Open Journal of Modellng and Smulaon, 204, 2, 44-53 Publshed Onlne Ocober 204 n ScRes. hp://www.scrp.org/journal/ojms hp://dx.do.org/0.4236/ojms.204.2406 Paral Avalably and RGBI Mehods o Improve Sysem Performance n Dfferen Inerval of me: he Drll Facly Sysem Case Sudy Eduardo Calxo, Glson Bro de Lma Alves Glson 2, Adelc Menezes de Olvera 3 UFRJ-COPPE, Ro de Janero, Brazl 2 UFF-LAEC, Ro de Janero, Brazl 3 Perobras S.A., Ro Grande do Nore, Brazl Emal: eduardo.calxo@homal.com Receved 29 July 204; revsed 30 Augus 204; acceped 25 Sepember 204 Copyrgh 204 by auhors and Scenfc Research Publshng Inc. hs work s lcensed under he Creave Commons Arbuon Inernaonal Lcense (CC BY). hp://creavecommons.org/lcenses/by/4.0/ Absrac he man objecve of hs sudy s o propose a mehodology o defne he operaonal avalably for a sysem n dfferen nerval of me based on Mone Carlo smulaon. In addon, s also an objecve o denfy crcal equpmen n such nerval of me and defne when carryng ou nspecons o deec and preven falures. Nowadays, many sofware packages whch apply Mone Carlo smulaon based on relably dagram block do no show he operaonal avalably defned by nerval of me. In mos of cases, here s no resul ha shows how sysem performs n specfc nerval of me. Dependng on suaon, s mporan o defne he operaonal avalably by dfferen nerval of me n order o follow up sysem performance along me. In order o solve such problem, s proposed he paral avalably mehodology based on sysem age. Indeed, such mehod regards equpmen age based n dfferen perod of me ha wll resuls n Paral Avalably. ha means, as nsance, n case of wo years of smulaon here wll be he cumulave operaonal avalably and paral operaonal avalably resuls for frs and second years for example. herefore, s also mporan o defne he nspecon me n each nerval of me (year) n order o deec possble equpmen falure and defne prevenve manenance o avod such falures ha wll be performed by RGBI mehod. In order o show such mehodologes, wll be carred ou a drll facly case sudy whch s requred o defne operaonal avalably of he sysem on he frs and second years as well as nspecon me. Keywords Paral Operaonal Avalably, Sysem Age, Probably Densy Funcon (PDF), How o ce hs paper: Calxo, E., de Lma Alves Glson, G.B. and de Olvera, A.M. (204) Paral Avalably and RGBI Mehods o Improve Sysem Performance n Dfferen Inerval of me: he Drll Facly Sysem Case Sudy. Open Journal of Modellng and Smulaon, 2, 44-53. hp://dx.do.org/0.4236/ojms.204.2406
E. Calxo e al. Relably Growh Based Inspecon (RGBI). Inroducon Nowadays, dfferen ypes of sofware appled on RAM analyss are based on Mone Carlo Smulaon mehod and he fnal resul s he cumulave operaonal avalably. Indeed, such resul s cumulave along smulaon me; n anoher words, akes no accoun all sysem downme along smulaon perod of me o calculae he operaonal avalably []. Whenever a hgh performance sysem s n conex, such resul wll be accomplshed as expeced, because he defned perod of smulaon s appropraed o operaonal avalably arge. By he oher way round, s no possble o verfy he operaonal avalably n a specfc nerval of me. Acually, for sysem wh hgh operaonal avalably performance, he paral resul s no a problem because when such sysem acheves operaonal avalably arge n cumulave perod of me, hey mosly acheve avalably arge n specfc nerval of mes as well. Even hough, s necessary n some cases o fnd ou he operaonal avalably n dfferen nervals of me o follow up sysem performance or even esablsh operaonal avalably arges for dfferen nerval of me. In some cases, n order o plan resources lke componen sock, servces order as well as plan prevenve manenance, s very mporan o know whch operaonal avalably sysem wll acheve n specfc nerval of me. herefore, such paral operaonal avalably resul s mporan o fnd ou whch equpmen wll fal n such nerval of me. Indeed, ha s usual for sysem ha acheves low operaonal avalably when consderng long cumulave perod of me. herefore, n hese cases, operaonal avalably s defned for he shor perod of me. Neverheless, mos of sofware does no ake no accoun he operaonal avalably n dfferen nerval of me because he smulaon resul shows only he cumulave operaonal avalably along years. Once we face such suaon, a possble soluon s o defne a fxed perod of me lke one year as nsance and smulae he sysem lfe cycle year by year. I means ha all smulaons wll be performed for one calendar year bu wll consder he sysem age. By hs way, on second year for example he sysem s one year older and he smulaon wll descrbe wha happen durng he second year. In addon, more han defne he paral operaonal avalably, s also mporan o defne he crcal equpmen, he bes nspecon and prevenve manenance me n order o avod falures. Unforunaely, n many cases he operaonal avalably s defned for a specfc nerval of me by calculang he average of cumulave operaonal avalably per me. Indeed, ha wll no solve he problem because s also mporan o verfy whch equpmen fals n dfferen nerval of me n order o preven such falures. he proposal paper wll presen he paral avalably and RGBI mehodologes applyng a drll facles case sudy n order o mprove such sysem performance. 2. Paral Avalably he Mone Carlos smulaon n RAM analyss has he man objecve o defne sysem operaonal avalably and crcal equpmens n order o suppor decsons by mplemenng mprovemens acons when s necessary [2]. Such operaonal avalably resul s cumulave along smulaon me and o have paral operaonal avalably values wo approaches are possble. Dscounng me on PDF (Probably Densy Funcon) parameers. Accounng age on smulaon me. On frs case, o regards change n PDF parameers s necessary o dscoun me on poson parameer n order o no modfy PDF characersc so f nended for example o ancpae n equpmen age n one year, such value s dscouned n poson parameer and f necessary o pospone one year s add such value n poson parameer. ha s easy o realze f been consderng a PDF wh Gaussan shape lke normal, lognormal, gumbel, logsc and loglogsc. Fgure shows normal PDF wh poson parameer dscouned n one year n order o smulae he second year of such equpmen lfe and fnd ou operaonal avalably on hs nerval of me. he blue PDF n Fgure s orgnal PDF and he black one s he me dscouned PDF. he equpmen Operaonal avalably s 00% n one year because here s no falure (normal PDF: µ = 2, σ = 0.). In addon, o fnd ou he equpmen operaonal avalably on second operaonal year s dscouned one year n poson parameer (µ = 2 µ = ). hus, he Mone Carlo smulaon s carred ou regard one year of smulaon me. 45
E. Calxo e al. RelaSof Webull++ 7 - www.relasof.com 4,000 3,200 Probably Densy Funcon Pdf Folo3\Daa Normal-2P RRX SRMMED FM F=00/S=0 Pdf Lne f() 2,400 Folo3\Daa 2 Normal-2P RRX SRMMED FM F=00/S=0 Pdf Lne,600 0,800 Eduardo Calxo Perobras 26/8/200 08:55:3 0,000 0,200 0,760,320,880 2,440 3,000 me, () Folo3\Daa : µ=2,0077, σ=0,077, ρ=0,9944 Folo3\Daa 2: µ=,000, σ=0,020, ρ=0,996 Fgure. PDF parameers dscouned me. Acually, when poson parameer s dscouned n one year, wheher furher nerval of me s smulaed he falure wll occur earler han expeced. hereby, such approach s correc only when he poson parameer dscouned by specfc me s hgher or equal han perod of smulaon me. In case of ohers PDF wh no Gaussan characerscs such lmaon s smlar. Wheher such approach s appled o a general PDF lke Welbul 3P for example, s necessary o dscoun me o locaon parameer. As nsance, f he locaon parameer value s fve years and s nended o know abou he second year, so once he locaon parameer s dscouned n one year he nex sep s perform smulaon for one year. Indeed, he lmaon n such approach s ha such smulaon resuls works only for he frs falure. he followng falure wll occur earler han smulaon resul because he real PDF parameer s dscouned. In Webul 3P case for example, once he locaon parameer (γ) s dscouned, he second falure wll earler han expeced. For example f s nended o smulae ffh year and he locaon parameer value s fve, once he locaon parameers (γ) s dscouned he frs falure occur n one year of smulaon as expeced bu he second one would also happen prevously because he poson parameer was dscouned. hereby, under such crcumsance, he locaon or poson parameer mus be updaed consanly o reproduce he paral avalably for he waned nerval of me. In addon, f beng consdered ha afer repars, equpmens s as good as new, such earler falure can no happen. In case of as bad as old, s accepable ha falure occurs n shor perod of me afer repar bu ha s no expeced [3]. Fgure 2 shows an example of Mone Carlo smulaon o descrbe draw work falure behavor on second operaonal year regards one year dscouned n PDF locaon parameer (γ). he draw work falure s represened by he Webull 3P PDF whch parameers are = 2.0, η = 0.29, γ = 0.86. Regardng ha he locaon parameer (γ = 0.86) s dscouned n one year n order o smulae he second year, he new PDF parameers wll be ( = 2.0, η = 0.29, γ = 0). herefore, when locaon parameer s dscouned and such value s no less han smulaon perod of me, he second falure wll no ake no accoun on he perod of me of 0.86 years as shown Fgure 2. hus he MBF s 3625 when would be 7533 h (γ = 0.86). In order o avod such problem, he second possbly s o ake no accoun sysem age o fnd ou paral operaonal avalably n dfferen nerval of me ha regards only downmes occurred n such nerval of me. 46
E. Calxo e al. Fgure 2. Drawwork (second year smulaed). he operaonal avalably mos be defned as oal me whch sysem s avalable o operae (upme) by oal nomnal me as shows equaon below. n = ( ) = n D where: = real me when sysem s avalable; = nomnal me when sysem mus be avalable. As menoned before, mosly, he Mone Carlo smulaon shows cumulave operaonal avalably bu o know paral operaonal avalably n dfferen nerval of mes s necessary o defne such perods of mes along oal perod of me and hen accoun downmes n each perod of me. Fgure 3 shows an example of me lne (0, n) dvded n hree nerval of me. he equaon whch represens Operaonal avalably along (0, n) s: = n L n k n n = = n L = n k = ( ) = + + + = n L n k n n D = = n L = n k = Indeed, regardng hree dfferen nerval of mes, he operaonal avalably along each perod of me wll be: Perod I Perod II n L = ( 0 ) = n L D n L = 47
E. Calxo e al. Perod III Fgure 3. me lne (0, n). ( ) D n L n k = ( ) D n k n = n k = n L n k = n L n = n k n where: = real me when sysem s avalable; = nomnal me when sysem mus be avalable. I s possble o consders as many nerval me as necessary depends on requremens and avalable daa. In hs specfc case, when Mone Carlo smulaon s performed, s necessary o defne sar age for sysem and regards one year as smulaon perod of me. hus, age for frs year s zero, for second s one and for hrd s wo years. Once sysem age s consdered n Mone Carlos smulaon, he smulaon resuls shows always wha happen afer aged me ha s he nerval of me ha mus be defned he operaonal avalably and crcal equpmen. Despe a correc approach, whenever s requred o know abou one specfc perod of me wll be necessary o age all equpmen represened on RBD (relably block dagram) or FA (faul ree analyss). Such approach would be ncluded n sofware packages o show he resuls n dfferen nerval of me auomacally. 3. Relably Growh Based Inspecon (RGBI) Indeed, s no always possble o overhaul he crcal equpmen defned by Mone Carlo smulaon by paral Avalably mehodology. In hs case, s necessary o defne nspecon me o check equpmen condon n order o defne prevenve manenance me n order o avod equpmen falures. In hs secon s proposed he relably growh mehod (Crow AMSAA) o predc he nspecon me for dfferen nerval of me. he relably growh approach s appled o produc developmen and suppor decsons o acheve relably arges afer mprovemen have been mplemened [4]. Varous mahemacal equaons models may be appled n relably growh analyss depend on how he es s carred ou as well as he ype of daa. Such mehods are: = n k 48
E. Calxo e al. Duanne; Crow Ansaa; Crow Exended; Lloyd Lpow; Gomperz; Logsc; Crow Exended; and Gomperz. he relably growh based nspecon (RGBI) mehod wll regards Crown AMSAA analyss mehodology o esmae fuure nspecons ha s also appled o assess reparable sysems (equpmen). hus, regardng complee daa whch nclude repars, he Non-Homogeneous Posson Process s appled [5], as shown n Equaon () below: Equaon () ( ) = ρ ( ) E N d he expeced cumulave number of falure can be descrbed also by Equaon (2) below: Equaon (2) E N o deermne he nspecon me, s necessary o use he cumulave number of falure funcon and, based on equpmen falure daa, o defne he followng cumulave falure number. Based on hs number, s necessary o reduce from such me he requred me o carry ou nspecon ask regardng he P-F nerval (poenal and funconal falure me). In fac, applyng such mehodology for drllng desel moor s possble o predc when he nex falure me wll occur and f reducng hs me by me requred o perform nspecon we have he sar nspecon me. he cumulave number of falures s en. herefore, applyng he expeced cumulave number of falures and usng he Crown AMSAA funcon parameers (λ =.5 and =.02) n Equaon (), he nex falure wll expeced o occur n 8.32 years as shown n Equaon (3). Equaon (3) E N 0 = = λ.02 λ E N = λ 0 = = 8.32.5 he nex em wll apply a case sudy concernng he boh mehods n order o show he advanages o defne sysem performance n dfferen nerval of me as well as nspecon me o keep such performance. 4. Drll Facles Case Sudy 4.. Paral Avalably Case Sudy In order o clarfy paral avalably approach, such mehod wll be appled n drll facly case sudy whch sysem avalably arge s 90% annually. In addon, s necessary o defne sock polcy and manenance polcy for wo years based n RAM analyss resuls. Indeed, he drll facly do no acheve hgh performance for over one year and some equpmen falures happen on frs year and ohers on second year. herefore, wll be carred ou wo smulaon regardng equpmens age n order o defne avalably and crcal equpmens for frs and second year. Before modelng RDB (relably dagram block) was performng equpmen lfeme daa analyss and one of he mos crcal equpmen s he compressor from ar compressor subsysem. able shows an example of compressor falure PDF. 49
E. Calxo e al. able. Falure daa. Equpmen Componen Dsrbuon me o falure (years) Parameers Compressor Webull η γ Ar compressor 0.67.69 0.74 Elecrc moor Exponecal MF 0.08 Afer carry ou he lfeme daa analyss, he RBD was buld up regardng he sx subsysem whch drll facly sysem comprses as shows Fgure 4. Performng smulaon for he frs year, sysem acheve 85.44% of operaonal avalably n one year and s expeced 23 falures. he operaonal avalably rank s an mporan ndex o suppor mprovemen decson [6]. Indeed, once equpmen n each subsysem are mosly n seres. By hs way, compressor s he avalably bole neck because have he lowes avalably of drll facly sysem. he avalably rank s shown n able 2. Once he compressor s he mos crcal equpmens, as recommendaon was proposed o analyze he ohers compressor relably and compare among han whch s he hghes relably n order o defne hgher relably requremen for compressors supplers companes. Indeed s expeced o compressor acheve a leas 00% of relably n wo year. Unforunaely, n drll facly sysem he compressor acheves 88.58% of avalably n one year. Consequenly, some mprovemen s requred n compressor. herefore, he followng acon s o defne beer relably requremens for desel pump or nsall oher sand by pump o acheve 00% of avalably n a leas one year as requred. Regardng hs addonal recommendaon, he drll facly sysem wll acheve 9.87% n one year, beng a lle hgher han he nal operaonal avalably arge ha was 90% n one year. Applyng he paral avalably mehods o analyze he second year, he drll facly sysem avalably n second year s 68.84% f no mprovemen n compressor be carred ou. Even hough, regardng hgh compressor relably, ha means mplemen mprovemen acon on he frs year, he drll facly sysem wll acheve 8.95% on second year. Acually, on second year oher equpmens ake place as more crcal n erms of mpac n sysem operaonal avalably. able 3 shows avalably rank on second operaonal year. Despe mprovemen n compressor, some oher mprovemen n ransmsson Box s requred o enable he sysem acheve operaonal avalably arge (90% n one year). herefore, relably requremens mus be defned for such equpmen. Indeed, wear ou s usual n such equpmen and even f s possble o have 00% of relably for such equpmen, s advsable o perform nspecons and prevenve manenance whenever s possble n order o keep ransmsson box avalable as long as possble on second year. hereby, f ransmsson box acheve 00% of operaonal avalably on second year, drll facly sysem wll acheve 9.25 % of operaonal avalably on second year. 4.2. Relably Growh Based Inspecon (RGBI) Case Sudy In order o defne he crcal equpmen nspecon me, s necessary o use he cumulave number of falure funcon and, based on equpmen falure daa, o defne he followng cumulave falure number. Based on hs number, s necessary o reduce from such me he requred me o carry ou nspecon ask regardng he P-F nerval (poenal and funconal falure me). In fac, applyng such mehodology for drllng desel moor s possble o predc when he nex falure me wll occur and f reducng hs me by me requred o perform nspecon we have he sar nspecon me. he cumulave number of falures s en. herefore, applyng he expeced cumulave number of falures and usng he Crown AMSAA funcon parameers (λ =.5 and =.02) n Equaon (), he nex falure wll expeced o occur n 8.32 years as shown n Equaon () as descrbed above. Equaon () 50
E. Calxo e al. Fgure 4. Drll facly subsysems. able 2. Avalably rank (year I). Paral operaonal avalably (frs year) Crown block 96.93% Desel pump 96.59% Compressor 95.38% able 3. Avalably rank (year II). Paral operaonal avalably (second year) Mud pump 96.8% ransmsson box 86.86% Compressor 85.48% E N = λ E N = λ.02 0 = = 8.32.5 he same approach s used o defne he followng falure usng Equaon (2), n whch eleven s used as he expeced cumulave number of falures as shown n Equaon (2). Equaon (2) E N = λ.02 E N = λ = = 9.5.5 In Equaon (3) below, he expeced number of falures used s welve. Equaon (3) E N = λ.02 E N = λ 2 = = 9.96.5 Afer defnng he expeced me of he nex falure, s possble o defne he approprae nspecons perod 5
E. Calxo e al. of me. Wheher s beng consdered one monh (0.083 year) as an adequae me o sar each nspecon he followng nspecon me afer nnh, enh and elevenh falure are: Inspecon 8.23 year (8.32 0.083); 2 Inspecon 9.07 year (9.5 0.083); 3 Inspecon 9.87 year (8.32 0.083); he remarkable pon s ha such mehodology regards relably growh or degrades o predc he followng falures along me. In RGBI mehod, whenever new falures occur, s possble o updae he model and ge more accurae values of cumulave expeced number of falure. he example of cumulave falure ploed agans me for a desel moor s presened n Fgure 5, usng cumulave falure funcon parameers =.02 and λ =.5. Based on such analyss, s possble o graphcally observe ha he nex falures (falures 0, and 2 ) wll occur on 8.32; 9.5 and 9.96 years, respecvely. ha means 0.92;.75 and 2.56 year afer las falure (7.4 years). Despe smple applcaon, RGBI analyss requres frs o have Crown AMSAA parameers model o have cumulave expeced number of falure. Such parameers can be esmae by Max lkelhood mehod by usng sofware applcaon. In dong so, whenever s possble, s advsable o use sofware o plo drecly he expeced number of falures graphs. In hs case, s possble o updae hsorcal daa wh new daa and plo expeced fuure falures drecly on graph. Applyng such mehodology for oher drll facly equpmens s possble o defne nspecon perod of me and depend o nspecon resuls prevenve manenance may be plan o ancpae equpmen fal. able 4 shows nspecon polcy defned for Compressor, Desel Moor, Crown Block and ransmsson Fgure 5. Inspecon Based n relably growh. able 4. Inspecon based n relably growh. Inspecons mes (years) Equpmen nspecon 2 nspecon 3 nspecon Compressor 0.36 0.8.25 Desel moor 0.84.67 2.48 Crown block.40.47.53 ransmsson box.36.42.47 52
E. Calxo e al. Box. Acually, despe Inspecon Based n Growh relably defne an exacly me o nspecon, addon nformaon s mus o be consdered lke logsc me o perform nspecon. Indeed, such me mus be dscouned of nspecon me n order o defne a range of me o carry ou nspecon n each equpmen. In Drll Facly Sysem equpmens was defned one monh (0.083) o perform nspecon and such me s dscouned by expeced falure me. Once agan s mporan o be aware abou he P-F nerval of me. 5. Conclusons he paral avalably mehodology has demonsraed how o perform RAM analyss consderng dfferen nerval of me for sysem whch has no hgh performance for long perod of me. herefore, s possble o assess such sysem performance along me bu n each nended perod of me n order o ake beer decsons relaed o operaonal avalably mprovemen. hereby, s possble o denfy crcal equpmen on he frs and second year and also denfy whch equpmen mpacs on sysem operaonal avalably n dfferen nerval of me. In addon, relably growh based nspecon mehod was carred ou o defne nspecon me for each crcal equpmen defned by paral avalably mehod n order o follow up her performance n dfferen nerval of me. Indeed, such mehod s very mporan because n many cases wll no possble o ake place crcal equpmen and a prevenve manenance polcy wll be requred based on nspecon polcy. he paral avalably mehod would be npu n some sofware o make easer such analyss s very mporan o verfy sysem s performance for each defned perod of me (yearly). he remarkable pon n paral avalably mehodology s o know whch equpmens wll be aged for a specfc perod of me and whch one wll no. Once such mehod s esablshed n a sofware model such analyss s performed auomacally. References [] Calxo, E. and Schm, W. (2006) Análse Ram do Projeo Cenpes II. ESREL, Esorl. [2] Calxo, E. (2006) he Enhancemen Avalably Mehodology: A Refnery Case Sudy. ESREL, Esorl. [3] Calxo, E. (203) Gas and Ol Relably Engneerng: Modelng and Smulaon. Elsever, USA. [4] Crow, L.H. (2008) A Mehodology for Managng Relably Growh durng Operaonal Msson Profle esng. Proceedngs of he 2008 Annual RAM Symposum, Las Vegas, 28-3 January 2008, 48-53. [5] O Connor, P.D.. (200) Praccal Relably Engneerng. 4h Edon. John Wley & Sons Ld., Hoboken. [6] Marzal, E.M. and Scharpf, E. (2002) Safey Inegraon Level Selecon. Sysemacs Mehods ncludng Layer of Proecon Analyss. he Insrumenaon, Sysems and Auomaon Socey. 53