Planning and Managing Copper Cable Maintenance through Cost- Benefit Modeling

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1 Planning and Managing Coppr Cabl Maintnanc through Cost- Bnfit Modling Jason W. Rup U S WEST Advancd Tchnologis Bouldr Ky Words: Maintnanc, Managmnt Stratgy, Rhabilitation, Cost-bnfit Analysis, Rliability Planning, Tlcommunication Ntwork, Tlphon Systm, Outsid Plant SUMMARY AND CONCLUSIONS This papr dscribs our work to rduc th cost, and improv th rliability of our outsid plant. Lacking adquat information, w cannot apply traditional lif-cycl cost modls. In this papr, w will focus on th procss and modling portions of our work. W dscrib th rhabilitation procss first, thn th dominant failur mods associatd with outsid plant quipmnt. This knowldg lads us into th stratgic modl w us to plan long trm rhabilitation, and th tactical modls w us to support immdiat rhabilitation dcisions. Although our work continus, w hav alrady improvd our us of rhabilitation funding in th following ways: In applying cost-bnfit modling to th rhabilitation procss, w hav simplifid th nginring analysis, and will continu to sav mony by guiding nginring dcisions. Our modls hav hlpd financ managrs with long-trm rhabilitation budgt planning, and hav providd thm with bttr control of th rhabilitation budgt. By applying scinc to this problm, w hav givn visibility to maintnanc and rliability planning. 1. INTRODUCTION Rgional Bll Oprating Companis (RBOC) maintain th outsid plant portion of th ntwork through rhabilitation. Ths coppr cabl facilitis ar costly, mission critical, and subjct to dgradation. Du to th amount and divrsity of th quipmnt, w cannot apply simpl lif cycl cost modls. Howvr, w can still apply rliability and oprations modls to improv th cost-ffctivnss of our rhabilitation. 1.1 Notation T ag of a givn unit of plant, in yars R rgion of th trritory whr th plant srvs: 1 = south, 2 = cntral, 3 = north I rgrssion intrcpt trm β rgrssion cofficint P(T, probability that th cabl is crackd, givn T and R Z(T, xpctd hazard rat for a twistd wir pair/loop, givn T and R C constant, > 1 FR failur rat, or hazard rat, for a unit of plant IFR(t) hazard rat at tim unit t λ failur rat, or hazard rat, for a twistd wir pair in a wt sction N total numbr of twistd wir pairs in th wt sction, xcluding faild pairs Pn(t N,λ) probability that n pairs hav faild by tim t, givn N and λ E(n t) xpctd numbr of failurs xprincd by tim t E(t) xpctd tim whn th cabl xhausts its supply of spar wir pairs A numbr of assignd pairs in th wt sction, th numbr of pairs in us 1.2 Nomnclatur Dfctiv Pair Rcovry th act of locating a fault in a dfctiv lin, and thn rpairing th fault, usually through rhabilitation. Th dfctiv lin is a faild twistd coppr pair that a tchnician could not rpair. Dfctiv Fill th proportion of coppr pairs in a unit of plant, or sction of cabl, that ar not availabl for us bcaus thy ar alrady srving a customr, or thy ar faultd. Dispatch th act of snding a rpair tchnician out to th fild to rstor srvic or to chang outsid plant facilitis in ordr to provid srvic. Facility Modification th act of changing th outsid plant in ordr to install srvic. Lgacy Systm a sourc of data and information intrnal to th corporation, oftn a larg databas holding information collctd from managmnt and control systms. Outsid Plant th portion of th tlcommunications ntwork that conncts th customr to th cntral offics; this is oftn twistd pairs of coppr wir, bundld into cabls, and connctd through splics and xposd accss points. Proactiv Rhabilitation th act of prforming maintnanc rplacmnt prior to non-rpairabl failur. Rhabilitation rplacing and rdsigning old portions of th outsid plant to rduc maintnanc xpns, and improv customr srvic. 1.3 Acronyms and Abbrviations PIC Plastic Insulatd Cabl RF 99RM-067: pag 1 RF

2 RBOC Rgional Bll Oprating Company Bcaus w lack sufficint information to apply traditional lif-cycl cost modls, w mad som assumptions that allow us to construct cost-bnfit dcision support modls. 1.4 Modl Assumptions 1. Th hazard function for dgradd outsid plant at tim t is of th form IFR ( t) = IFR( t 1) * C 2. Coppr cabl dos not crack within its first yar of lif. 3. Any portion of th outsid plant that nginrs considr for rhabilitation has dgradd and is xprincing an incrasing hazard rat. If this assumption wr not tru, th rhabilitation job would not b cost-ffctiv, so w would not complt th work. 4. Coppr pairs in a wt sction ach hav a constant hazard rat. 2. REHABILITATION PROCESS Cost-bnfit modls nabl us to chang th traditional rhabilitation procss into a mor cost-ffctiv on. Gnrally, th procss rquirs nginrs to collct information from lgacy systms and fild tchnicians. Thy hav availabl a known amount of cash to allocat to rhabilitation jobs. Thir goal is to gain th bst bnfit from this rhabilitation budgt. Whr th procss was onc informal, w hav addd structur to th currnt procss. 2.1 Informal Rhabilitation Procss (1) Until rcntly, th rhabilitation procss was ad-hoc. Think of th procss as having thr portions: 1. Budgt Each yar, nginrs would writ a businss cas that outlins th xpctd payback from a rqustd budgt. 2. Enginring Aftr th annual funding cycl, nginrs would bgin collcting information from lgacy systms. This information would indicat which portions of th outsid plant cost th company most to maintain, and providd th poorst srvic to our customrs. Enginrs would thn ask for information from th fild tchnicians. Tchnicians would indicat to th nginrs which units of plant thy bliv ndd rhabilitation. Enginrs would thn dcid which parts of th plant to rhabilitat, and thy would dsign larg, xpnsiv rhabilitation jobs. 3. Construction Finally, construction would complt th work. In most cass th rsult was fwr dispatchs for rpairs and installations, and bttr srvic for our customrs. But w couldn t b sur that w wr doing th right amount of rhabilitation, or if w wr applying our rsourcs in th bst way possibl. 2.2 Currnt Procss Through modling, w hav improvd th currnt rhabilitation procss: Stratgic Modls hav hlpd us stimat th rhabilitation budgt w nd to control outsid plant failurs. At a high lvl, th stratgic modl compars th cost of rhabilitation to th impact w xpct on dispatchd rpairs, dispatchd installation, and facility modifications. This hlps financ managrs undrstand th valu of maintaining our outsid plant, and guids thm in thir dcision of funding rhabilitation. W us th stratgic modl to crat rhabilitation scnarios, and thn w compar th rsults. Tactical Modls hav providd nginrs with ways to assss th cost of maintaining portions of th outsid plant, and th cost-ffctivnss of rhabilitation work on ths portions of plant. W bgan with simpl spradsht dcision support tools, and ar now intgrating th dcision support tools into a systm that can gathr information from lgacy systms. Th nginring portion of th currnt procss involvs two phass: 1. First Cut at th bginning of th yar, w provid th nginrs with a list of units of plant to considr rhabilitating. 2. Scond Cut aftr nginrs dsign th work, thy compar th cost and bnfit xpctd from ach proposd rhabilitation job. In addition, w ar closing th loop on rhabilitation work. W plan to masur th rsults from last yar s nginring ffort, thn us this to improv th modls, and to guid nginring and financial dcisions. 3. DOMINATING OUTSIDE PLANT FAILURE MODES Thr ar two dominant outsid plant failur mods: crackd PIC, and wt sction. Ths ar dominant bcaus thy ar frqunt, costly to maintnanc, and srvic affcting. Both ar th rsult of dgradation, so thy appar in oldr outsid plant. Through fild studis of outsid plant failurs, w hav found that th dominant failur mod for coppr cabl facilitis is what w call crackd PIC. Crackd PIC is a dgradation phnomnon whr stabilizrs lach out of th plastic insulation ovr tim. Whn cabl is dirctly xposd to th air, such as in tchnician accss points, ths stabilizrs lav th insulation fastr. Ovr tim, th insulation bcoms brittl. With tmpratur cycling, and with tchnicians moving th wir, th brittl insulation cracks, and xposs th coppr wir. Th xposd wir circuit is mor likly to short, ground, or cross with anothr circuit. This causs dgradation, or complt loss of srvic. An additional failur mod that w ar concrnd about is what w call a wt sction. This occurs whn a cabl shath is damagd, and allows watr to ntr th cabl. RF 99RM-067: pag 2 RF

3 Manufacturing dfcts crat pinhols in th insulation on twistd wir pairs. In a wt sction, th watr corrods th coppr through ths pinhols, and vntually th quality of srvic dgrads. Wt sctions, bcaus thy can rsult from damag, ar not strong candidats for traditional lif-cycl cost modls. Ths failur mods, bcaus thy rsult from dgradation, ar important drivrs to th modls w hav dvlopd. Rf. 1 provids mor discussion on this subjct. 4. STRATEGIC AND TACTICAL MODELS OF OUTSIDE PLANT RELIABILITY AND OPERATIONS In this sction, I discuss th modls that support th rhabilitation procss. Our constraints, common in many industris and applications, dirct us to crat uniqu modls. I will xplain th failur modl w us as part of th stratgic modl. I will also xplain th important failur and oprational modls w us within our tactical modls. 4.1 Constraints to Modling and Implmntation Th availabl data prsnts som intrsting constraints to our modling, and thrfor to implmntation. W suspct ths constraints, or similar ons, ar common in othr industris. Plant Ag Although our systms can tll us how much cabl w hav at ach ag, w cannot obtain th ag of a givn outsid plant componnt without dirct inspction. This would rquir xcavation in som cass, and would still b inaccurat. Du to both growth and rhabilitation projcts, a givn coppr pair may consist of various ags of cabl. Failur History and IFR At bst, w hav on to two yars worth of rpair rcords. Bcaus plant hazard rat is strongly influncd by sasonal and annual wathr pattrns, w cannot accuratly modl th hazard function. Simpl modls with simpl assumptions srv our nds bst. Failur Mod History Our rporting mchanisms do not collct componnt and failur mod information. Howvr, w can combin narrativ information, and othr rportd cods to stimat th typ of componnt that is dgradd th most in a unit of plant. As a rsult of ths constraints, traditional modling tchniqus do not work wll for us. For xampl, a proportional intnsity modl might work wll for cabl failurs if w had th data to support this approach. 4.2 Stratgic Modl Th stratgic modl considrs ach of ths cost factors: facility modifications, dfctiv pair rcovry, th cost of rhabilitation, and th impact from dispatch rpairs. Ths dispatchd rpairs rsult whn customrs xprinc troubl with thir srvic; thn w isolat th troubl byond th cntral offic, and snd a tchnician to th fild to rpair th lin. In this subsction, I will xplain th portion of th stratgic modl that prdicts th numbr of dispatchd rpairs. Although th complt modl accounts for th othr costs, w us much simplr modls for th othr costs. In th futur, w hop to improv our modls for facility modifications, dfctiv pair rcovry, and th cost of rhabilitation. Th stratgic modl provids an xpctd cost for maintaining plant with a givn profil. Th profil is dfind by th amount of plant in ach combination of ag and rgion. In this subsction, a loop will b th xpctd lngth of coppr pair for a customr s lin. W fit a logistic rgrssion modl to a small data st. Th data was manually collctd as part of a sparat, commissiond study on insulation cracking in coppr cabl. Th logistic rgrssion modl is of th form P( T, = 1+ ( T * βt + R* β R+ I ) ( T * βt + R* β R+ I ) Eq (2) provids th probability that a sction of cabl, or a loop, has crackd PIC problms, givn its ag and th rgion in which it srvs. Using this probability function, and conditioning on assumption 2 that coppr cabl dos not crack in th first yar, w stimat th xpctd amount of plant that is crackd at ach ag and location combination. W apply our hazard rat assumption 1 (q (1)), sampl dgradd plant, and masur th chang in hazard rat ovr th yar to approximat th hazard function. Th rat of failur for an arbitrary loop dpnds on th ag at which it bgan to crack. For an arbitrary loop dfind by an ag and location combination, th rat of failurs is th convolution of (a) th distribution of th ag it bgins to crack, and (b) th distribution of th hazard rat for a loop. W approximat this with T Z( T, = [ P( t, P( t 1, ] * C t= 1 Through a Mont Carlo approach, w stimat th rat of dispatchd failurs that various rhabilitation scnarios yild. By making assumptions about th plant rplacd through various rhabilitation scnarios, w build plant profils for rhabilitation and apply ths to q (3). Aftr adding th costs from dispatchd failurs, facility modifications, rcovrd pairs, and rhabilitation; w hav cost comparisons for th scnarios w considrd. 4.3 Tactical Modl for Wt Sctions ( T t) * FR Our modl must compar th costs of rplacing th wt sction today, or waiting until w must rplac it in an mrgncy. I will xplain th concpt of a wt sction rplacmnt, and thn xplain our simplifid failur modl. (2) (3) RF 99RM-067: pag 3 RF

4 W us this failur modl to gnrat cost stimats, and thn calculat financial masurmnts to support dcisions. A wt sction rplacmnt is a proactiv rhabilitation of a wt sction of cabl. This is th concpt: if w do not rplac today, w will rplac mor cabl in a futur mrgncy to put customrs back in srvic. Manwhil, customrs will xprinc troubl, and w must dispatch for rpairs. Bcaus th faults xist insid th cabl, th tchnician cannot rpair th troubls. Instad, sh must giv th customr anothr pair ach tim. Evntually, if not rplacd proactivly, this cabl will run out of spar pairs. Thn, w must rplac this cabl in an mrgncy. Undr assumption 4, that coppr pairs in a wt sction hav a constant hazard rat, w hav N Pn t N =! (, λ) (1 n!( N n)! ) This stats that th probability of xprincing n troubls in this wt sction ovr a givn tim intrval t is a binomial function with xponntially distributd succss/failur proportions. From q (4), w can asily calculat th probability distributions for th numbr of troubls in a givn yar, and th probability of xhausting th cabl in a givn yar. Howvr, th rror introducd through assumption 4 dos not justify this dtail in our modl. Instad, w us xpctd valus. Th numbr of failurs w xpct to xprinc by tim t, and th amount of tim w xpct to pass bfor th cabl xhausts ar, rspctivly, E( n t) = N * A ln( ) E( t) = N λ Using qs (5) - (6), w can modl all th cash flows in th modl, and calculat financial masurmnts to hlp nginrs dcid whthr to rplac or wait. Hr ar th important cash flows to considr: Cost of dispatchs for kping customrs in srvic. Costs of rplacing th cabl today, and whn w xpct it could xhaust in th futur. λ* t n* λ* t λ* t N n Scrap valu of th rplacd cabl. Dprciation valu of th nw cabl rplacd today, or in th futur. 4.4 Tactical Modl for Gnral Rhabilitation Much lik th wt sction modl, our modl for othr rhabilitation work must compar th cost of complting a rhabilitation job now, vrsus waiting. In this subsction, I will xplain our currnt stat of knowldg for modling th first cut in th nginring procss, which I dscribd in (4) (5) (6) sction 2.2. Nxt, I will xplain how th modls for th scond cut diffr. Finally, I will point out som ways w want to improv ths modls. Although w dvlopd ths modls indpndntly, w latr found Rf. 2, which xplains similar, but mor complx modls. In this subsction, I rfr to a unit of plant. This I dfin to b all th outsid plant quipmnt srving customrs through a givn cross connction. Th cross connction is th first point of accss for a tchnician byond th cntral offic. Simply put, a unit of plant srvs a larg nighborhood of customrs. Th first cut is a list of potntial rhabilitation jobs, with prsnt valu costs for ach major typ of outsid plant componnt. Each potntial rhabilitation job is associatd with a unit of plant. W calculat th prsnt valu, aftr-tax cost ovr a givn horizon, sparatly for ach major typ of outsid plant componnt. With th xcption of th cost of rhabilitation, th cost catgoris w modl in th first cut ar th sam as thos w dscribd for th stratgic modl: dispatch rpairs, facility modifications, and dfctiv pair rcovry. Includd in ths costs ar tax and dprciation ffcts. Dispatch Rpairs undr assumption 3 rgarding rhabilitation jobs, w apply th hazard function dscribd in assumption 1, q (1). W stimat th currnt hazard rat as th avrag dispatch rpair rat ovr th past 12 months. Facility Modifications through a rgrssion modl, w prdict th futur numbr of facility modifications basd on th currnt lvl of facility modifications, th dfctiv fill rat, and th growth in dmand for that ara. Dfctiv Pair Rcovry w only stimat th missd opportunity cost for providing srvic through a rcovrd pair if w xpct to us all xisting pairs for growing dmand in th ara. From th growth rat, w stimat whn w might nd th rcovrd pair. W also stimat th numbr of dfctiv pairs w might rcovr, and stimat th bnfit w xpct to rciv from th rcovrd pair in th futur. This is our lost opportunity cost. W normaliz ths costs for ach major typ of outsid plant quipmnt basd on th numbr of customrs affctd, and th amount of that typ of quipmnt w xpct to impact. Th first basis maks fair th comparisons btwn units of plant. Th scond basis maks fair th comparisons btwn th typs of quipmnt in th plant. Th scond cut in th nginring procss diffrs from th first in two important ways: What is compard in th scond phas, nginrs hav xamind th costs for th typs of quipmnt in th unit of plant, and hav nginrd work. In th scond cut, w compar th impact from th work proposd in ach unit of plant. Basis for comparison in th scond phas, nginrs hav stimatd th cost of th rhabilitation work, and improvd th stimats of RF 99RM-067: pag 4 RF

5 th impact w xpct. In th scond cut, w compar th rhabilitation jobs basd on th nt prsnt valu, instad of nt prsnt cost, ovr an assumd horizon. Th dcision support systm w ar constructing must facilitat th futur changs w plan. Svral paramtrs in ths modls nd to b updatd priodically. For xampl, w must updat th cost of capital, corporat tax rat, and th hazard function. This is an advantag bcaus it allows for a robust modl. As w obtain bttr information about th impact on various plant componnts and cost catgoris, w can improv our cost stimats in th modls, and provid mor accurat comparisons. W hop to improv our modls as w captur nw information. For xampl, considr our modl for facility modifications. W hop to compar stochastic procss modls to our rgrssion modl, and improv our prdiction of futur facility modifications. Our dsir to srv customrs motivats us to tackl our givn constraints, which ar typical in many industris. Whil w work to rliv som of th data limitations, w hav immdiat nds to cost-ffctivly maintain our coppr outsid plant. Through undrstanding th failur mchanisms and crating modls to support cost-bnfit dcisions, w hav lvragd our maintnanc dollars and cratd a framwork for futur improvmnts. ACKNOWLEDGMENT This work is succssful and maningful du to th hard work of Michll Vig and Lisa Ruiz, and th sponsorship of Kn Marcott. I thank Randy Lutz, Dick Hwitt, and Laura Stanly for hlping to initiat this work. REFERENCES 1. D. McCarty, G. Hoopr, Th Fin Art of Fault Locating, 1989; abc TlTraining, Inc. 2. G.W. Augnbaugh, H.T. Stump, Th Facility Analysis Plan: Nw Mthodology for Improving Loop Plant Oprations, BSTJ, vol 57, no 4, 1978 Apr, pp Jason W. Rup, PhD U S WEST Advancd Tchnologis 4001 Discovry Driv Bouldr, Colorado USA BIOGRAPHY Jason Rup compltd th BS and MS dgrs from Iowa Stat Univrsity in Industrial Enginring. Aftr transfrring to Txas A&M Univrsity, h rcivd th PhD in Industrial Enginring undr an Oprations Rsarch program. In acadmia, h conductd rsarch in command and control, communication and information ntwork prformanc modling, prformability modling of flxibl systms, and tool changing problms. H now works at U S WEST Advancd Tchnologis as a mmbr of th Mathmatical and Statistical Modling Group. H acts as in intrnal consultant to oprations problms, focusing on rliability issus. H oftn applis th skills of rliability, stochastic procsss, and statistics to U S WEST problms. H is a mmbr of IEEE and IIE. RF 99RM-067: pag 5 RF

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