Bayesian decisin-makin f industial pductin facilities and pcessin ueddine HASSII Faculty f Sciences, Es senia Univesity Oan, ALERIA Hassini.nueddine@univ-an.dz Saim ZOUAIRI ADRS, Cité du checheu IAP, Es Senia Univesity Oan, ALERIA Abstact- Decisin n a statey f effective pedictive Reliability, Availability, Maintainability and Safety (RAMS), by the applicatin f Bayesian netwks, while ensuin a bette pesevin f the peats and installatin safety in its entiety. A Bayesian netwk is an acyclic diected aph whee ndes epesent discete andm vaiables value (ue, False), and the links influences between the vaiables cnditinal dependencies. Relatins between vaiables ae deteministic pbabilistic. In a cntext f isk manaement, the causal elatinships between diffeent events (cause-effect) that can save any installatin dysfunctin shuld be taken int accunt, inteatin the cnditinal pbabilities, based n the pinins f expets field and n the data minin. Bayesian etwks have becme a tl f uncetain easnin, mnitin tasks such as diansis, pedictin, and decisin makin. his makes Bayesian netwks a subject f eseach f atificial intellience. he pcessin f data thuh infeence allws us t analyze up-and-dwn and enich the basis f feedback thuh the acquisitin f bsevatins (evidence). In this study we pesent the cntibutin f Bayesian netwks t pductin and pcessin f natual as and an applicatin example will be iven f a cmpnent (bile) f the liquefied natual as cmplex Lz industial facility lcated in Azew, westen Aleia. Keywds: Bayesian netwks, Reliability, Availability, Maintainability, Safety, Liquefied atual as I. IRODUCIO Bayesian etwks ae intepetable and flexible aphical mdels f epesentin pbabilistic elatinships between multiple entities css the actin. At a qualitative level, the stuctue f a Bayesian etwk descibes the elatinships between these entities in the fm f cnditinal independence elatins. At a quantitative level, lcal css elatinships between the actin entities ae epesented by cnditinal pbability distibutins. Fmally, a Bayesian netwks is defined by a aph stuctue, a family f cnditinal pbability distibutins P and thei paametes, specifyin tethe a jint distibutin n a set f andm vaiables. A Bayesian netwks is a aphical mdel that epesents the cnditinal independence between a set f andm vaiables [], it is a epesentatin f the jint pbability distibutin (JPD, Jin Pbability Distibutin) []. he cnditinal independence elatins can simplify the cmputatin f cetain distibutins and the Bayesian netwks that we shall have t build will epesent the cnditinal independence elatins existin in the system cnsideed. illustate u pupses, cnside thee andm vaiables A, B and C. Accdin t pbability they, thei jint pbability is witten as the pduct f cnditinal pbabilities as fllws: 978--77-0069-9//$6.00 0 IEEE P(A,B,C)P(A)P(B/A)P(C/A,B) () If A is independent fm B, the abve equatin can be witten as fllws: P(A,B,C)P(A)P(B)P(C/A,B) () Equatin () may be epesented by a aph as shwn in Fiue. Fiue : aphical epesentatin f equatin with Bayesian etwks. Each nde cespnds t a vaiable. Each aw epesents a dependency between vaiables and is assciated with the pbability density f the sn-paent cncept []. A Bayesian netwk epesents a pbability distibutin n the jint distibutin that admits the fllwin: P ( X ) P ( X i Pa ( X i )) (3) i A C his decmpsitin f the jint distibutin can lead t pweful infeences alithms. hey make Bayesian netwk, mdelin tls and easnin, handy when situatins ae uncetain data incmplete. hey ae useful f classificatin pblems whee the inteactins between the diffeent citeia can be mdeled by cnditinal pbability elatins. When the netwk stuctue is nt iven a pii by an expet, it is pssible t be leaned fm a database. he seach f Bayesian netwk stuctue is nt simple, mainly due t the fact that space eseach is detailed supe expnentially with the numbe f vaiables. With the definitin f cnditinal independence and ppeties f cnditinal independence, we can enealize the cnstuctin f Bayesian netwks in case f andm elements vay widely. he Bayesian netwks can analyze lae amunts f data t extact useful knwlede f decisin makin, cntl pedict the behavi f a system, dianse the causes f a phenmenn, and s n. Bayesian netwks ae used in many fields: health (diansis, lcatin f enes), industial (cntl f bts autmatns), maketin (data minin, custme elatinship manaement), and bank manaement (financial analysis, decisin suppt, isk manaement). B
In the industial field f dependability, incidents and accidents ae ae events but have t manae. Risk manaement equies the develpment f statistical and pbabilistic analysis usin all elevant infmatin available t vecme the limitatins f insufficient feedback. Indeed, the Bayesian netwks ffe many advantaes ve the fequentist pespective; the "bjectivity" in fequentist statistics has been btained by inin any a pii knwlede f the measued pcess. But in the field f technly, thee always sme pi knwlede f the pcess and the eliminatin f these data is a waste f data (which can tun int financial cst). Bayesian statistics uses bth infmatin suces: pi infmatin we have abut the system and the infmatin cntained in the data. hey ae cmbined usin Bays theem. he Bayesian appach is nw peceived as vey suitable f applicatins that must manae a cetain level f uncetainty. Indeed, the pbabilities f Bayesian netwks eflect deees f tust in the tuth f ppsitins. Ou wk is a cntibutin f mdelin Bayesian netwks t pvide decisin suppt in the field f dianstics, simulatin and ptimizatin f maintenance. II. SYSEM IDEIFICAIO Any industial cmplex is cmpsed f seveal systems; it can be implemented me less fa fm uban aeas. In tansptatin facilities and pcessin f eney pducts, the dane is mnipesent and technlical hazads multiple. As an example we have based u study n the isks elated t a Liquefied natual as cmplex [3]. he cmplex L/z, is lcated in the industial zne f Azew (west Aleia), nea a lae ppulatin, the cmplex has wate-tube biles that pvide steam f divin the cmpess 9 lines liquefactin and electical eney cnsumed by the plant (ttal pwe input : 0 000 HP). F pactical easns we limit u study t a sinle cmpnent f the cmplex: a steam bile. he bile is a device used t heat wate and pduce steam when wate is heated abve atmspheic pessue [3]. It is a wate-tube bile; type FH 6'-'-9' pessuized at 77 bas a stamped, ttal tubula suface:.80 m. Stamp aue 77 ba Supe heate utlet abslute pessue 66.7 ba Output steam dy tempeatue 00 C Inlet tempeatue 0 C III. SAISICAL SUDY A. he Analysis f Vaiance: he analysis f vaiance (AOVA) aims t study the influence f ne me facts n a quantitative vaiable. he AOVA is summaized with a multiple cmpaisn f means fm diffeent samples cnsistin f diffeent mdalities f facts [, ]. We pesent a summay f the diffeent staes f an AOVA. ). Calculatin pcedue: Samples size: n, n tal samples sizes: Sum f failues: i, k k ni i tal f failues Sums: k i i Aveae Failues: X tal Vaiance: SC X X X n ( i ) i i i k Vaiance between classes (inte-up): j SC n Vaiance within each class (inta-up): SC X tal vaiance (Means Squaes tal): Inte-up vaiance (up k): Inte-up vaiance: SC k Statistical Decisin: F If Fcal Flu If Fcal Flu cal SC k < ( k, k ) ddl and 0.0 > (, ) j j k j i i j nj SC α then accept H 0 k k ddl and α 0.0 then eject H 0 he hypthesis is H0: "he system is wkin cectly ". simplify calculatins, we adpted the cdes iven in able able : pat f the list f cdes adpted f the statistical study Cmpnent Cde Anmaly Cde Cntlle A Pluin b Bune B Failue d Bile C Leakae f Heath F Hih level h Indicatin dial I Lw level l asket J eneal dysfunctin DYSF Level f wate L Explsin EXPL Pump P Pipe Valve V e..; Bile leak: Cf he table f statistics, fm yeas suvey, f failues in the secnd bile f cmplex L/z is iven in able :
able : statistics fm u suvey f the failue f the bile cmplex L/z Vaiable Cf Vf f b Vd Ad Fh Ld Bd Id Pd Jd Yea/tatin X X X3 X X X6 X7 X8 X9 X0 X X 007 6,00 7,00,00 0,00,00,00,00 3,00 7,00 3,00 3,00 0,00 006 6,00,00,00 8,00,00,00,00,00 3,00 3,00,00 8,00 00 3,00 3,00 3,00 7,00,00 0,00 0,00,00 3,00 3,00,00 3,00 003,00,00 3,00 6,00,00 0,00 0,00,00,00,00,00,00 000,00,00,00 6,00,00 0,00 0,00,00,00,00 0,00,00 999,00,00,00 6,00,00 0,00 0,00,00,00,00 0,00,00 997,00,00,00 3,00 0,00 0,00 0,00,00,00,00 0,00,00 99,00,00,00 3,00 0,00 0,00 0,00,00,00,00 0,00 0,00 993,00 0,00,00,00 0,00 0,00 0,00,00 0,00 0,00 0,00 0,00 99 0,00 0,00 0,00,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 99 0,00 0,00 0,00,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 990 0,00 0,00 0,00,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 tal bs. tal Xi 3,00,00 8,00 7,00,00 3,00,00 7,00,00 7,00 6,00 6,00 Aveae,9,83,33 0,8,0 0, 0,7,,7, 0,0,7 SC 73 SC 87 SC 36 F able 3: Results f the statistical study cal 3,8 (, ),08,6,09 k k ddl (,3,), α 0.0 F lu.86 F cal > F heefe eject H0 lu B. Pincipal Cmpnent Analysis: he pupse f pincipal cmpnent analysis is t explain the maximum vaiance with the least numbe f pincipal cmpnents [6]. ). Pincipal cmpnent: he pincipal cmpnents ae linea cmbinatins f iinal vaiables calculated with the citein f maximum vaiance. he main cmpnents ae centeed, uncelated, and deed fm the laest t the smallest vaiance. he pincipal cmpnents analysis is cmmnly used as a step in a seies f tests. F example, we can use the pincipal cmpnents t educe u data and avid the multiple c lineaity when we have t many pedictins ve the numbe f bsevatins [7, 8]. With the pincipal cmpnent analysis, we can ften discve unsuspected elatinships, allwin us t intepet the data in new ways. Fiue : Eien values accdin t the pincipal cmpnents C. Intepetatin: Accdin t fiue, the fist pincipal cmpnent has a vaiance 0.0 (equal t the laest Eien value and accunts 080 (8%) f the ttal vaiatin in the data. he secnd pincipal cmpnent (vaiance 070) is 0939 (93.9%) f the ttal data vaiatin. he fist pincipal cmpnent with a vaiance equal t the Eien values eate than epesent 0939 (93.9%) f the ttal vaiability, suestin that pincipal cmpnents explain adequately the vaiatin in the data. D. Cnstuctin f Bayesian etwk: Cnstuctin f the B es thuh thee staes: Identificatin f vaiables and thei space Definin the stuctue f the B Statuty definitin f jint vaiables pbability he vaiables ae identified thuh discussin between the expets and the mdele. 3
he secnd step is t identify linkaes between vaiables that is t say, answe the questin in what cnditins, the vaiable Xi des influence the vaiable Xj? ypically, this step is dne by queyin expets and is based n feedback, f cuse, if it exists. he last step is t lean the pbability tables f knts assciated with diffeent vaiables. We distinuish tw cases dependin n the psitin f a vaiable Xi in the Bayesian etwk: he vaiable Xi has n paents; the expets shuld expess the law f mainal pbability f X he vaiable Xi has elatives expets must expess the dependence f the vaiables in Xi paents. he tansfmatin, by expets, f texts int pbabilities is a delicate stae in the cnstuctin f the Bayesian etwk. Hweve, a thuh discussin with the expets can lead t a qualitative assessment, that is t say when smethin is clea, expets can usually expess if it is "likely," "unlikely," hihly unlikely ", etc.. In this cntext it is pssible t use a cnvesin table f qualitative assessments f pbability, as the scale f Lichtenstein and ewman [9], as descibed in Fiue 3. hee may be vaius ways t detemine the pbabilities f ndes. F example, we can deduce P (DYSF 'ue') fm the histy f the bile. But in the absence f such data, it is always pssible t appeal t values f subjective pbabilities evaluated by expets. Fiue 3: Cespndence between pbabilities and qualitative assessments IV. SRUCURE OF BAYESIA EWORK A questinnaie was iven t tw expets t help us extact sme pbabilities, and based n the scale descibed in Fiue 3; we deduce the pssible values f diffeent pbabilities. Othe pbabilities ae extacted fm the feedback [7]. Cnsidein the expnential cmplexity f Bayesian etwks, and based n the methd f pincipal cmpnent analysis, and with the help f the tw expets, we can identify the Bayesian etwk cespndin t events that may affect the ppe functinin f the bile, as descibed in Fiue, with the nmenclatue iven belw: f: pipe leak Vd: valve failue Ll: Vaiable Level f wate vey lw Id: vaiable measuement indicats failue Fh: vaiable pessue cmbustin chambe vey hih DYSF: vaiable dysfunctin f the bile EXPL: vaiable isk f explsin Vd Ll DYSF EXPL Fiue : Bayesian etwk cespndin t the peatin cnditin f the bile Fh f Id
B. Elicitatin f pbabilities: Vd f Id 0.6 0.7 0. We just elicited the pbability if the vaiable is the tue state, the pbability f the state whee the vaiable is false can be deduced by cmplementaily, f example: P (Vd 'False') - P (Vd 'ue'). F jint pbabilities, we can wite: Vd ue False L 0.6 0. f ue False Fh 0.7 0. Fh ue False L ue False ue False Dysf 0. Id ue False Dysf ue False ue False Expl 0.8 0. 0. 0 In fact, the mst imptant use f Bayesian etwks is the evisin f evey pbability f bseved events. Let: Vd X f X Ll X3 Fh X DYSF X Id X6 EXPL X7, X, X, X, X, X, X ) / Pa( X )) () 3 6 7 F u example, we have:, X, X, X, X, X, X ) ) ) / X ) / X ) () 7 i 3 6 7 3 / X3, X ) 6) 7 / X, X 6 ) We can use Bayesian ule t calculate a psteii pbability f each pssibility (we take 0 false, ue), then: 3, X 3 / X (6), X / X (7) he mdel can answe the questin "what is the likelihd that thee is a valve failue, knwin that thee is a malfunctin f the bile"? x, X x, X3, X x, X x, x, x {0,} 3 / X 0, X 0, X3, X 0, X 0, X 0, X3, X, X + 0, X, X3, X 0, X 0, X, X3, X, X + +, X 0, X3, X 0, X, X 0, X3, X, X + +, X, X3, X 0, X, X, X3, X, X (8) + + 3 / X 0,63/0,867 0,6 iven that:, X, X, X, X 0,867 X, X 3, X 3, X {0,} i i X X3 X X7 Fiue : Bayesian etwk by simplifyin chane f vaiables in Fiue V. SAISICAL IFERECE he mst inteestin task we want t slve with Bayesian etwks is pbabilistic infeence, f example, cnside the state f the vaiable "pessue f the cmbustin chambe vey hih " and the vaiable "Level f wate vey lw", and assumin we bseve that thee is a malfunctin f the bile (the evidence), then accdin t u Bayesian etwk thee is tw pssibilities: eithe thee is a stn pessue in the cmbustin chambe, thee is a apid decease in the level f the uppe balln [3,0]. If we apply equatin 3 n the Bayesian etwk f Fiue, we have: X X X6 VI. DISCUSSIO he pbability f failue f the valve knwin that thee is a malfunctin f the bile is ve 0% (6.%). his allws us t update the pi pbability f the vaiable "valve failue ", me than that it allws us t make decisins cncenin the manaement f spae pats, as well as pecautinay measues t be taken t avid accidents and incidents which will induce maj cnsequences n the cmpany and the ecsystem. In fact, the mst imptant use f Bayesian etwks is the evisin f pbabilities f bseved events. A Bayesian etwk pvides inteestin fmalism when it is necessay t measue the uncetainty f scenais that descibe chanes f states f a mdel. Unde uncetainty, the system state is unknwn and the causal chains allw pedictin unde what cnditins a scenai can happen. he Bayesian etwk attempts t extact knwlede t aive at a decisin [0]. he paticula inteest f Bayesian etwks is t simultaneusly cnside a pii knwlede f expets and data minin. he inteest als t use Bayesian etwks is the analysis f uncetain events s that they allw a qualitative desciptin f the diffeent vaiables epesentin these events (the causal aph) and quantitative desciptin f dependencies between events (cnditinal pbabilities). he pinciple f isk assessment adpted by LZ and illustated in Fiue 6 cnsides that the isk index is deived
exclusively fm the pduct f tw facts: the pbability f its ccuence and its seveity. But f a isk manae, it is nt easnable t assin a pbability fequency f ccuence f an incident withut cnsidein the events that detemine its nset, in paticula thse tiein events and thse educin the impact f the incident. Similaly, we cannt estimate the impact f the incident withut takin int accunt the facts events that influence and have a diect impact n the avity f the disaste. Fequency pbability Risk assessment Impact Fiue 6: Pinciple f isk assessment adpted by LZ Cetainly, the isk measue in the L/z actual pcedue is used t piitize incidents but it emains insinificant because it did nt infm us, in a iven situatin, n human mateial lsses caused by each incident. With Bayesian etwks, this assessment will be included in the causal appach inteatin bth: he isk itself, he events as a esult, On tie events, he settins that educe the impact f isk. With this appach t causatin, pvided thuh the cnstuctin f Bayesian etwk, assessin the isk caused by the malfunctin f the bile des nt take int accunt nly its pbability and its diect impact, but als ties (tube leak valve failue) and measuin instuments. S by explitin all the infmatin n these elements int elatins, each isk assessment will be meaninful in elatin t the envinment whee it can happen. VII. COCLUSIO he applicatin f Bayesian etwks n the bile has enabled us t make a pedictin f failue and dysfunctin f the system. Results can be quantifiable statin fm an ascendin analysis a psteii analysis fm the Bayesian etwk. hus we can thuh this analysis apply a maintenance plicy t ensue bette availability thuh manaement f spae pats, t ensue adequate secuity f the system. REFERECES [] K.R. Kch, Intductin t Bayesian Statistics, nd Ed., Spine, 007 [] H. Ziv, D. J. Richadsn, Cnstuctin Bayesian etwk Mdels f Sftwae estin and Maintenance Uncetainties, Intenatinal Cnfeence n Sftwae Maintenance, 997 [3] K. Heseltn, Bile Opeat s Handbk, he Faimnt Pess Inc, USA, 00 [] K. P. Muphy, Dynamic Bayesian etwks: Repesentatin, Infeence and Leanin, PhD hesis, Bekeley, 00 [] C. Sta, P. Shi, An Intductin t Bayesian Belief etwks and thei Applicatins t Land Opeatins, DSO Systems Science Labaty, Austalia, 00 [6] J. Peal, Causality: Mdels, Reasnin and Infeences, Cambide Univesity Pess. 000 [7] W. M. Blstad, Intductin t Bayesian Statistics. nd ed., Jhn Wiley, 007 [8] Y. Xian, Pbabilistic Reasnin in Multiaent Systems: A aphical Mdels Appach, Cambide Univesity Pess, 00 [9] S. Lichtenstein, J. R. ewman, Empiical scalin f cmmn vebal phases assciated with numeical, pbabilities, Psychnmic Science, 9 (0), 967, 63-6 [0] M. eil, M. ail, D. Maquez,. Fentn and P. Heaty, Mdellin dependable systems usin hybid Bayesian netwks, Reliability Enineein & System Safety. 93(7), 008, 933-939. 6