece probability, the coectio of the evets ad the fuzziess of the fault degree, ad it is carried out. A effective ethod for fault diagosis of hydraulic syste is ade, so the slip fault of autoatic trasissio is aalyzed. I this paper, a fuzzy fault tree ethod based o T-S fuzzy fault tree is proposed for the diagosis ad aalysis of autoatic trasissio. 2. T-S fuzzy Fault Tree A ew T-S fuzzy fault tree is costructed by usig T-S gates istead of traditioal logic AND gates. I the ew fault tree, the failure probability ad the degree of failure of each basic evet are replaced by fuzzy ubers. Figure shows the T-S fuzzy gate fault tree odel. Where, 2, 3, 4, 5 is basic evets. Gate a ad gate b are logic gate. DOI: /oalib Ope Access Library Joural

3 2.. zzy Nuber Figure. zzy fault tree. Cosiderig that traditioal failure trees have less historical failure data for basic evets i practical applicatios, fuzzy logic is itroduced. Usig fuzzy ubers to represet the failure probability of each basic evet, the establishet of a fault tree is o loger depedet o a large uber of failure data. I the T-S fuzzy fault tree, the degree of each fault is usually represeted by the fuzzy uber i the iterval [0, ]. The trapezoidal ebership fuctio µ ( ), show i Figure 2, is used as the ebership fuctio of fuzzy ubers. µ ( ) = ( a b a b ) () 0,,,, l l r r The ebership fuctio epressio of Figure 2 as follows: al bl ( 0 al bl) 0 al bl < 0 al bl µ ( ) = 0 al < 0 + ar + ar + br + a < + a + b br ar + b r < 0 r 0 r r a r is sup- where 0 is the ceter of a fuzzy uber support set, a l ad portig radius, b l ad b r is area of fuzzy. Accordig to Figure 2, we ca see, whe al ar 0 fuctio is a triagle ebership fuctio; whe bl br 0 defiite uber. (2) = =, trapezoid ebership = = fuzzy uber as a DOI: /oalib Ope Access Library Joural

4 Figure 2. Mebership fuctio of fuzzy uber T-S zzy Gate Fault Tree Algorith The T-S fuzzy odel is coposed of a series of IF-THEN fuzzy rules. It is a oliear odel, which is used to describe the associatio betwee evets ad for a T-S fuzzy gate. The rules of the odel are epressed as follows [7]: If i ( i =, 2,, ) is basic evet variable, y is superior variable, Fl ( =, 2,, ) is fuzzy set, ad the rules is l( l =, 2,, ) ; if is F l, 2 is F l 2,, is F l, the y is y l. If the ebership fuctio of the µ, the the output of T-S odel as follow: fuzzy set is F ( ) l µ F ( ) µ F ( ) l (3) y = y l = = So basic evets ad superior evets T-S fuzzy gates are show i Figure 3. If the fuzzy uber: { 2 k 2 } { 2 k } { 2 k,,,, 2, 2,, 2,,,,, } ad {, 2,, k y y y y } idicates the degree of failure of the botto evet ad the superior evet respectively. Their rage of values as follow: 2 2 k 0 < < < 2 k < 2 < < 2 2 k 0 < < < 2 ky 0 y < y < < y The T-S fuzzy gate algorith is described as follows: i i2 The rules is l( l =, 2,, ) ; if is, 2 is 2,, is i, the l 2 l 2 the probability, y is y, is P ( y ), the probability, y is y, is P ( y ),, k the probability, y is y y l k, is P ( y y ). Where i =, 2,, k, i2 =, 2,, k2,, i =, 2,, k. The total uber of rules is, we ca get the equatio of : i= i l (4) = k (5) Assuig that the degree of failure of a basic evet is ( ) ( ) ( ), 2 2 P i P i,, P i. The the possibility of the rules l( l =, 2,, ) eecutio as follows: i i2 i ( ) ( ) ( ) P = P P P (6) l 0 2 Therefore, the abiguity of the superior icidet is: DOI: /oalib Ope Access Library Joural

5 Figure 3. T-S logic gate. l l ( ) = 0 ( ) P y PP y 2 l l 2 P( y) = PP 0 ( y) (7) ky l l ky P( y ) = PP 0 ( y ) If the i ( i =, 2,, ) fault level is = {, 2,, }. Accordig to the T-S fuzzy odel, the fuzzy possibility of the fault level of the upper evet ca be calculated as follows: where l ( ) = βl ( ) ( ) P y P y P y P y P y P y 2 l 2 ( ) = βl ( ) ( ) ky l ky ( ) = βl ( ) ( ) β l ( ) = µ ( ) ( ) µ (9) = i= = Additioally, µ ( ) is the degree of ebership of the fuzzy set correspodig to the fault status of the copoet i the l rule. Therefore, takig Figure as a eaple, if the fuzzy possibility of the degree of failure of the basic evet is kow, accordig to the T-S gate rule, the fuzzy possibility of the failure degree of the upper evet ca be estiated usig forulas ad forulas, respectively T-S zzy Iportace The T-S fuzzy iportace degree is the cotributio of the failure of the iiu cut set of a copoet or syste to the occurrece probability of the top (8) DOI: /oalib Ope Access Library Joural

6 evet. It is a fuctio of the tie. The reliability paraeters of the copoet ad the syste structure are widely used i practice [8]. The fuzzy subset of the fault status ( ) failure probability of the kow copoet =, 2,, is P, It s ebership fuctio is µ P ; The fuzzy subset of the failure probability of the top evet T fault status T q is P ( P i, P i 2,, P i ), where 2 ( i =, 2,, k, i 2 =, 2,, k 2,, i =, 2,, k ), It s ebership fuctio is µ P. Defiitio: The fuzzy subset of the failure probability of copoet with failure status ( =, 2,, ) is P. It s T-S fuzzy iportace for the syste top evet T is obtaied by followig equatio: ( ) = (, = ) (, = 0 ) IT q E PTq P PTq P µ d 0 P µ 0 P, Tq,0 µ d 0 P µ 0 P, Tq,0 d = where PT ( q, P = ) failure of its top evet T. PT ( q, P = 0 ) idicate fuzzy subset, whe P is, The probability of idicate fuzzy subset, whe P is 0, The probability of failure of its top evet T. Cobiig Equatios (6) ad (7) with 0 ad istead of P, the two itegral ters represet the ceter-of-gravity values of the fuzzy subset of the probability of failure of the syste top evet T failure degree T whe P is 0 ad, respectively. q d (0) Defiitio: The followig forula is epressed T-S fuzzy iportace of basic evets: k ( ) ( ) I = I k () Tq = Tq where, k idicate the uber of o-zero fault coditios for the part. If the fault status fuzzy uber is represeted by (0, 0.5, ), the I is k is 2. T ( ) q the ifluece of each fault state o the average fault state of the syste durig the chage of copoet fault status fro 0 to. 3. T-S zzy Fault Tree Aalysis Eaple 3.. Hydraulic Autoatic Trasissio T-S zzy Fault Tree Establish T-S fuzzy fault tree [9] [0] as show i Figure 4,, 2,, 6 is basic evets, T is top evet, y, y2, y 3 is iterediate evets. Accordig to the actual fault coditio, suppose that there are three kids of states i the degree of failure of the basic fault ad iterediate evet of the fuzzy fault tree of the autoatic trasissio T-S (Table ): o fault, ior fault, ad coplete fault, which are (0, 0.5, ), respectively. The paraeter is al = ar = 0.2, bl = br = 0.3. T-S fuzzy gate rule algorith ca be obtaied fro epert eperiece ad historical data i Tables 2-4. I Tables 2-4, each lie represets a fuzzy rule, for eaple, the secod lie i Table 2 represets the rule. The degree of failure is 0, 2 is 0, 3 is 0, 4 is 0, 5 is 0.5, the the possibility of y, whe its degree of fault is (0, 0.5, ), is (0.3, 0.4, 0.3). DOI: /oalib Ope Access Library Joural

7 Figure 4. T-S fuzzy fault tree of hydraulic autoatic trasissio. Table. Naes of each evets i the T-S fuzzy fault tree of a autoatic trasissio. Evet code Evets ae Evet code Evet ae T Autoatic trasissio slip 7 Quality deterioratio of hydraulic oil y Mechaical wear 8 Oil pipe depressio y 2 Oil proble 9 Type of oil is wrog y 3 Oil leakig 0 Iproper adustet of throttle positio sesor Frictio disc wear of clutch Seal rig daage of clutch pisto 2 Frictio disc wear of brake 2 Daage of pisto seal rig of brake 3 Wear ad bur of brake belt 3 Daage of pisto seal rig of shock absorber 4 Oil pup wear 4 Filter blockage 5 Uidirectioal clutch skiddig 5 Mai oil road leak 6 Aboral hydraulic oil surface 6 Mai pressure valve proble Table 2. T-S fuzzy gate G2. Rule y DOI: /oalib Ope Access Library Joural

8 Table 3. T-S fuzzy gate G3. Rule y Table 4. T-S fuzzy gate G. Rule y y 2 y 3 T Accordig to Tables 2-4, the fuzzy possibility of a superior evet fault ca be calculated by the fuzzy possibility or the degree of failure of the basic evets, ad the the fuzzy possibility of the top evet ca be estiated Epert Ivestigatio Method Cobied with Cofidece Ide Correctio I practical egieerig appraisal applicatios, weighted average epert surveys are ofte used to obtai iaccurate or icoplete failure data [] [2]. To study the applicatio of T-S fuzzy fault tree i trasissio slip diagosis. This article DOI: /oalib Ope Access Library Joural

9 iteds to obtai the fuzzy failure probability of the basic evet through the epert survey ethod based o the revisio of epert cofidece ide. The data of the eperts selectio, ratig ad eperts udgets are all take fro the literature []. Eperts are selected accordig to acadeic qualificatios, legth of service ad other coditios. The eperts ivolved i the ivestigatio coe fro first-lie aageet, aiteace ad desig persoel. The copositio of the eperts is show i Table 5. Calculatio forula such as forula () ( v ) 4 r r r r r ω = ν () = Ordiary epert survey ethods geerally assue that all eperts have full cofidece i their ow udgets, but they are ot practical whe applied. I order to iprove the accuracy of the fuzzy failure probability, this article itroduces the cofidece ide ethod of the literature [] to further correct the data obtaied by the coo epert survey ethod. Table 6 is the survey table of failure rates of basic evets i the fault tree of the autoatic trasissio shift failure. The probability rage is based o icoplete statistical data ad is cobied with persoal work eperiece. Fill i the cofidece ide ad select the cofidece ide for yourself. It is 0. ~. Based o the epert survey ethod odified by the cofidece ide ad usig the weighted average idea, the overall evaluatio process for the probability of a certai basic evet by all eperts is as follows. ) If the uber of eperts participatig i the survey is. There are N basic evets. Accordig to Table 5, the calculatio weight of the ith epert is w i, ad he udges the probability of occurrece of the th basic evet as L, R, ad the cofidece ide of udgig hiself as K ( 0< K ). The cofidece ide is, idicatig that the epert has full cofidece i his udget ad high credibility; ad the cofidece ide is 0., idicatig that the credibility of the epert s udget result is very low. 2) The iterval of the probability iterval of the epert udget is obtaied by = R L. 3) If = 2, the the cotributio of the ith epert to the fial cuulative result of the th basic evet occurrece probability is: ( ),, ( ) P = w i k k + (2) 4) The probability of the occurrece of the th basic evet, the fial result of the cofidece ide correctio ad the epert weight accuulatio, such as the follow Equatio (3) p = p (3) i= p is a fuzzy uber of the isosceles triagular. Accordig to the statistical aalysis of the autoatic trasissio slippage fault data ad the epert survey with the cofidece ide correctio, the reliability data of the copoets are show i Table 6. DOI: /oalib Ope Access Library Joural

10 Table 5. Copositio of eperts. Rule r Nuber r Coefficiet v r Weight w r Table 6. zzy failure rate of each basic evet of autoatic trasissio. Evet code Evet ae Autoatic trasissio slip zzy failure rate / 0 7 Evet code (2.20, 2.75, 3.09) 9 Evet ae Quality deterioratio of hydraulic oil zzy failure rate / 0 7 (.3,.43,.74) 2 Mechaical wear (2.0, 2.33, 3.5) 0 Oil pipe depressio (0.25, 0.56, 0.74) 3 Oil proble (.80, 2.20, 2.84) Type of oil is wrog (.80, 2.24, 3.02) 4 Oil leakig (0.92,.6,.88) Frictio disc wear of clutch Frictio disc wear of brake Wear ad bur of brake belt (.58, 2.8, 2.78) 3 (4.40, 5.62, 6.84) 4 (.90, 2.24, 3.58) 5 8 Oil pup wear (0.80,.20,.60) 6 Iproper adustet of throttle positio sesor Seal rig daage of clutch pisto Daage of pisto seal rig of brake Daage of pisto seal rig of shock absorber Mai pressure valve proble (., 2.27, 3.) (2.25, 2.53, 3.) (2.58, 2.93, 3.2) (.62, 2.23, 2.82) (0.5, 0.83,.2) 3.3. zzy Possibility of Higher Level Evets Calculated by zzy Probability of Basic Evet Failures Accordig to Table 6, the failure rate of these copoets is the failure rate whe the failure state is 0.5, ad the failure rate assuig that the failure level is 0.5 is equal to the failure rate whe the failure degree is. Cobiig Equatios (6) ad (7) with MATLAB, the likelihood of a iterediate evet blurrig is as follows: 8 l l ( 2 = 0.5) = 0 ( 2 = 0.5) P y pp y pp 0 ( y2 0.5) pp 0 ( y2 0.5) p0 p ( y2 0.5) 7 ( 4.2, 5.66, 6.32) 0 = = + = + + = = 8 l l ( 2 = ) = 0 ( 2 = ) P y pp y pp 0 ( y2 ) pp 0 ( y2 ) p0 p ( y2 ) 7 ( 3.67,5.23,6.38) 0 = = + = + + = = Siilarly, the fuzzy possibility of differet states of other iterediate evets ca be calculated. We ca kow i Table 7. I the sae way, the likelihood of the top evet beig calculated is as follows: DOI: /oalib Ope Access Library Joural

11 Table 7. zzy possibility of iterediate evet. Iterediate evet Probability of fuzzy fault 0.5/ 0 7 / 0 7 y (5.20, 9.95, 2.708) (0.056, 9.452, 26.32) y 2 (.629, 2.4, 3.225) (2.94, 4.488, 5.236) y 3 (4.592, 8.564,.425) (8.699, 5.32, 9.548) 7 ( = 0.5) = ( 8.3, , ) 0 PT 7 ( = ) = ( , , ) 0 PT The calculatio results show that the probability of failure of autoatic trasissio slippig is the sae order of agitude as the probability of failure of each copoet. The possibility of failure of the T-S fuzzy fault treetop evet is far greater tha the possibility of failure of each copoet. This result is i accordace with the actual situatio, which verifies the accuracy ad feasibility of the T-S fuzzy fault uber i the autoatic trasissio fault aalysis process. Take the gravity value of each evet as its failure probability, ad accordig to forula (0), obtai the T-S fuzzy iportace degree whe y is 0.5 whe copoet is 0.5, as follows: I ( ) = E P ( 0.5, P = ) P ( 0.5, P = 0 ) = Siilarly, the T-S fuzzy sigificace of the fault states of the copoets of 0.5 ad ca be obtaied as show i Table 8. Accordig to Equatio (), cobied with the T-S fuzzy iportace of the fault states 0.5 ad, the T-S fuzzy sigificace at 0.5 is obtaied. ( ) 0.5 ( ) ( ) I0.5 6 = I I = 0.4 Siilarly, the T-S fuzzy iportace of each copoet is obtaied, as show i Table 9. Give the fuzzy subset of the failure probability of the copoet s fault state, it ca be kow fro Table 9 that whe the syste is i a half-fault state (0.5), the iportace of is greatest, which is the weak lik i the process of trasissio slip. The we ca get the troubleshootig sequece: 6, ( 2, 5, 4 ), 2 ( 5 ), 9, 8, 3,, 3, 7, 4 ( 0, 6 ). Whe the autoatic trasissio is i a coplete fault state (), the iportace of each copoet is fro large to sall: 2, 4,, 6, 3, 4, 5, 3 ( 0 ), 8, 6,, 9, 2, 7, 5, It ca be see that whe the syste copletely fails, the iportace of the basic evet 2, 4,, 6 is large, the ipact o the top evet is also the greatest. Other copoets also have a certai ifluece, but the degree of ifluece is sall. I suary, the aalysis result of the slip fault of the autoatic trasissio based o the T-S fuzzy fault tree is basically i accordace with the situatio o DOI: /oalib Ope Access Library Joural

12 Table 8. T-S fuzzy iportace of each copoet failure state. (a) The fuzzy iportace of the fault state T-S 0.5 I I (b) The fuzzy iportace of the fault state T-S 0.5 I I (c) The fuzzy iportace of the fault state T-S 0.5 I I Table 9. Iportace of T-S abiguity for each basic evet. T-S fuzzy iportace I I T-S fuzzy iportace I I site. The level of oil level, clutch frictio, filter pluggig, etc. are all weak poits. If there is slippage fault, it should be a key poit for troubleshootig durig troubleshootig, so as to reduce syste failure rate ad iprove oral reliability operatio. 4. Coclusios This paper cobies fuzzy logic ad T-S odels with traditioal fault trees ad proposes the applicatio of T-S fuzzy fault trees to autoatic trasissio fault diagosis. The ethod effectively overcoes the probles of difficulty i obtaiig the failure probability. The ucertaity of the likage betwee evets, ad the iability describes the degree of syste failure i the traditioal fault tree aalysis. The quatitative descriptio is ore cosistet with the egieerig applicatio. Copared with the traditioal fault tree odel assesset ethod, this ethod ca effectively eert the advatages of fuzzy logic iferece, thus solvig DOI: /oalib Ope Access Library Joural

13 the proble of ucertaity of the syste failure echais, reducig the difficulty of the costructio; cobiig the epert s cofidece i their ow evaluatio ad correctig the paraeters ad the survey data to triagular fuzzy ubers ca greatly iprove the accuracy of the aalysis usig oly coo fault trees ad closer to the real situatio. The T-S fuzzy fault tree aalysis eaple of autoatic trasissio slip failure, ad the epert eperiece ad historical data with epert survey ethod of cofidece ide correctio are cobied, to calculate the fuzzy failure rate of the top evet ad to get the fuzzy iportace of the basic evet. Fially the ipact of the weak liks of syste reliability is foud, which ca provide referece for overhaul ad fault diagosis of autoatic trasissios. Refereces [] Zhao, D.X. ad Qi, R. (205) The Curret Status ad Developet Tred of Chia s Autoobile Trasissio. Highways & Autootive Applicatios,, [2] Che, Z. ad Peg, J. (204) Fault Failure ctio Aalysis Method for Hydraulic Cotrol Syste of Electroically Cotrolled Autoatic Trasissio. Desig ad Research, 4, [3] Che, Y.Y. (2005) Fault Tree Aalysis of FTA. Beig Jiaotog Uiversity, Beig. [4] Taaka, H., Fa, L.T., Lai, F.S., et al. (983) Fault-Tree Aalysis by zzy Probability. IEEE Trasactios o Reliability, 32, [5] Fa, B.Q., Wag, G.H., Wei, X.P., et al. (202) Research o Fault Diagosis of Equipet Measureet ad Cotrol Equipet Based o T-S zzy Fault Tree. Sciece, Techology ad Egieerig, 2, [6] Yao, C.Y., Lv, J., Che, D.N., et al. (205) Cove Model T-S Fault Tree ad Iportace Aalysis Methods. Joural of Mechaical Egieerig, 5, (I Chiese) [7] Sog, H., Zhag, H.Y. ad Wag, X.R. (2005) zzy Fault Tree Aalysis Based o T-S Model. Cotrol ad Decisio, No. 8, (I Chiese) [8] Yao, C.Y., Zhag, Y.Y., Wag, X.F., et al. (20) Iportace Aalysis Method of zzy Fault Tree Based o T-S Model. Chia Mechaical Egieerig, 22, (I Chiese) [9] Cui, T.T. (205) Fault Diagosis of Hydraulic Autoatic Trasissio Based o zzy Fault Tree. Wireless Iteret Techology, 6,. [0] Hu, N. (204) Troubleshootig Method of Electrical Hydraulic Syste through the Applicatio of Coputer. Chiese Hydraulics & Peuatics, 204, [] Zheg, J.J., Li, C.F. ad Zhao, D.A. (20) Risk Assesset of Shield Tuel Costructio Cost Usig zzy Fault Tree. Chiese Joural of Geotechical Egieerig, 33, [2] Qi, J., Hu, X. ad Gao, X. (204) Quatitative Risk Aalysis of Subsea Pipelie ad Riser: A Eperts Assesset Approach Usig zzy Fault Tree. Iteratioal Joural of Reliability ad Safety, 8, DOI: /oalib Ope Access Library Joural