Plan compliance process for underground coal mines


 Clifford Harrington
 4 months ago
 Views:
Transcription
1 Pln complince pocess fo undegound col mines by A.A. Angelov* nd K. Nidoo* J o u n l Synopsis This ppe pesents unique method of monitoing the effectiveness of the plnning pocess s well s the execution of mine plns. The method pimily detemines the degee of devition fom the oiginl mine plns by comping ctul mined es to initilly plnned mining es. The pefomnce of mining opetions is lso mesued by comping ctul nd plnned tonnges fo pticul peiod. Once the degee of devition fom mine plns hs been estblished the cuse/s of the devition cn be detemined though simple fult tee nlysis. Accute identifiction of the esons of devition cn id the mine in selecting possible methods to coect the devition. It is, howeve, beyond the scope of this ppe to discuss the methods employed in coecting such devitions, s ech mining opetion will hve unique cuses of pln devition nd methods of emedying them. Devitions fom the pln getly ffect the yields obtinble, which in tun ffects the life of mine, thus hving negtive economic nd finncil implictions. Accodingly, this ppe pesents poject mngement method which ims to educe isk by impoving plnning systems to ensue optimum ovell extction of col eseves. Intoduction Col mining is cpitl intensive, high volume business in which the efficient mngement of lgescle excvtion, pocessing nd tnspot ctivities is citicl to economic pefomnce (Scott, 2004). In ecent yes consume demnd fo low enegy pices nd incesed competition fom ltente enegy souces hve esulted in the decline of theml col pices in el tems (Mohing, 2001). In ode fo col to etin its sttus s pefeed enegy souce, it must be deliveed to the custome t n ffodble pice. To combt this decline in theml col pices, poduces must impove poductivity to educe thei poduction costs (Mohing, 2001). Plnning is essentil in ll mining opetions to ensue the optiml ovell extction of col eseves. Mine plnning is dependent not only on the qulity of the geologicl infomtion suppoting the pln but lso on the ctul pmetes equied fo execution of tht pln. These pmetes could nge fom equipment vilbilities nd utiliztion to geotechniclly elted inteuptions, plnt thoughput tes nd extenl mket influences (Osbone, 2007). The success of ny mining compny ests in its bility to effectively mnge cpitl investment so s to ensue cceptble stkeholde etuns within n ovell sttegic context (Smith et l., 2006). Complince with mine plns is fundmentl to the poject mngement pocess nd theefoe it is impotnt to monito ny devition fom mine plns nd effectively emedy the sitution if possible. In ecent yes the emphsis hs been on the quntifiction of col ecovey though the vlue chin, s shown in Figue 1. This pocess, known s econcilition, ttempts to mesue the poduction pefomnce in mining opetions by tcking the flow of col though the vlue chin between the col in situ nd the point of sle (Scott, 2004). The econcilition pocess cn evel the effectiveness of the plnning ssumptions nd opetionl pefomnce thus mesuing how effectively the col esouce is being utilized. This pocess, howeve, does not monito whethe mining opetions e cied out ccoding to the poposed plns. The method pesented in this ppe, known s pln complince, ims to compe ctul mining pctice to the ppoved mine plns fo specific time. The pln complince mesuement is n impotnt function in minel extction nd pocessing s it mesues the pecision of the estimtion nd opeting pocedues (Osbone, 2007). This pocess is lso vluble tool fo ssessing cuent mining pctices nd povides guidnce on whee impovements cn be * Univesity of Petoi, South Afic. The Southen Aficn Institute of Mining nd Metllugy, SA ISSN X/ Ppe eceived Oct. 2008; evised ppe eceived Feb P p e The Jounl of The Southen Aficn Institute of Mining nd Metllugy VOLUME 110 NONREFEREED PAPER MAY
2 Pln complince pocess fo undegound col mines THE THE COAL VALUE HAIN Envionment Soucing nd blending Discds Blending Emissions (Kyoto Potocol) Explotion Mine Plnning Mining Col peption Expot stockpile Impot stockpile Use Geologicl dt bse Plnning dt bse Poduction dt bse Mine stockpile Use stockpile Ash Coe vlue chin Knowledge/ dt bse Feedbck loop Poduct qulity dt bse Tnspot Col poduces need to develop focus fom explotion to combustion. They must intoduce nd exploit lening loops to the benefit of themselves nd thei uses Souce: SAIMM (The Southen Aficn Institute of Mining nd Metllugy) Figue 1 The col vlue chin (Moley et l., 1999) mde. Poductivity enhncements should be sought thoughout the entie col vlue chin, stting with explotion though to the ultimte convesion (Mohing, 2001). Pln complince cn be used fo ssisting the mine in identifying nd mnging the potentil impcts ssocited with devitions fom the ppoved plns. The pln complince mesuement should not be confused with esouce econcilition. It must be stted tht it is not substitute fo esouce econcilition but the is intended to enhnce the econcilition of esouces (Osbone, 2007). Mine plnning pocess The plnning pocess is concened with the physicl exposue of col in given peiods nd t specific qulities nd tonnges. It is theefoe impetive tht thee is cle undestnding of the isks ssocited with the specific loctions of col tonnges nd qulities, since they vy sptilly coss the col esouce (Steffen, 1997). Steffen (1997) descibes thee distinct levels of plnning: life of mine pln, longtem pln, nd shottem pln, ech closely intelinked nd epesenting diffeent level of isk. In the life of mine (LOM) pln the mineble col eseve is defined togethe with equied infstuctue nd cpitl costs. Effots duing this stge e imed solely t educing costs. The longtem pln (LTP), mking use of the estblished eseves nd mining boundies, ims to develop n opeting nd mining sttegy. The objectives of this sttegy e to mximize vlue nd minimize isk fo investos while t the sme time to mximize the life of mine. These objectives seem to be contdictoy since mximum NPV cnnot coespond to minimum isk o mximum life. The LTP should be constucted in such wy tht suitble compomise between the objectives is eched (Steffen, 1997). Steffen (1997) sttes tht shottem plnning (STP) pplies to oneye peiod within single business cycle nd is concened pimily with the dytody scheduling of gde to the plnt nd poduction equiements fo the fist 12 to 18 months of the LTP. Shottem plnning hs s its mjo objectives: Gde contol Cost contol Equipment utiliztion Cpitl poductivity Lbou poductivity. As mentioned elie, the pln complince method ssesses the effectiveness of the plnning nd scheduling pocess s well s mining pefomnce. Fo effective contol of ny pocess, the inputs nd outputs must be clely defined nd mesuble (Osbone, 2007). Mine plnning is dependent on numbe of pmetes, nmely: Geologicl nd geotechnicl dt Mining method selected Equipment nd degee of mechniztion Efficiency of pocessing plnt Economics, mket conditions, nd othe fctos. Ech of the bove plnning pmetes contins cetin degee of uncetinty, which incopotes level of isk within the mine plnning pocess. Risks ssocited with plnning e elted to the confidence which pplies to the minel esouce (geology nd gde distibution), the mining pln (geotechnicl), nd the business ssumptions (pice fluctutions). These isks cn be ddessed by impoving infomtion in the cse of the fist two nd by poviding flexibility within the pln in the cse of the ltte, but the isk cn neve be edicted (Steffen, 1997). Yield contol Detemining the economic life of mine fo minel esouce is key decision vible duing the plnning pocess. The LOM is mostly diven by the te of extction (Smith et l., 2006). It is theefoe petinent tht n optimum extction sttegy is selected encompssing the entie esouce. In ode to ensue tht n optiml mine extction sttegy is selected, the plnned yield ove the LOM must be stictly dheed to. Yield contol efes to the pctice of extcting col t cetin plnned yield so tht the optiml LOM cn be chieved. Yield in this context efes to the popotion of plnt poduct tonnes to feed tonnes into the plnt. The feed to plnt tonnes is the poduction tonnes fom undegound. Yield cn be simply epesented s follows: 242 MAY 2010 VOLUME 110 NONREFEREED PAPER The Jounl of The Southen Aficn Institute of Mining nd Metllugy
3 Pln complince pocess fo undegound col mines [1] Steffen (1997) stted tht n undestnding of the gde distibution nd tonnge distibution of the totl esouce is pivotl to developing pope mine pln since the life of the mine is sensitive only to the mining sttegy o gde utiliztion, which is the scheduled mill hed gde nd the development costs. In ode to undestnd the concept of yield contol, some explntoy notes bout gde contol e descibed in the next two pgphs. Gde contol is key plnning objective in the hd ock mining industy. Gde contol is the pocess by which mineble unit is deemed to be bove o below cetin cutoff gde (Binsden, 1991). Hd ock mine pesonnel e ll too fmili with the concept of gde contol nd e we tht stict gde contol cn mximize the vlue of the oe mined nd fed to the mill. A gold o pltinum mine s sensitivity to gde is usully much gete thn ny othe fcto (Binsden, 1991). The concept of gde contol ws modified to suit the col mining industy since the gde of col esouce would efe to col clssifiction bsed on degee of puity, which is the quntity of inognic mteil o sh left fte buning. Mine pesonnel t col mine do not mesue gde nd tonnge but insted mesue yield nd tonnge, since cetin btch of col would be sent to the wsh plnt fte which pecentge would be discded nd the emining potion sold s theml stem col to the inlnd o expot mket. Gde contol in the hd ock mining context is equivlent to yield contol in the col mining context since both ffect the finl sleble poduct. opetions s they e plnned. Recods of plnned nd ledy minedout mining blocks e stoed within the dtbse (Steynfd et l., 2003). The outputs of the XPAC plnning model consist of monthly plnned mining es. These es e deived fom ppoved twoye nnul plns. The fist shot nge foecst pln (SRF) is detemined six months pio to mining, nd will be efeed to s the budget pln. The ltest estimte pln (LE), which is detemined one month pio to mining, is n updted vesion of the budget pln nd incopotes the most uptodte infomtion fo the peiod in question. The pln complince pocess will be detemined fo both the budget nd ltest estimte plns. The budget nd LE es cn be expoted fom XPAC to compute ided design (CAD) pogm, such s MicoSttion, whee the budget nd LE es cn be visully comped to the ctul mined es. Figue 2 shows gphicl epesenttion of the budget (ed, blue nd geen blocks) es of specific sections in the mine s well s the LE es (blck blocks) nd ctul mined es fo single month. Once the plnned nd ctul mining es hve been inteposed the e(s) of ovelp (pink block) cn be detemined. This e of ovelp consists of the ctul mined e which flls within the budget nd LE plnned es. Tble I gives the bbevited nmes of the diffeent es s well s shot desciption. J o u n l P p e Pln complince pocess Befoe the pln complince pocess cn be pesented it is necessy to fist explin the poduction plnning nd scheduling pctices s well s the compute softwe used. These pctices vy in detil fom one mine site to nothe mine site, but they ll contin simil steps. Initil explotion dt e stoed in dtbse nd geologicl model is developed to estimte the in situ col quntities nd qulities within the poposed mining boundy. This model is the best vilble desciption of the col to be mined nd the poducts it will yield, pio to mining nd pocessing tking plce (Scott, 2004). The plnning pmetes togethe with the dt fom the geologicl model e used to identify likely mining es using plnning model. All plnning nd scheduling e done though pogm clled XPAC Auto Schedule, which is mine plnning nd scheduling softwe system developed by Runge Mining in Austli (Steynfd et l., 2003). XPAC is softwe ppliction developed fo foecsting, eseve dtbse nd mine scheduling mngement. The dtbse functionlity of the pogm mkes it simple to impot in situ dt petining to the qulity of the col eseves nd the mount of tonnes vilble. These dt e nlysed within XPAC to detemine suitble mining es. It is the esponsibility of the pogm opeto to schedule mining es in such wy tht n optiml yield is chieved thoughout the LOM. Finl schedules cn be epesented gphiclly. Peiod pogess plots depict the mining Figue 2 Gphicl compison of budget, LE nd ctul mined es Tble I Abbevition nd desciption of es used in the complince clcultions Abbevition Budget LE Actul Act/budget Act/LE Desciption Initilly plnned mining e (6 months pio to mining of tht e) Plnned mining e (1 month pio to mining of tht e) Actul mined e Actul mined e tht fell within the budget mining e Actul mined e tht fell within the LE mining e The Jounl of The Southen Aficn Institute of Mining nd Metllugy VOLUME 110 NONREFEREED PAPER MAY
4 Pln complince pocess fo undegound col mines Mining pefomnce Plnt pefomnce Physicl conditions Geogphicl Complince C1 Tonnes Complince C2 Equipment utiliztion Qulity of geologicl infomtion Actul mined es Pln Pefomnce P1 Figue 3 Inputs nd outputs of the plnning nd pln complince pocess Once the espective es of compison e obtined pln complince cn be detemined by clculting the complince metics. The fomule used fo the detemintion of the complince metics e bsed on the es descibed in Tble I. Figue 3 illusttes the diffeent inputs nd outputs of the plnning nd pln complince pocesses. Figue 4 is detiled desciption of the diffeent steps followed in the pln complince pocess. It must be noted tht the metic pln pefomnce P1 is not dependent on the clcultions of the othe two metics nd is plced lst in Figue 4 to show logicl ode of the pocess. Assumptions The quntity of col ctully mined fom the plnned e (Act/Budget) is clculted ssuming tht the eltive density (RD) nd vege mining height fo this e is the sme s tht of the entie ctul mined e fo ech section. This ssumption llows us to pply the following esoning in ode to clculte the unknown quntities of tonnes. To clculte tonnes the following fomule e used. [8] Sptil complince C1 This is the ctul mined e enclosed in the plnned e comped to the totl plnned e fo given time peiod. [2] Clculte es of plnned nd ctul col extction Clculte plnned mining es (m2) (budget nd LE) Clculte ctul mining es (m2) Clculte ctul mining es (m2) within budget nd LE es Expot plnned mining blocks fom XPAC to MicoSttion V8 Softwe Input month end suvey dt into MicoSttion V8 Softwe Tonnes complince C2 This is the quntity of col ctully mined fom the plnned e, comped to the totl quntity of col contined in the plnned mining e fo given peiod. [3] [4] Clculte ctul col tonnes mined fom plnned es Detemine geogphicl complince metics C1 Obtin ctul mined tonnes Obtin budget tonnes Clculte ctul tonnes within budget nd LE es Input finl suveyed tonnes Input budget tonnes fom XPAC Clculte LE tonnes Obtin LE tonnes fom XPAC Pln pefomnce P1 This is the totl quntity of col mined comped to the plnned quntity of col to be mined fo given peiod. [5] [6] [7] Figue 4 Pln complince pocess Detemine col tonnes complince metics C2 Detemine pln pefomnce P1 Detemine cuse of devitions Remedy poblem if possible 244 MAY 2010 VOLUME 110 NONREFEREED PAPER The Jounl of The Southen Aficn Institute of Mining nd Metllugy
5 Pln complince pocess fo undegound col mines whee The following cn thus be concluded: Ae A = Act/Budget, Act/LE Ae B = Totl Actul e [9] [10] Eqution [10] is tue only if the Kfcto fo both es is equl. In the cse fo the Act/Budget nd Act/LE tonnes this is ptilly tue since Ae A is enclosed by Ae B, nd the potion of ovelp hs ppoximtely the sme Kfcto s the totl e. Mining dynmics pln complince The pln complince pocess is simple enough to be pogmmed in Micosoft Excel. The disdvntge of this ppoch is tht the ctul mined es must be mnully detemined in Bentley s MicoSttion fist befoe being impoted into Excel. XPAC dt e esy to impot into Excel; howeve, some dt soting pio to the clcultion will need to be pefomed. Detemintion of the pln complince fo pticul month cn tke sevel hous thus becoming n duous pocess. To solve the poblem of inefficiency Runge hve developed Mining Dynmics. Mining Dynmics is built using open stndds nd cn opete in both 2D nd 3D envionments. The dvntge of Mining Dynmics is tht it cn esily econcile dt fom numbe of diffeent softwe pckges, considebly speeding up the pocess of pln complince. As mentioned elie, opeting mines use one softwe pckge fo thei plnning nd scheduling execise (XPAC) nd nothe to pocess nd stoe its suvey dt (Bentley s MicoSttion). Mining Dynmics utomticlly ccesses the input pln (plnned dt) nd suvey dt (ctuls dt) nd outputs the pln complince esults in timely mnne bck into the poduction cycle. The esults e not only pesented in tbul fomt but lso in visul fom, s shown in Figue 2. Tble II Undegound sections, sem type, nd vege mining height Sem Avege mining height Section 7 No m Section 11 No m Section 30 No m Section 32 No m Section 35 No m Section 36 No m Section 38 No m Figue 5 Pecentge of tonnes mined fom the espective sems J o u n l P p e Degee of devitions The pln complince pocess ws pplied t Dougls Colliey, col mine locted in the Witbnk colfields. Duing the time of the study the mine ws poducing 8.5 million tonnes of sleble col, pe nnum, fom both undegound nd open pit opetions. It supplied its poducts into the expot, nd inlnd col nd sluy mkets. The complince clcultions wee pplied only to the undegound sections mining the No.1, 2 nd 4 sems, s shown in Tble II. The mjoity of the tonnes wee mined fom the No. 2 sem, s shown in Figue 5. The mine used fully mechnized bod nd pill method to extct the col fom undegound. Dougls Colliey commenced mining opetions in 1898 nd the undegound potion of the mine closed t the end of As mine nes the end of its life, col eseves become scce, focing the mine to econside es peviously thought to be too difficult to mine. These es e usully ne the mine boundy nd e enowned fo poo geologicl conditions. The esults fom the pln complince Figue 6 Pln complince metics fo the budget pln Figue 7 Pln complince metics fo the LE pln The Jounl of The Southen Aficn Institute of Mining nd Metllugy VOLUME 110 NONREFEREED PAPER MAY
6 Pln complince pocess fo undegound col mines pocess e shown in Figue 6 nd Figue 7. The esults obtined show tht complince with the budget pln is less thn 10% fo both e nd tonnes. This mens tht ppoximtely 90% of the mining ctivities duing the fou months fom July to Octobe 2007 wee occuing in es tht wee not plnned six months pio to mining. The vege pln pefomnce, which is n indiction of the quntity of col plnned nd ctully mined, is well ove 100% fo the fist qute. This is n indiction tht moe tonnes of col wee mined thn ws ctully plnned six months pio to mining tht specific e. The esults fo the ltest estimte pln, Figue 7, show slight impovement in pln complince but decese in pln pefomnce. The pln complince is ppoximtely 50% fo e nd tonnes. These esults evel tht lmost hlf of the mining pctices occued in es not initilly plnned fo one month pio to mining of those es. The pln pefomnce fo the LE pln is not only lowe but shows gdul decese. This is conty to the esults obtined duing the budget pln pefomnce. It indictes tht cuent poduction levels e behind if comped with the ltest estimte pln but hed if comped to the budget pln. Cuse of devitions Once the esults fom the pln complince pocess hve been clculted they must be intepeted. The intepettion of the esults will ssist the mine in detemining the undelying esons fo ny devitions. Devitions fom pln eitete the fct tht mining is high isk business. A iskconsequence ppoch to pln complince is essentil in defining the isk citei s it enbles mine plnnes to tke ccount of the specific consequences of devitions fom pln (Tebugge et l., 2006). A pln complince isk scenio tble shown in Tble III is combintion of C1, C2 nd P1 metics tht cn occu in the execution of pln. The combintions e nged in eltion to the mgnitude of the negtive impct on the LOM nd col eseve utiliztion. The e of the sque blocks epesents the e of pln complince. The level of isk inceses with educed e of complince. It should be noted tht fo scenios 2 to 5, vible mining height nd vible col density cn hve n influence on the col Tble III Pln complince isk scenios 246 MAY 2010 VOLUME 110 NONREFEREED PAPER The Jounl of The Southen Aficn Institute of Mining nd Metllugy
7 Pln complince pocess fo undegound col mines mining esults. An incese in ny of the two fctos cn esult in n incese in both the C2 nd P1 metics. The pocess of detemining the cuse of devition fom plns needs to incopote ll the possible es which cn ffect the complince to given pln. To detemine the exct cuse of devition fult tee nlysis cn be used. Poposed fult tee nlysis digms fo the thee metics e shown by Figues 8, 9, nd 10. Detemining the cuse of devition fom mine plns cn become difficult nd timeconsuming ctivity since in most cses multiple esons fo deviting fom mine plns e possible. The mjo spects ffecting the chievement of mine plns e illustted in Figue 11. A few of the mjo cuses of devition which hve been identified though undegound visits nd obsevtions will be discussed futhe. Geologicl uncetinty The geologicl discipline is one of mny disciplines on the mine which opete within conditions of uncetinty. Uncetinty bout geologicl discontinuities, chnges in sem thicknesses, nd col qulities e just few souces of uncetinty ffecting the chievement (o nonchievement) of the mine pln (Tebugge et l., 2006). The mjo cuse of devition fom the pln is due to negotition of smll geologicl fetues tht cuse cetin distubnce, mking it difficult nd t times impossible fo J o u n l P p e Figue 8 Fult tee nlysis of geogphicl complince C1 Figue 9 Fult tee nlysis of tonnes complince C2 The Jounl of The Southen Aficn Institute of Mining nd Metllugy VOLUME 110 NONREFEREED PAPER MAY
8 Pln complince pocess fo undegound col mines Figue 10 Fult tee nlysis of pln pefomnce P1 Geology Public elltions Mine pln Humn esouces Achievement of mine plns Opetions Geotechnicl Mco econimics Qulity Assunce (Mngement) Figue 11 Souces of uncetinty ffecting the chievement of mine plns (Tebugge et l., 2006) mining. In most cses these geologicl fetues e not intesected duing pospecting o tetiy dilling, nd would not ppe on the oiginl mine plns. Anothe eson fo the bsence of cetin geologicl fetues cn be s esult of specific pospecting needs which t the time did not include the full extent of ll the possible mineble col sems. It is common pctice in mines tht when dyke o fult is encounteed on pticul sem it is extpolted to othe colsems, which e mining o going to mine in the e of the geologicl fetue. The pinciple of extpoltion ssumes tht geologicl fetues e fily continuous. If these fetues e isolted to specific sem they would not ppe on plns nd would not extend to djcent colsems incesing the level of geologicl uncetinty. Mining pctices Devitions fom pln e lso esult of the inefficiencies of the mining ctivities. Any devitions fom the selected mining hoizon will esult in vibility in mining height. In most cses ovemining will tke plce. Consequently this will esult in eduction in yield vlues nd n incese in col density, s shown in Figue 12. The effect of incesed mining height nd density is seen in the vition between the C1 nd C2 metics. In pinciple C1 should be equl to C2 if the plnned mining hoizon is mintined, but esults show tht this is seldom the cse. The numbe of tonnes clculted fom specific e is bsed on the eltive density of col, the extent of the e, nd the mining height. Since both density nd mining height incese, with the ltte hving gete ffect, moe tonnes will be mined fom pticul e. Thus the C2 metic will be highe thn the C1 metic when the plnned mining height hs been exceeded. The C1 metic will emin unffected by chnges in height o density since it is n e metic. Opetionl devitions Opetionl devitions such s ventiltion poblems, oof flls, ftlities o ccidents nd unplnned equipment downtime would hve negtive effects on pln complince. 248 MAY 2010 VOLUME 110 NONREFEREED PAPER The Jounl of The Southen Aficn Institute of Mining nd Metllugy
9 Pln complince pocess fo undegound col mines J o u n l Figue 12 Result of ovemining on ctul density nd yield P p e Figue 13 Totl monthly plnned nd ctul yields fo Octobe 2007 Poo mchine utiliztion such s excessive tmming, fequent eplcement of CM picks nd slow cble extension time lso effect complince with the pln. Softwe pogm The mine plnne esponsible fo opeting the XPAC softwe lso plys cucil ole in chieving high level of pln complince. If the XPAC model is slightly incomplete in tems of djustment fctos nd cetin dilution effects, it would yield pln tht is esily susceptible to devition s esult of lck of dt built into the model. To compound this poblem futhe, ny inexpeience fom the plnne in mnipulting the XPAC model to ccommodte cetin vibles tht my influence the poduction nd ultimtely the LOM could esult in lge nd continuous devitions fom the plns poduced in XPAC. Adjustment fctos nd vibles should be eviewed on continuous bsis in ode to detemine whethe they e elevnt to cuent mining pctices. Effects of devitions The devition fom the ppoved mine pln hs the effect of lteing the plnned yield. The finl ctul yield cn be eithe highe o lowe thn the initil plnned yield. In most cses the fome sitution is pevlent. Figue 13 shows the diffeence in plnned nd ctul yields fo ech section in single month. A highe thn expected ovell yield obtined t pesent would esult in lowe futue yield vlue. Given tht thee is cetin degee of uncetinty in mket conditions 30 to 40 yes in the futue, lowe thn expected yield cn lowe pedicted pofits, potentilly ceting unfesible mining opetions. Ovepoduction of col will deplete the col eseve t highe te thn initilly plnned thus loweing the LOM. Moe col now will men less col in the futue if the initil LOM is to be mintined. If the te of poduction is not educed nd is llowed to continue bove the plnned te, the LOM will be shotened considebly. Conclusions Mintining high degee of pln complince is beneficil s well s pofitble to mine s it ensues optiml utiliztion of the col eseve thoughout the plnned LOM. A high level of pln complince is indictive of good contol of the mining opetion fom the conceptuliztion of the pln to its finl execution. Devitions fom plns e inevitble but continuous updting of the pln s esult of unfoeseen cicumstnces will educe the vition between the plnned nd ctul mining opetion. The bsic pinciple in plnning The Jounl of The Southen Aficn Institute of Mining nd Metllugy VOLUME 110 NONREFEREED PAPER MAY
10 Pln complince pocess fo undegound col mines is to ttempt to mio futue mining conditions undegound bsed on both pevious nd cuent cicumstnces. With n enhnced knowledge of wht s to come plnne cn set cetin djustment fctos tht eithe decese o incese poduction tes. The discipline of mines is lso necessy to ensue tht mining occus in the plnned es nd t the plnned tempo. The im of mining opetions is the optiml extction of col eseves. As mine nes the end of its life thee e economic nd socil pessues to extend the life of mine whee it is techniclly nd economiclly fesible. Pln complince is thus method which monitos the effectiveness of the shot nd longtem mine plnning systems s well s poduction pefomnce. A fult tee nlysis cn be used to detemine the cuse of devitions nd possible sttegies to emedy the poblems. Pln complince is theefoe method tht cn be used to impove the plnning systems nd educe the isk of the mining opetions. Acknowledgements This ppe is published by pemission of BHP Billiton Enegy Col South Afic (BECSA). The uthos expess thei gtitude to BECSA fo the suppot nd oppotunity to publish this ppe. M Get Vente of BECSA is gtefully cknowledged fo his contibution though thoough discussion. Refeences 1. BRINSDEN, W.K. Spotlight on gde contol. Fifth nnul semin of The Austlin Institute of Geoscientists Sttegies fo Gde Contol, Obsevtion City, Scboough, Peth, 15 Novembe pp MOHRING, R.P. Keynote Addess: Col mining the futue. J. South Af. Inst. Min & Metll, vol. 101, pp MORLEY, C. SNOWDEN, V., nd DAY, D. Finncil impct of esouce/eseve uncetinty. J. South Af. Inst. Min & Metll, vol. 99, pp OSBORNE, V. Pln Complince Mesuement Dft BMA Guideline. Intenl consultnt epot fo BHP Billiton Enegy Col South Afic SCOTT, A. BTRAK Guide: The BMA Wy fo Tcking nd Reconciling Col Recovey. Vesion 1. Intenl consultnt epot fo BHP Billiton Enegy Col South Afic SMITH, G.L., PEARSONTAYLOR, J., ANDERSEN, D.C., nd MARSH, A.M. Poject vlution, cpitl investment nd sttegic lignment tools nd techniques t Anglo Pltinum. Second Intentionl Pltinum Confeence Pltinum Suges Ahed, 8 12 Octobe pp STEFFEN, O.K.H. Plnning of open pit mines on isk bsis. J. South Af. Inst. Min & Metll, vol. 97, pp STEYNFAARD, D.J., LOUW, W.C., KOTZE, J., SMITH, J., nd HAVENGA, B.H.J. New developments on mine plnning nd gde contol t Sishen Ion Oe Mine. J. South Af. Inst. Min & Metll, vol. 103, pp TERBRUGGE, P.J., WESSELOO, J., VENTER, J., nd STEFFEN, O.K.H. A isk consequence ppoch to open pit slope design. J. South Af. Inst. Min & Metll, vol. 106, pp The Southen Aficn Institute of Mining nd Metllugy Founded in 1894 is ognising the 4th Intentionl Pltinum Confeence Pltinum in tnsition: Boom o Bust Sun City, South Afic, Octobe, 2010 Confeence Secetit Jcqui vn de Westhuizen, Hed of Confeencing The Southen Aficn Institute of Mining nd Metllugy P O Box 61127, Mshlltown, 2107, South Afic Tel: /7 Fx: o Web: 250 MAY 2010 VOLUME 110 NONREFEREED PAPER The Jounl of The Southen Aficn Institute of Mining nd Metllugy
GFI MilAchive 6 vs H&S Exchnge@PAM GFI Softwe www.gfi.com GFI MilAchive 6 vs H&S Exchnge@PAM GFI MilAchive 6 H&S Exchnge@PAM Who we e Genel fetues Suppots Micosoft Exchnge 2000, 2003 & 2007 Suppots distibuted
More informationHighest Pefomnce Lowest Pice PRODUCT COMPARISON GFI MilAchive vs Symntec Entepise Vult GFI Softwe www.gfi.com GFI MilAchive vs Symntec Entepise Vult GFI MilAchive 6 Symntec Entepise Vult Who we e Genel
More informationGFI EventsMnge vs Netikus.net EventSenty GFI Softwe www.gfi.com GFI EventsMnge vs Netikus.net EventSenty GFI EventsMnge EventSenty Who we e Suppot fo MS SQL Seve Suppot fo MSDE / MS SQL Expess Suppot fo
More informationGFI MilAchive 6 vs EMC EmilXtende Achive Edition GFI Softwe www.gfi.com GFI MilAchive 6 vs EMC EmilXtende Achive Edition GFI MilAchive 6 EMC EmilXtende Achive Edition Who we e Genel fetues Suppots Micosoft
More informationScreentrade Car Insurance Policy Summary
Sceentde C Insunce Policy Summy This is summy of the policy nd does not contin the full tems nd conditions of the cove, which cn be found in the policy booklet nd schedule. It is impotnt tht you ed the
More informationGFI MilAchive 6 vs Wtefod Technologies MilMete Achive GFI Softwe www.gfi.com GFI MilAchive 6 vs Wtefod Technologies MilMete Achive Genel fetues Suppots Micosoft Exchnge 2000, 2003 & 2007 Suppots distibuted
More informationN V V L. R a L I. Transformer Equation Notes
Tnsfome Eqution otes This file conts moe etile eivtion of the tnsfome equtions thn the notes o the expeiment 3 witeup. t will help you to unestn wht ssumptions wee neee while eivg the iel tnsfome equtions
More informationby K.H. Rutsch*, P.J. Viljoen*, and H. Steyn* The need for systematic project portfolio selection
An investigtion into the cuent pctice of poject potfolio selection in esech nd development division of the South Aficn minels nd enegy industy by K.H. Rutsch*, P.J. Viljoen*, nd H. Steyn* J o u n l Synopsis
More informationOrbits and Kepler s Laws
Obits nd Keple s Lws This web pge intoduces some of the bsic ides of obitl dynmics. It stts by descibing the bsic foce due to gvity, then consides the ntue nd shpe of obits. The next section consides how
More information(1) continuity equation: 0. momentum equation: u v g (2) u x. 1 a
Comment on The effect of vible viscosity on mied convection het tnsfe long veticl moving sufce by M. Ali [Intentionl Jounl of Theml Sciences, 006, Vol. 45, pp. 6069] Asteios Pntoktos Associte Pofesso
More informationSummary: Vectors. This theorem is used to find any points (or position vectors) on a given line (direction vector). Two ways RT can be applied:
Summ: Vectos ) Rtio Theoem (RT) This theoem is used to find n points (o position vectos) on given line (diection vecto). Two ws RT cn e pplied: Cse : If the point lies BETWEEN two known position vectos
More informationtools for Web data extraction
HTMLwe tools fo Web dt extction Thesis pesenttion 1 Student: Xvie Azg Supeviso: Andes Tho Tble of contents Intoduction Dt Extction Pocess Dt Extction Tools Relized tests Futue Wok 2 Intoduction We e going
More informationGFI MilEssentils & GFI MilSecuity vs Tend Mico ScnMil Suite fo Micosoft Exchnge GFI Softwe www.gfi.com GFI MilEssentils & GFI MilSecuity vs Tend Mico ScnMil Suite fo Micosoft Exchnge Exchnge Seve 2000/2003
More informationThe strategic and tactical value of a 3D geotechnical model for mining optimization, Anglo Platinum, Sandsloot open pit
The sttegic nd tcticl vlue of 3D geotechnicl model fo mining optimiztion, Anglo Pltinum, Sndsloot open pit by A. Bye* J o u n l Synopsis Sndsloot open pit is situted on the nothen limb of the Bushveld
More informationRandom Variables and Distribution Functions
Topic 7 Rndom Vibles nd Distibution Functions 7.1 Intoduction Fom the univese of possible infomtion, we sk question. To ddess this question, we might collect quntittive dt nd ognize it, fo emple, using
More informationGFI MilEssentils & GFI MilSecuity vs Bcud Spm Fiewll GFI Softwe www.gfi.com GFIMilEssentils & GFI MilSecuity vs Bcud Spm Fiewll GFI MilEssentils 12 & GFI MilSecuity 10 Bcud Spm Fiewll Who we e Integtes
More informationGFI MilEssentils & GFI MilSecuity vs Symntec Bightmil 6 & Anti Vius GFI Softwe www.gfi.com GFI MilEssentils & GFI MilSecuity vs Symntec Bightmil 6 & Anti Vius GFI MilEssentils & GFI MilSecuity Bightmil
More informationAdaptive Control of a Production and Maintenance System with Unknown Deterioration and Obsolescence Rates
Int J of Mthemtic Sciences nd Appictions, Vo, No 3, Septembe Copyight Mind Rede Pubictions wwwjounshubcom Adptive Conto of Poduction nd Mintennce System with Unknown Deteiotion nd Obsoescence Rtes Fwzy
More informationLaplace s Equation on a Disc
LECTURE 15 Lplce s Eqution on Disc Lst time we solved the Diichlet poblem fo Lplce s eqution on ectngul egion. Tody we ll look t the coesponding Diichlet poblem fo disc. Thus, we conside disc of dius 1
More informationIntro to Circle Geometry By Raymond Cheong
Into to Cicle Geomety By Rymond Cheong Mny poblems involving cicles cn be solved by constucting ight tingles then using the Pythgoen Theoem. The min chllenge is identifying whee to constuct the ight tingle.
More informationCharacteristics of an effective selfdirected work team in the goldmining industry
Chcteistics of n effective selfdiected wok tem in the goldmining industy by A. Nel* nd J. Pien* J o u n l Synopsis The gold mining industy in South Afic stnds to benefit much fom the implementtion of
More informationImplementation and Evaluation of Transparent FaultTolerant Web Service with KernelLevel Support
Poceedings of the IEEE Intentionl Confeence on Compute Communictions nd Netwoks Mimi, Floid, pp. 6368, Octobe 2002. Implementtion nd Evlution of Tnspent FultTolent Web Sevice with KenelLevel Suppot
More information(Ch. 22.5) 2. What is the magnitude (in pc) of a point charge whose electric field 50 cm away has a magnitude of 2V/m?
Em I Solutions PHY049 Summe 0 (Ch..5). Two smll, positively chged sphees hve combined chge of 50 μc. If ech sphee is epelled fom the othe by n electosttic foce of N when the sphees e.0 m pt, wht is the
More informationr (1+cos(θ)) sin(θ) C θ 2 r cos θ 2
icles xmple 66: Rounding one ssume we hve cone of ngle θ, nd we ound it off with cuve of dius, how f wy fom the cone does the ound stt? nd wht is the chod length? (1+cos(θ)) sin(θ) θ 2 cos θ 2 xmple 67:
More informationInstope bolting for a safer working environment
text:templte Jounl 2/3/10 9:34 AM Pge 47 Instope bolting fo sfe woking envionment by P. Henning* nd P. Feei* J o u n l Synopsis Rock fll ccidents continue to be the min cuse of ftl nd seious injuies in
More informationThe preparation of activated carbon from South African coal
The peption of ctivted cbon fom South Aficn col by Q.P. Cmpbell*, J. R. Bunt*, H. Ksini, nd D.J. Kuge* J o u n l Synopsis Activted cbons used in the pecious metls extction industy e chcteized by lge intenl
More informationHousing as a Commodity
Housing Issues nd Policy, Ubn Studies Pogmme, CUHK URSP300 Housing s Commodity by D Edwd CY Yiu Associte Pofesso Dept of Geogphy nd Resouce Mngement, Chinese Univesity of Hong Kong Expected Outcomes Wht
More informationSoftware Engineering and Development
I T H E A 67 Softwae Engineeing and Development SOFTWARE DEVELOPMENT PROCESS DYNAMICS MODELING AS STATE MACHINE Leonid Lyubchyk, Vasyl Soloshchuk Abstact: Softwae development pocess modeling is gaining
More informationCurvature. (Com S 477/577 Notes) YanBin Jia. Oct 8, 2015
Cuvtue Com S 477/577 Notes YnBin Ji Oct 8, 205 We wnt to find mesue of how cuved cuve is. Since this cuvtue should depend only on the shpe of the cuve, it should not be chnged when the cuve is epmetized.
More informationExam in physics, Elgrunder (Electromagnetism), 20140326, kl 9.0015.00
Umeå Univesitet, Fysik 1 Vitly Bychkov Em in physics, Elgunde (Electomgnetism, 146, kl 9.15. Hjälpmedel: Students my use ny book(s. Mino notes in the books e lso llowed. Students my not use thei lectue
More informationClearPeaks Customer Care Guide. Business as Usual (BaU) Services Peace of mind for your BI Investment
ClerPeks Customer Cre Guide Business s Usul (BU) Services Pece of mind for your BI Investment ClerPeks Customer Cre Business s Usul Services Tble of Contents 1. Overview...3 Benefits of Choosing ClerPeks
More informationFatigue knowledge a new lever in safety management
text:templte Jounl 1/20/11 12:43 PM Pge 1 Ftigue knowledge new leve in sfety mngement by W.J. Theon* nd G.M.J. vn Heeden J o u n l Synopsis The pupose of the ppe is to give n intoduction to the concept
More informationr Curl is associated w/rotation X F
13.5 ul nd ivegence ul is ssocited w/ottion X F ivegence is F Tody we define two opetions tht cn e pefomed on vecto fields tht ply sic ole in the pplictions of vecto clculus to fluid flow, electicity,
More informationG.GMD.1 STUDENT NOTES WS #5 1 REGULAR POLYGONS
G.GMD.1 STUDENT NOTES WS #5 1 REGULAR POLYGONS Regul polygon e of inteet to u becue we begin looking t the volume of hexgonl pim o Tethedl nd to do thee type of clcultion we need to be ble to olve fit
More information2.016 Hydrodynamics Prof. A.H. Techet
.016 Hydodynmics Reding #5.016 Hydodynmics Po. A.H. Techet Fluid Foces on Bodies 1. Stedy Flow In ode to design oshoe stuctues, suce vessels nd undewte vehicles, n undestnding o the bsic luid oces cting
More informationMarketing Logistics: Opportunities and Limitations
Mketig Logistics: Oppotuities d Limittios Pethip Vdhsidhu 1, Ugul Lpted 2 1 Gdute School, MBA i Itetiol Busiess, The Uivesity of the Thi Chmbe of Commece VibhvdeeRgsit Rod, Dideg, Bgkok, 10400, Thild
More informationSOEPpapers on Multidisciplinary Panel Data Research
Deutsches Institut fü Witschftsfoschung www.diw.de SOEPppes on Multidiscipliny Pnel Dt Resech 136 Thoms Conelissen John S. Heywood Uwe Jijhn S, Pefomnce Py, Risk Attitudes nd Job Stisfction Belin, Octobe
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationTitanium: the innovators metal Historical case studies tracing titanium process and product innovation
Titnium: the innovtos metl Histoicl cse studies tcing titnium pocess nd poduct innovtion by S.J. Oosthuizen* J o u n l Synopsis This ppe exmines innovtion in eltion to the vilbility of new mteil: the metl
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationHealth insurance exchanges What to expect in 2014
Helth insurnce exchnges Wht to expect in 2014 33096CAEENABC 02/13 The bsics of exchnges As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum mount
More informationDlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report
DlNBVRGH + + THE CITY OF EDINBURGH COUNCIL Sickness Absence Monitoring Report Executive of the Council 8fh My 4 I.I...3 Purpose of report This report quntifies the mount of working time lost s result of
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationHealth insurance marketplace What to expect in 2014
Helth insurnce mrketplce Wht to expect in 2014 33096VAEENBVA 06/13 The bsics of the mrketplce As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum
More informationPROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY
MAT 0630 INTERNET RESOURCES, REVIEW OF CONCEPTS AND COMMON MISTAKES PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY Contents 1. ACT Compss Prctice Tests 1 2. Common Mistkes 2 3. Distributive
More informationTechnology comparison of CFB versus pulverized fuel firing for utility power generation
Technology compison of CFB vesus pulveized fuel fiing fo utility powe genetion by J. Utt* nd R. Giglio* J o u n l Synopsis Recent developments in ciculting fluidized bed (CFB) oncethough supeciticl technology
More informationSmall Business Networking
Why Network is n Essentil Productivity Tool for Any Smll Business TechAdvisory.org SME Reports sponsored by Effective technology is essentil for smll businesses looking to increse their productivity. Computer
More informationINITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS
INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS Vesion:.0 Date: June 0 Disclaime This document is solely intended as infomation fo cleaing membes and othes who ae inteested in
More informationIlona V. Tregub, ScD., Professor
Investment Potfolio Fomation fo the Pension Fund of Russia Ilona V. egub, ScD., Pofesso Mathematical Modeling of Economic Pocesses Depatment he Financial Univesity unde the Govenment of the Russian Fedeation
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationJaERM SoftwareasaSolution Package
JERM SoftwresSolution Pckge Enterprise Risk Mngement ( ERM ) Public listed compnies nd orgnistions providing finncil services re required by Monetry Authority of Singpore ( MAS ) nd/or Singpore Stock
More informationTest Management using Telelogic DOORS. Francisco López Telelogic DOORS Specialist
Test Mngement using Telelogic DOORS Frncisco López Telelogic DOORS Specilist Introduction Telelogic solution for Requirements Mngement DOORS Requirements mngement nd trcebility pltform for complex systems
More informationUnleashing the Power of Cloud
Unleshing the Power of Cloud A Joint White Pper by FusionLyer nd NetIQ Copyright 2015 FusionLyer, Inc. All rights reserved. No prt of this publiction my be reproduced, stored in retrievl system, or trnsmitted,
More informationThe LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero.
Poject Decision Metics: Levelized Cost of Enegy (LCOE) Let s etun to ou wind powe and natual gas powe plant example fom ealie in this lesson. Suppose that both powe plants wee selling electicity into the
More informationThe Pitfall of Using Sharpe Ratio
Finnce Lettes, 3, 1, 8489. he Pitfll of Using Shpe Rtio MeiChen Lin * nd PinHung Chou b Ntionl United Univesity, iwn, ROC b Ntionl Centl Univesity, iwn, ROC Abstct We show tht when etuns e iid, the
More informationSTUDENT RESPONSE TO ANNUITY FORMULA DERIVATION
Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts
More informationReasoning to Solve Equations and Inequalities
Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing
More informationAvoided emissions kgco 2eq /m 2 Reflecting surfaces 130
ANALYSIS OF GLOBAL WARMING MITIGATION BY WHITE REFLECTING SURFACES Fedeico Rossi, Andea Nicolini Univesity of Peugia, CIRIAF Via G.Duanti 67 0615 Peugia, Italy T: +9075585846; F: +90755848470; E: fossi@unipg.it
More informationThe Supply of Loanable Funds: A Comment on the Misconception and Its Implications
JOURNL OF ECONOMICS ND FINNCE EDUCTION Volume 7 Numbe 2 Winte 2008 39 The Supply of Loanable Funds: Comment on the Misconception and Its Implications. Wahhab Khandke and mena Khandke* STRCT Recently FieldsHat
More informationAn Introduction to Omega
An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei iskewad chaacteistics? The Finance Development Cente 2002 1 Fom
More informationTreatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3.
The nlysis of vrince (ANOVA) Although the ttest is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the ttest cn be used to compre the mens of only
More information2 DIODE CLIPPING and CLAMPING CIRCUITS
2 DIODE CLIPPING nd CLAMPING CIRCUITS 2.1 Ojectives Understnding the operting principle of diode clipping circuit Understnding the operting principle of clmping circuit Understnding the wveform chnge of
More information1 Numerical Solution to Quadratic Equations
cs42: introduction to numericl nlysis 09/4/0 Lecture 2: Introduction Prt II nd Solving Equtions Instructor: Professor Amos Ron Scribes: Yunpeng Li, Mrk Cowlishw Numericl Solution to Qudrtic Equtions Recll
More informationCurve Sketching. 96 Chapter 5 Curve Sketching
96 Chpter 5 Curve Sketching 5 Curve Sketching A B A B A Figure 51 Some locl mximum points (A) nd minimum points (B) If (x, f(x)) is point where f(x) reches locl mximum or minimum, nd if the derivtive of
More informationUnderstanding Basic Analog Ideal Op Amps
Appliction Report SLAA068A  April 2000 Understnding Bsic Anlog Idel Op Amps Ron Mncini Mixed Signl Products ABSTRACT This ppliction report develops the equtions for the idel opertionl mplifier (op mp).
More informationBasic Analysis of Autarky and Free Trade Models
Bsic Anlysis of Autrky nd Free Trde Models AUTARKY Autrky condition in prticulr commodity mrket refers to sitution in which country does not engge in ny trde in tht commodity with other countries. Consequently
More informationQuestions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing
M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow
More informationEcon 4721 Money and Banking Problem Set 2 Answer Key
Econ 472 Money nd Bnking Problem Set 2 Answer Key Problem (35 points) Consider n overlpping genertions model in which consumers live for two periods. The number of people born in ech genertion grows in
More informationSmall Business Cloud Services
Smll Business Cloud Services Summry. We re thick in the midst of historic sechnge in computing. Like the emergence of personl computers, grphicl user interfces, nd mobile devices, the cloud is lredy profoundly
More informationfor Student Service Members and Veterans in Indiana
Apil 2009 The Highe Eduction Lndscpe fo Student Sevice Membes nd Vetens in Indin Mtin Stenbeg, Shelley McDemid Wdswoth, Jo Vughn, nd Ryn Clson Mility Fmily Resech Institute t Pudue Univesity Suppot Len
More informationMath Review 1. , where α (alpha) is a constant between 0 and 1, is one specific functional form for the general production function.
Mth Review Vribles, Constnts nd Functions A vrible is mthemticl bbrevition for concept For emple in economics, the vrible Y usully represents the level of output of firm or the GDP of n economy, while
More informationChapter 3 Savings, Present Value and Ricardian Equivalence
Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,
More informationDRIVER BEHAVIOR MODELING USING HYBRID DYNAMIC SYSTEMS FOR DRIVERAWARE ACTIVE VEHICLE SAFETY
DRIVER BEHAVIOR MODELING USING HYBRID DYNAMIC SYSTEMS FOR DRIVERAWARE ACTIVE VEHICLE SAFETY Pin Boyz, Amdeep Sthynyn, John H.L. Hnsen Eik Jonsson School o Engineeing nd Compute Science Univesity o Texs
More informationOperations with Polynomials
38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply
More informationThings to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request.
Retiement Benefit 1 Things to Remembe Complete all of the sections on the Retiement Benefit fom that apply to you equest. If this is an initial equest, and not a change in a cuent distibution, emembe to
More information9 CONTINUOUS DISTRIBUTIONS
9 CONTINUOUS DISTIBUTIONS A rndom vrible whose vlue my fll nywhere in rnge of vlues is continuous rndom vrible nd will be ssocited with some continuous distribution. Continuous distributions re to discrete
More informationGRAVITATION 1. BASIC FORCES IN NATURE
GRAVITATION. BASIC ORCES IN NATURE POINTS TO REMEMBER. Bsing on the ntue nd eltive stength the bsic foces in ntue e clssified into fou ctegoies. They e ) Gvittionl foce ) Electomgnetic foce 3) Stong Nucle
More information867 Product Transfer and Resale Report
867 Poduct Tansfe and Resale Repot Functional Goup ID=PT Intoduction: This X12 Tansaction Set contains the fomat and establishes the data contents of the Poduct Tansfe and Resale Repot Tansaction Set (867)
More informationResearch on Risk Assessment of the Transformer Based on Life Cycle Cost
ntenational Jounal of Smat Gid and lean Enegy eseach on isk Assessment of the Tansfome Based on Life ycle ost Hui Zhou a, Guowei Wu a, Weiwei Pan a, Yunhe Hou b, hong Wang b * a Zhejiang Electic Powe opoation,
More informationNetwork Configuration Independence Mechanism
3GPP TSG SA WG3 Security S3#19 S3010323 36 July, 2001 Newbury, UK Source: Title: Document for: AT&T Wireless Network Configurtion Independence Mechnism Approvl 1 Introduction During the lst S3 meeting
More informationA framework for the selection of enterprise resource planning (ERP) system based on fuzzy decision making methods
A famewok fo the selection of entepise esouce planning (ERP) system based on fuzzy decision making methods Omid Golshan Tafti M.s student in Industial Management, Univesity of Yazd Omidgolshan87@yahoo.com
More informationMAGNETIC FIELD AROUND CURRENTCARRYING WIRES. point in space due to the current in a small segment ds. a for field around long wire
MAGNETC FELD AROUND CURRENTCARRYNG WRES How will we tckle this? Pln: 1 st : Will look t contibution d to the totl mgnetic field t some point in spce due to the cuent in smll segment of wie iotsvt Lw
More informationCarterPenrose diagrams and black holes
CatePenose diagams and black holes Ewa Felinska The basic intoduction to the method of building Penose diagams has been pesented, stating with obtaining a Penose diagam fom Minkowski space. An example
More informationFinancing Terms in the EOQ Model
Financing Tems in the EOQ Model Habone W. Stuat, J. Columbia Business School New Yok, NY 1007 hws7@columbia.edu August 6, 004 1 Intoduction This note discusses two tems that ae often omitted fom the standad
More informationApplication Bundles & Data Plans
Appliction Appliction Bundles & Dt Plns We ve got plns for you. Trnsporttion compnies tody ren t onesizefitsll. Your fleet s budget, size nd opertions re unique. To meet the needs of your fleet nd help
More informationBinary Representation of Numbers Autar Kaw
Binry Representtion of Numbers Autr Kw After reding this chpter, you should be ble to: 1. convert bse rel number to its binry representtion,. convert binry number to n equivlent bse number. In everydy
More informationHumana Critical Illness/Cancer
Humn Criticl Illness/Cncer Criticl illness/cncer voluntry coverges py benefits however you wnt With our criticl illness nd cncer plns, you'll receive benefit fter serious illness or condition such s hert
More informationProject Recovery. . It Can Be Done
Project Recovery. It Cn Be Done IPM Conference Wshington, D.C. Nov 47, 200 Wlt Lipke Oklhom City Air Logistics Center Tinker AFB, OK Overview Mngement Reserve Project Sttus Indictors Performnce Correction
More informationGraphs on Logarithmic and Semilogarithmic Paper
0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl
More informationPolynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )
Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +
More informationCorporate Compliance vs. EnterpriseWide Risk Management
Corporte Complince vs. EnterpriseWide Risk Mngement Brent Sunders, Prtner (973) 2364682 November 2002 Agend Corporte Complince Progrms? Wht is EnterpriseWide Risk Mngement? Key Differences Why Will
More informationest using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.
9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,
More informationHealth insurance exchanges What to expect in 2014
Helth insurnce exchnges Wht to expect in 2014 33096CAEENABC 11/12 The bsics of exchnges As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum mount
More informationMathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100
hsn.uk.net Higher Mthemtics UNIT 3 OUTCOME 1 Vectors Contents Vectors 18 1 Vectors nd Sclrs 18 Components 18 3 Mgnitude 130 4 Equl Vectors 131 5 Addition nd Subtrction of Vectors 13 6 Multipliction by
More informationv o a y = = * Since H < 1m, the electron does not reach to the top plate.
. The uniom electic ield between two conducting chged pltes shown in the igue hs mgnitude o.40 N/C. The plte seption is m, nd we lunch n electon om the bottom plte diectl upwd with v o 6 m/s. Will the
More informationAccording to Webster s, the
dt modeling Universl Dt Models nd P tterns By Len Silversn According Webster s, term universl cn be defined s generlly pplicble s well s pplying whole. There re some very common ptterns tht cn be generlly
More information32. The Tangency Problem of Apollonius.
. The Tngeny olem of Apollonius. Constut ll iles tngent to thee given iles. This eleted polem ws posed y Apollinius of eg (. 6070 BC), the getest mthemtiin of ntiquity fte Eulid nd Ahimedes. His mjo wok
More informationOr more simply put, when adding or subtracting quantities, their uncertainties add.
Propgtion of Uncertint through Mthemticl Opertions Since the untit of interest in n eperiment is rrel otined mesuring tht untit directl, we must understnd how error propgtes when mthemticl opertions re
More informationExperiment 6: Friction
Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht
More information