Pip Wall Thiknss Disions Using Wibull Analysis H. Paul Baing, P.E. Baing & Assoiats, In. Humbl, TX Equipmnt Insption Fo Mhanial Intgity MNs Stat Univsity ampus Stam Alumni nt Lak hals, LA May 29, 997 Oganizd by Lak Aa Industis MNs Engining Patnship
Pip Wall Thiknss Disions Using Wibull Analysis H. Paul Baing, P.E., Baing & Assoiats, In., P.O. Box 3985, Humbl, TX 77347, Phon: 28-852-68, FAX: 28-852-3749 Abstat Wibull analysis is usd on th data fom pip wall thiknss insptions to st insption intvals and assign isks fo xding th minimum wall thiknss. A small data-st of atual pip thiknss adings, obtaind fom an atual opating loop, a usd to illustat th mthod and ational. Wibull Analysis Wibull analysis is an ngining tool fo analyzing lif-data. Th Wibull analysis quantifiation thniqu is th tool of hoi fo liability ngins aound th wold (Abnthy 996). Intodution of us findly softwa has takn WA out fom sah oganizations and mad it a main lin tool fo us at vy ngining lvl in many oganizations (Fulton 997) Th Wibull analysis issu fo studying pip wall thiknss masumnts is to dfining th liability (o th omplmnt--whih is unliability) of th pip to ontain fluids o gass so that isks a managabl. Wibull analysis povids a tool fo quantifying isks as wall thiknss dass with tim and us. Th WA tool is vy appopiat fo inlusion into th gim of isk-basd insption thniqus fo gnating isk numbs and hlping to auatly pdit whn, wh, and how pip will fail unlss otiv ation ous to pvnt pip wall failus. Knowing th isk numbs allows stting statgis to manag th isk; i..: ) Apt th isk and ontinu opating, 2) Rjt th isk and tak otiv ation, o 3) onsid businss altnativs onsiding tim, mony, and safty. Risk is vy losly latd to liability and podut safty. Risk is dfind as an onomi aspt of safty as (Ison 996) : Risk$ = pobability of a failu*xposu*$onsquns. Th pobabililty of failu (POF) and xposu lmnts in th alulation li btwn 0 and. onsqun $s fo osts vay fom up to and inluding X millions of dollas. This statmnt of isk is th xptd montay valu fo an vnt o st of vnts. Wibull analysis hlps to dfin failu pobabilitis fo isk alulations. Exposu issus lat to gogaphi boundais o dang zons and th valu is oftn takn as.0. onsquns (th dolla numb) f to th maximum finanial liability inud. ost onsquns inlud: ) failu osts, 2) osts (apital and xpns) fo otion of futu failus, 3) fins (and law suits) inud as a sult of th failu, and 4) lost goss magin whn th onomi funtion of th opation annot b aid out baus of th failu. Risks a also dsibd in gnal tms (Hnly 992 o Taylo 996) as fqunis (vnts p unit of tim) multiplid by th magnitud (onsquns p vnt). As individuals, whn th failu ats (daths) a blow fatality p million yas w a not so onnd. Fo opating plants, th dath ats at whih w bom not so onnd dpnds on th numb of daths that an ou. If on pson is killd in a plant, popl a not so onnd whn th dath at is blow 7 fatalitis p million yas but if up to 0 popl an di, popl a not so onnd at a failu at of about fatality p 0 million yas. Fo this pap, failu ats a of intst, howv th appoah is ditd towad th POF ath than th failu at. Of ous isks a divn by failu pobabilitis--a statmnt of unliability (Baing 993). Rliability has many dfinitions (Omdahl 988). If pais a not possibl, liability is th duation o pobability of failu-f pfoman und statd onditions. If pais a possibl, liability is th pobability that an itm an pfom its intndd funtion fo a spifid intval und statd onditions. Dpndability is a singl wod dfinition fo liability. 2 of
Rliability dfinitions inlud pobabilitis with valus btwn 0 (liability is absnt--asy to gt) and (liability is pft--impossibl). Rliability is diffiult baus pobabilitis hang with tim. Unliability--th pobability fo failu--is th omplmnt of liability. Quantifying liability also quantifis isks whn montay valus a inludd and this is wh Wibull analysis is hlpful--a majo issu is having data to analyz. Wibull analysis was onivd by Waloddi Wibull in 937 and publily dislosd in th Jounal of Applid Mhanis of th Amian Soity of Mhanial Engining in 95. Wibull laimd th thniqu " may somtims nd good svi."--h did not guaant it would always wok. In th pati of liability ngining, Wibull analysis has bom th lading mthod fo analyzing lif data. Wibull analysis usually follows this fomat: ) Aumulat dist sampls of lif data 2) Plot th data on Wibull pobability plots 3) Intpt th plot as if th data fit a ontinuos distibution 4) Us data fo failu foasting and pdition 5) Evaluat otiv ation plans 6) Whn possibl, intodu finanial alulations into th analysis to avoid th us of pobabilitis, i.., onsid th mony of isks and optimum plamnt alulations involving both tim and mony. Most ngins hav toubl with lif data baus thy annot plot th data as it ontains only "x" vnts masuing tim to failu. Whn ngins an't mak a plot of th data, thy oftn lak a physial undstanding of th fats. Wibull analysis podus a staight-lin plot of th data--if th data dos not fall onto a staight lin, thn th wong typ of distibution has bn sltd o uvatu in th data plots hlp diagnos what is physially ouing suh as: ) Mixtus of failu mods. 2) Tim oigins a not loatd a zo tim 3) Aging sal paamts not auatly flt th ot masumnt fo failu On vy valuabl fatu of a Wibull pobability plot is th "y" axis showing th umulativ distibution funtion (DF). Fo liability data, th Wibull "y" axis magnifis th pntag of failus in th low potion of th uv--this potion is usually of most intst to ngins. This ondition is illustatd in Figu. O u n D F 20 5 99 95 90 80 70 60 50 40 30 W/ Wibull Pobability Pap % 2 Eta Bta ^2 n/s 0 00 Figu : Wibull Pobability Pap ~50% Distan ~50% Distan Th low 20% of th failu data oupy oughly th low 50% of th distan on th hat. This situation magnifis aly failus. On a Wibull plot, th "y" axis is a log-log funtion sulting in th unusual divisions. Th "x" axis is a simpl log funtion. Eta dsibs wh th tnd lin osss th 62.3% dashd lin. Bta dfins th tnd lin slop passing though th data. Th offiint of dtmination, ^2, dsibs th goodnss of fit of th tnd lin to th data points. Th total numb of data points in th data st is dsibd by n, and s dfins th numb of suspnsions o nsod units in th data st. Wibull plots a wll known fo dsibing th lif of ball baings. Figu 2 shows a Wibull plot fo ball baings tstd at a onstant havy load. Eah data points psnt th numb of volutions at whih ah baing fails. Ball baings a atd at th B lif (i.., % of th population is xptd to fail). Fo this baing th B lif is,000,000 volutions. Th dfinition of "B" is dsibd (Gitn 997) as "Buhinlitzit wh 3 of
Buh = Fatu/bakag, Einlit = initiation, and Zit = tim, i.. fatu initiation tim". Th ball baing industy uss a standad isk of % failu fo th advtisd load ating. Engins slting th baings must judg if this isk lvl is too sv fo th appliation--if so, th baing loads must b datd. O, if gat isks a allowd, th O u n D F % 20 5 99 95 90 80 70 60 50 40 30 W/ Baing Lif--onstant Load of,000 lbs 2 Eta Bta ^2 n/s 5.4E+06.35 0.975 /0 0000 00000 E+07 E+08 Ag To Failu (volutions) Wibull Tst Data Figu 2: Ball Baing Lif Ratd At B- baing may b havi loadd. Th Wibull uv, plus a fw dsign uls, and th known onsquns allow th ngin to mak asonabl businss disions in slting th appopiat baing. Noti th "y" axis sal of a Wibull plot is a masumnt of unliability. Unliability divs isk. Fo opating plants, a ntal businss issu is th ost of unliability (Baing 996). High plant liability dus quipmnt failu osts. Failus das podution and limit goss pofits. Boosting liability, by duing th ost of unliability, impovs businss pfoman. Th la ason fo duing unliability is splld: mony. Th motivation fo impoving liability is staightfowad fo a businss plan: Impov liability, Rdu unliability osts, Gnat mo pofit, and Gt mo businss. W talk about liability (a good wod), but w masu failus (a bad wod). Failus dmonstat vidn of unliability with unfavoabl ost onsquns fo businsss. Failus in most ontinuous poss industis a masud in poss downtim. utbaks/slow-downs in output a also failus. Failus qui a la dfinition fo oganizations making liability impovmnts. Failus a loss of funtion whn th funtion is ndd patiulaly fo mting finanial goals. Rliability quimnts fo businss hang with omptitiv onditions and businss isks th playing fild is always tilting. Unliability valus hang with businss onditions. You don t nd th bst liability in th wold fo you businss you just nd a ost advantag ov you fist omptito. Evn low ost industy povids nd liability impovmnt pogams liability dos not stand still and unliability osts inas. Motivations fo liability impovmnts a divn by th ost of unliability this tlls th magnitud of th pain. Wh th pain ous within th plant is impotant. Why th pain ous gts to th oot aus of th poblm fo otiv impovmnt pogams. Don t ly on a magi bullt to fix liability poblms. Sldom will oting on itm aus a big hang in ovall liability. Rliability tools showd thi al valu in th 930s, '40s, and '50s whn usd on xoti militay pogams. Fotunatly many liability tools suh as Wibull analysis do not nd a okt sintist to us thm ost fftivly. Som simpl liability tools povid big gains quikly and df th us of highpowd tools fo squzing out th maining impovmnts. In all ass, so ads fo liability impovmnts in businss nd masumnts in dollas. Us of liability tools is volutionay: Stat liability impovmnt pogams with simpl aithmti and spadshts. Quantify impotant ost and failu numbs. Gain momntum with good maintnan patis. Impov tamwok using total 4 of
podutiv maintnan pogams. Us oot aus analysis to ffiintly solv poblms. Lan and us a host of staightfowad liability ngining tools to solv poblms. Spu impovmnt pogams by using statistis to quantify and undstand satt in th sults. Wibull analysis tools a impotant statistial mthods fo squzing fats fom a fw pis of infomation. Good fats about isks qui an odly poss R E P Root aus Analysis Total Podutiv Maintnan Good Eng., Maint., & Opating Patis Figu 3: Rliability Hiahy within plants to mak su things a don otly and th ot things a pfomd. Figu 3 shows th hiahy dpnding on having low lvl pogams opational as pdnts to aomplish high lvl objtivs suh as isk assssmnt. Th data fo Wibull analysis will b substantially flawd if a fim foundation is not stablishd to ontol th haos of failus. Th liability impovmnt hiahy uss a host of nw tools to du both failus and th ffts of failus. This wok-poss initiativ is to gain a bahhad and xpand titoy by impovmnts. Fw lasting impovmnts a maintaind without impoving liability as a wok-poss using fou impotant pogams (whih also podus good data): Good ngining, maintnan, and opation patis a good manufatuing patis (GMP) whih uss th bst-of-lass patis fo doing ativitis. This quis having taind popl at vaious lvls with a ommitmnt to on-going taining. Us good podus and patis to avoid alamitis. Tah nw thniqus and vify th wokfo has aptd thm as quimnts fo ot pfoman suh as pision alignmnt of otating quipmnt along with pision alignmnt of all piping and quipmnt. Stat tamwok btwn maintnan and podution dpatmnts. Total podutiv maintnan (TPM) is a way of lif fo involvmnt of podution psonnl into appopiat maintnan tasks fo tnd loving a of both quipmnt and posss. Aim TPM fo fftiv us of quipmnt and loss pvntion by a pvntiv maintnan ffot, gt involvmnt of all popl fom top to bottom in th oganization. Pomot pvntiv maintnan though th TPM pogam by us of slf-ditd small wok goups. Root aus analysis (RA) woks on dfining poblms into atgois suh as popl, podus, o hadwa. Dmonstat RA solutions to poblms will pvnt un, mt th oganization goal, and b within an individual ontol fo pvnting un. Rliability ngining pinipls (REP) uss nw tools to solv th vital fw old nagging poblms. Many tools us bathtub onpts to math ot tools to ost fftiv statgis by applying sin and ngining to liabilityntd maintnan (RM) ffots. Wibull analysis is on of th vy valuabl tools fo making th data tll a quantifiabl stoy about isks using ag to failu data. Aquiing good data fo quipmnt failus sounds asy. It is a diffiult task. Abnthy, ibid., says aquiing quipmnt failu data has th basi quimnts (itms -3); and fo ommial businsss, add two oth lmnts (itms 4-5): ) Dfin an unambiguous tim oigin, 5 of
2) Dfin a sal masuing th passag of tim, 3) Th maning of failu must b ntily la, 4) Masu ost onsquns fo failu, and 5) Gain data analysis xptis fo using data. A thoughtful plan to aqui a fw pis of afully loggd ag-to-failu data fo quipmnt is btt than vast quantitis of pooly plannd data. Popl in many plants say thy lak any data (Baing 995). In fat, data is all aound thm in vaious dgs of usfulnss. Most industial plants hav bn aquiing quipmnt failu data fo many yas and sldom is th data analyzd in a sintifi mann. Raly do popl aquiing th data s th data usd to solv thi poblms. Th nt sult is vast data banks of naly uslss infomation aquid haphazadly and annotatd pooly. Today s task is to min though pils of xisting data whil aquiing nw ag-to-failu data in a afully thought-out mann so it an b usd fo an onomi advantag. Th ky phas to mmb is ag-tofailu and of ous that quis a onsistnt dfinition of failu. Th fild of liability offs many thnial guidlins fo how data should b aquid, annotatd, and usd fo analysis. In many ass, failus nd a dath tifiat just as ous with human failus. Dath tifiats fo humans hav bn so podutiv in poduing analyzabl sults, that it now illgal in th ivilizd wold fo a pson to b buid without a dath tifiat listing ag and aus of dath (th oot(s) aus of dath). Spifi failu data is not always availabl. Substantial failu-at data xist in th litatu awaiting us of fats fo impoving plants and quipmnt (IEEE 984) (RA 994) (Baing 997-wbsit). Nw data initiativs by th nt Fo hmial Poss Safty (PS 989) using povn skills of data analysis xpts at Dt Nosk Vatas (OREDA 992), a undway fo aquiing data fom hmial plants and finis. quik look sults, o find into statistial dtails poviding ih dsiptions whn onvtd into staight lin plots of tim-to-failu against umulativ hans fo th failu. Most ngins nd gaphial psntation of data to fully undstand poblms. Pobability tools a gowing in impotan with th us of psonal omputs that gnat th uvs with as. Wibull pobability hats a th tools of hoi fo failu poblms baus thy oftn tll failu mods (how omponnts di) and th pobability of failu: Infant motality us a un to failu statgy, han failus us a un to failu statgy, o Wa-out failu mods onsid a timd plamnt statgy basd on osts. Data fom Wibull plots suppot RM disions basd on highly idalizd bathtub uvs. (Moubay 992) Wibull plots tll omponnt failu mods. Wibull hats a patiulaly valuabl fo pointing ot dition fo finding oot auss of poblms using a fw data points. Lag quantitis of data add onfidn to th dision making poss, but at onsidabl gat xpns fo aquiing both failus and data. Th motivation fo using pobability hats is to undstand failu data and du ostly failus by appopiat otiv ations. onsid th uvs in Figu 4. O U R R E N E D F % 95 90 80 60 70 50 40 30 20 5 2 99 W/ Pump B--Bak-up Pump Runs Only Whn Pump A Fails WinSMITH Wibull Softwa Pump Sal Lif Statgy 0 Pump Sal Lif (months) Figu 4: Wibull Plot Fo Pump Sal Lif Pump A--Pimay Pump Run To Failu Eta Bta ^2 n/s.402 2.5 0.983 /0 Pump B 38.32 3.90 0.983 /0 Pump A Failu data is haoti baus of satt in th data. Data satt an b studid aithmtially fo fist, 6 of
Th slop of th lin tlls th failu mod is waout and th pobability fo failu an b ad ditly fom th Y-axis. In Figu 4, Pump B s sal lif is shot. By standing and waiting fo duty it xpins a svi 38./.4 = 3.7 tims mo sv than Pump A using th atio of haatisti lif valus shown in th figu (wath fo th haatisti valu masus to appa again on pip wall thiknss masumnts). Knowing th pobability fo suss/failu fom pobability plots is an impotant fat fo assssing isks. Pobability hats a asily intptd, and simpl plots of pobabilitis multiplid by osts an b plottd against tim to quantify disions and onsid altnativs. In pati w sldom hav too many data points fo assssing isks. Wibull plots us fw data and hlp th dision making poss som data is btt than no data fo making ost fftiv disions. Pip Wall Thiknss Data Pip wall thiknss data is bing od in lag quantitis ov long piods of tim in hmial plants and finis (Sni 997). Most pip data is not signifiant but som data has gat impotan. Sni pots th ARO Los Angls finy, with 437 mils of piping and 32,000 thiknss monitoing loations, has odd 59,000 data points (i.., th lowst ading found at ah thiknss monitoing loation). P&IDs (piping and instumnt diagams) sultd in isomti dawings of piping iuits, and th dawings w studid fo loalizd ffts of damag mhanisms. Points susptibl to loalizd dtioation suh as injtion points o known oosiv systms w studid to find aas o zons whih psnt th highst oosion ats so that pip wall thiknss masumnts a odd at th wost as onditions. Most data was odd by ultasoni tsting. Plaing a wath on th pip wall thiknss has sultd in a signifiant dution in fis duing th six yas this study has bn undway baus piping is plad bfo it has ahd th nd of lif as th isks a managd. In ontinuous possing plants, most data is aquid at piodi intvals basd on adings fom fou, ight, o 2 loations in a band aound th iumfn. In most plants th pati of taking only on wall thiknss masumnt has bn abandond as a good woking pati baus th pati has not bn patiulaly fftiv in finding th smallst wall thiknss. Majo qustions ais fom plant pip suvy ffots: ) Sldom is a wall failu odd at loss of ontainmnt--how dos this math Wibull quimnts fo ag to failu data? 2) Sin atastophi failu is not oftn odd what and how is th failu itia stablishd? 3) How a piodi masumnt intvals dtmind? Piping systms failu ous whn th pip annot ontain th intnal ontnts--ith th stngth is too low (fom wong matial sltion, fatigu, stss oosion, t.) o th stss is too high (ovloads, loss of wall thiknss, unobsvd abuss, t.) sulting in an intfn zon btwn loads and stngths. Pip failu is oftn (not always) divn by high iumfntial stsss o though-wall hols fom slugs, t. A pioitizing systm must b usd to onsid th vital fw situations to b quantifid by spaating th vital issus fom th tivial many that a not wothy of a quantifiabl study. Tabl shows th thiknss data fom a piodi insption pogam. Data is takn fom a pip oss stion ov a piod of tim flting th ag/us of th pip at six loations in masumnt plan. This data shows small vaiations within ah ya. Lo Tabl : Wall Thiknss masumnts (mils) 2 4 6 3 3 3 34 309 308 308 305 2 36 38 3 35 305 300 302 298 3 308 300 298 30 295 29 295 292 4 305 305 302 304 295 294 290 289 5 38 3 304 305 300 299 295 285 8 2 4 7 of
6 32 38 33 33 308 305 300 295 Th svi fo this pip has a high isk fo fi and lost podution fom th plant along with a high pobability of injuy to a lag numb of popl and dath to a fw popl. Th finanial onsqun of a failu has th potntial fo a total loss of $85,000,000. Th isk fo this ondition must b ontolld to lss than $,000; and sin human fatalitis a likly, th maximum allowd pobability of failu pmittd is 0.0%. P o b i l i t y O f F a i l u Pobabililty Of Failu Vsus Tim.0.008.006 %.004 Pobability At Wall Thiknss = 0.236".002 0 0 2 4 6 8 2 4 6 O u n D F % 80 90 60 70 40 50 30 20 5 2.5.2. Eta Bta ^2 n/s.3599 54.64 0.965 6/0.3374 47.22 0.95 6/0.30903 56.2 0.958 6/0.332 57.48 0.89 6/0.30475 54.09 0.89 6/0.30243 50.43 0.963 6/0.307 5.82 0.928 6/0.2977 45.65 0.945 6/0.2885 45.65 Minimum Wall Thiknss Radings.05 Ya 8.02 Ya 6 W/.0 Ya 4.236 <Log>.325 Wall Thiknss (inhs) Ya 4 Figu 5: Wibull Plot Of Wall Thiknss Ya Ya 2 Ya Ya 2 A staightfowad alulation of th pobability of failu using Risk$ = POF*$onsquns shows th POF = $,000/$85,000,000 = 0.0002 = 0.02%. Fo human lif at isk-- th pobability of failu is dsid at lss than 0.0% o 99.99% liability. Th minimum wall thiknss ndd fo pssu ontainmnt is stimatd fom Balow's stsss at 0.047" with an additional stimatd 0.033" fo bnding stsss, plus and stimatd 0.05" fo misllanous small abuss fo a total stimat of 0.3". This minimum stimat, as judgd by mmbs of th assssmnt tam, may b too low fo som unusual onditions by a fato of.8 to ov unknown onditions and thus th patial minimum stimat is 0.236". A Wibull plot in Figu 5 shows how wall thiknss vais. E t a Figu 6: Pobability Of Failu Vsus Tim Noti thiknss valus at 0.0% a appoahing th minimum limit of 0.236" as tim passs. Tabl 2 shows th pobability of failu at th limit of 0.236".32.35.3.305.3.295.29.285.28 st to ontol th isk at 0.0%. Tabl 2: Pobability of Failu (%) Fo A Minimum Wall Thiknss of 0.236 inhs.2e 2.4E 4 2.6E 6.2E Ag (yas) haatisti Lif Vsus Tim Tnd Lin Of Atual Data y to 4 ys Low Limit Allowd = 0.2885" Extapolation Fom 4 y to 20 y 0 5 5 20 25 Ag (yas) Figu 7: haatisti Thiknss Vsus Tim 8 9.8E 3.7E 20.6 ys, 0.2885 2 3.2E -04 4 2.7E -03 Th tnd hat in Figu 6 shows a plot of th data fom Tabl 2. It is not la fom this plot whn th tnd lin will intst th pobability of failu at 0.0%. Most of th infomation lis at low valus 8 of
fo POF. If th y-axis is onvtd to a log sal, th tnd lin is also not obvious. haatisti wall thiknss valus fom Figu 5 povid a la signal fo pojting th nd of usful lif as shown in Figu 7. Th minimum lin, a Wibays stimat, is stablishd in Figu 5 by using th slop of wall thiknss lins and passing th minimum wall lin though th maximum allowd isk--this finds th minimum allowd valu o ta as 0.2885". This minimum valu fo ta boms th low limit valu fo Figu 7, i.., a itial valu. Th gssion tnd lin fo ta valus vsus tim is pojtd fom ya 4 though th minimum ta and thy intst at 20.6 yas. Whn should th nxt pip wall insption ou? Th last insption was at 4 yas and nd of usful lif is pojtd to ou at 20.6 yas? Phaps a asonably pudnt mthod would b to inspt at th maining half-lif (mayb /4 lif if mony is not tight and wois a high) at ~7 yas--followd by subsqunt tsting at futu half-livs. In gnal, pip wall thiknss valuations oftn gt th a bfo th hos. Too muh tsting is pfomd whn isk a vy low (ya 2 though ) and too littl tsting ous na nd of lif (ya 7 though 2). Th onomi issu is to pfom ost fftiv tsting wh isks waant th tst-- whih says as isks is, mo insption should b pfomd to know and validat th isks. By th way, whn th pip is movd fom svi at th nd of it's usful lif (say 20.6 yas) without failu, th ag would b odd as suspndd data and would not b odd as a lital failu. Using th data tnd lin data fom Figu 7 and th Wibays lin slop fom Figu 5, a onsistnt data st of POF an b dvlop. Whn this data is usd with th plamnt ost, a ost uv an b onstutd. Th ost would b ompisd of man tim to plamnt, han of unplannd failus tims th unplannd ost and han of plannd failus tims th plannd ost. Th sulting onomi uv may podu an optimum plamnt intval diffnt than th 20.6 ya lif dsibd abov. This alulation quis infomation on th plannd plamnt ost not povidd in this xampl. Summay Bakgound infomation has bn povidd fo how Wibull plots a usd. A vaity of situations w shown fo Wibull plots inluding how poduts a load-atd basd on th pobability of failu. Wibull analysis was ondutd on a data st of pip pip wall thiknss. Risk lvl was stablishd fo th pip loop basd on human safty quimnts. Wibull plots w ppad and tnds of th isks w podud. Th Wibull tnds fo isk hangs w not patiulaly hlpful fo pojting nd of lif baus of th satt in th data. Satt in th data is what ompliats th analysis of typial data sts. A mthod was dsibd fo finding th pojtd nd of lif using th haatisti wall thiknss valus and plotting th haatisti thiknss valus on a tnd hat. Th tnd hat inludd th itial wall thiknss valu dtmind fom th Wibull plot. Whn th tnd lin of dasing haatisti thiknss valus intstd with th itial minimum wall thiknss, th maximum allowd isk was ahd whih sultd in a funtional nd of lif basd on human safty onsidations. This thniqu hlpd pdit nd of lif. Th nxt insption intval was basd on using th pojtd maining half-lif. Subsqunt insptions would also ou basd on th maining half-lif-- this ondition quis modation of th viwpoint basd on xptd oosion at. Fo xampl, if poo opating patis ou and oosion ats is, it would not b pudnt to igno th atual dtioating ffts to sustain a alulatd half-lif fo th nxt insption. Th agumnt fo th nxt insption piod is to pfom th insption at a ost fftiv intval without xding th isk budgt. 9 of
Us plant dtioation and failu data with nw tools to solv liability poblms in patial ways. Businsss annot affod too-littl no too-muh liability liability must b hamonizd with ost issus by solving top lvl itms on th Pato list. As xptis in using failu data (o dtioation data) gows, us Wibull analysis to hlp with poblm solving by putting statistis to wok on patial poblms. This usually quis taining staffs in us of nw liability tools to gain a omptitiv businss advantag by inasing skills to du osts. Rfns Abnthy, D. Robt B., 996, Th Nw Wibull Handbook, 2 nd dition, Slf publishd, Noth Palm Bah, FL, Phon: 407-842-4082. Baing, H. Paul, 993, Rliability Engining Pinipls, Slf publishd, Humbl, TX, Phon: 73-852-68. Baing, H. Paul, and Wb, David P., 995, Wh Is My Data Fo Making Rliability Impovmnts, Hydoabons Possing Magazin 4 th Intnational Rliability onfn, Houston, TX. Baing, H. Paul, 996, Patial Rliability Tools Fo Rfinis and hmial Plants, National Ptolum Rfins Assoiation--Plant Maintnan onfn and Exhibition, Nashvill, TN. Baing, H. Paul, 997, wold wid wb sit addss fo Wibull failu data at http://www.baing.om/wdbas.htm Baing, H. Paul, 996, An Ovviw Of Rliability Engining Pinipls, Engy Wk 996 onfn, PnnWll onfns & Exhibitions, Book IV, Houston, TX. nt Fo Poss Safty, 989, Guidlins Fo Poss Equipmnt Rliability Data, Amian Institut of hmial Engins, Nw Yok. Fulton, Ws, 996, Patns Softwa onsisting of WinSMITH Wibull vsion 2.0E and WinSMITH Visual vsion 2.0E fo Windows 3., Windows 95 and Windows NT, Fulton Findings, Toan, A, Phon: 3-548-6358. Gitn, Fd K., 997, Psonal ommuniation by -mail in Fbuay 997 fom his addss at 2625.3@ompusv.om. Hnly, Enst J., Hiomitsu. Kumamoto, 992, Pobabilisti Risk Assssmnt, IEEE Pss, Nw Yok. Ison, W. Gant, lyd F. oombs, J., Rihad Y. Moss, 996, Handbook of Rliability Engining and Managmnt, 2 nd dition, MGaw-Hill, Nw Yok. Moubay, John, 992, Rliability-ntd Maintnan, Industial Pss, Nw Yok IEEE Std 500-984: IEEE Guid to th olltion and Psntation of Eltial, Eltoni, Snsing omponnt, and Mhanial Equipmnt Rliability Data fo Nula-Pow Gnating Stations, John Wily & Sons, In., Nw Yok. Omdahl, Tay Philip, 988 Rliability, Availability, and Maintainability (RAM) Ditionay, ASQ Quality Pss, Milwauk, WI, Phon: -800-248-946 OREDA-992 (Offsho Rliability Data), ontat DNV Thnia, 6340 Pak Tn Pla, Suit 0, Houston, TX 77084, phon 28-72-6600. RA-NPRD-95, 994 Nonltoni Pats Rliability Data 995, Rliability Analysis nt, PO Box 4700, Rom, NY 3442-4700, Phon: (800)-526-4802 Taylo, J. R., 994, Risk Analysis fo Poss Plant, Piplins and Tanspot, E & FN Spon, London. of
Sni, Mi and Tony Ladbat, May 997, "On los Insption", Oil & Gas Poss Intnational, onhill Publiations Ltd., Issu 3, London. BIOGRAPHI INFORMATION- H. Paul Baing Manufatuing, ngining, and liability onsultant and autho of th basi liability taining ous Rliability Engining Pinipls. Mo than thity-fiv yas of ngining and manufatuing xpin in dsign, podution, quality, maintnan, and liability of thnial poduts. ontibuto to Th Nw Wibull Handbook, a liability ngining txt publishd by D. Robt B. Abnthy. Namd as invnto in six U.S.A. Patnts. Rgistd Pofssional Engin in Txas. Eduation inluds a MS and BS in Mhanial Engining fom Noth aolina Stat Univsity, and patiipatd in Havad Univsity's th wk Manufatuing Statgy onfn. Visit th wold wid wb sit at http://www.baing.om fo oth bakgound dtails onning liability, failu dat, and lif yl osting, o snd -mail to hpaul@baing.om onning insption o liability issus. May 28, 997 of