A Reliabilitybased Opportunistic Predictive Maintenance Model for koutofn Deteriorating Systems


 Amy Scott
 1 years ago
 Views:
Transcription
1 A blicatio of CHEMICAL ENGINEERING TRANSACTIONS VOL Gest Editors: Erico Zio Piero Baraldi Coyright 203 AIDIC Servizi S.r.l. ISBN ; ISSN The Italia Associatio of Chemical Egieerig Olie at: DOI: 0.33/CET3383 A Reliabilitybased Oortistic Predictive Maiteace Model for kotof Deterioratig Systems Ta K. Hyh* a Ae Barros a Christohe Béreger b a Uiversité de Techologie de Troyes ICD & STMR UMR CNRS re Marie Crie CS Troyes cedex Frace b Gisalab CNRS Greoble Istitte of Techology re des Mathématiqes BP Sait Marti d Hères cedex Frace Motivated by the effectiveess of coditiobased maiteace (CBM for sigleit systems we develo i this aer a oortistic redictive maiteace model for a kotof deterioratig system. This model reflects the joit effects of ecoomic deedece ad CBM decisio o the maiteace cost. Ulike most existig CBM models whose maiteace decisiomakig relies directly o a coditio idex of degradatio level we base the decisio o the reliability of each comoet comted coditioally o its degradatio level. This makes the model robst with resect to (w.r.t. measremet errors more efficiet ad easier to otimize comared to a corresodig degradatiobased maiteace model.. Itrodctio With the dissemiatio of coditio moitorig techiqes CBM is owadays a very romisig aroach to imrove the drability reliability ad safety of idstrial systems ad hece to brig ot cometitive advatages. Over the last few decades may CBM models have bee develoed ad sccessflly alied for sigleit systems or comoets (Jardie et al However i ractice a idstrial system sally cosists of several comoets which may stochastically ecoomically ad/or strctrally deed o each other (Cho et Parlar 99. Becase of these iteractios the otimal maiteace strategy of mltiit systems is ot a simle jxtaositio of otimal strategies of their comoets (Castaier et al As a coseqece meros CBM models existig i the literatre caot be roerly alied for mltiit systems. This aer therefore aims to develo a ew CBM model for a k otof deterioratig system i the cotext of ecoomic deedece amog comoets. By defiitio ecoomic deedece imlies that cost savig ca be eared whe several comoets are maitaied together rather tha searately (Dekker et al Obviosly cosiderig joitly both ecoomic deedece ad CBM decisio ca lead to sigificat savig i maiteace cost. However the literatre of sch maiteace models is somewhat limited. Geerally these models are orieted toward two mai aroaches amely groig maiteace ad oortistic maiteace (Dekker et al I the former re CBM strategies are firstly alied for comoets to determie their otimal maiteace times ad the ecoomic deedece amog comoets is take ito accot by groig these otimal times (see e.g. (Bovard et al. 20. I the latter maiteace decisios sally follow cotrollimit rle with i additio to roer revetive maiteace thresholds of comoets oe or several oortistic thresholds itrodced to exloit the ecoomic deedece (see e.g. (Tia ad Liao 20. Comared to the latter the former does ot well characterize the joit effects of CBM ad ecoomic deedece becase of two relatively ideedet stages of maiteace decisios. This is why we focs oly o oortistic CBM models i the reset aer. Moreover like most existig models whose maiteace decisiomakig relies directly o a coditio idex of degradatio level we base the decisio o the reliability of each comoet comted coditioally o its degradatio level. We will show i followig that sig coditioal reliability istead of degradatio level ca make the model more efficiet robst w.r.t. measremet errors ad easier to otimize. Please cite this article as: Hyh K.T. Barros A. Bereger C. 203 A reliabilitybased oortistic redictive maiteace model for kotof deterioratig systems Chemical Egieerig Trasactios DOI: 0.33/CET
2 The remaider of the aer is orgaized as follows. Sectio 2 is devoted to describe the system ad to comte the reliability of comoet ad system. I Sectio 3 we reset a reliabilitybased oortistic redictive maiteace strategy ad the associated cost model. The erformace ad robstess of this strategy are aalyzed i Sectio 4 by comarig with a degradatiobased oortistic CBM strategy. Fially we coclde the aer ad give some ersectives i Sectio System modelig ad reliability aalysis We cosider a kotof system whose comoets degrade stochastically ideedetly ad gradally over time. To describe sch a system oe sally relies o lifetime models (Wag These models are however disadvataged i characterizig the system behavior becase they caot reflect roerly the itermediates states (i.e. degradatio state of system. To avoid this drawback we base the system modelig o stochastic rocesses. This will hels s to comte more fiely the comoet ad system reliabilities. I the followig for a easier aalysis we divide the system ito comoet level ad system level. 2. Comoet level Cosiderig the ith comoet i = 2 of the system its accmlated degradatio level at time t ca be smmarized by a scalar radom variable X it. Withot ay maiteace actio this variable evolves as a cotiostime mootoically icreasig stochastic rocess { Xit } t 0 with X i0 = 0. As a case stdy a homogeeos gamma rocess with shae arameter αi ad scale arameter β i is sed to describe the degradatio ath { Xit } t 0 (see also (va Noortwijk 2009 for a thorogh review o the se of gamma rocess i maiteace modelig. As sch the desity fctios of the degradatio icremet Xit Xis betwee two times s ad t 0 s t is give by αi( t s αi( t s βix f i α ( i t s β = β i i xi e { xi 0} Γ ( αi ( t s where Γ ( α = (0 α + e d is the Eler gamma fctio. The behavior of sch a degradatio ath deeds closely o the cole of arameters ( αi βi ad its average degradatio rate ad variace are give by mi = αi βi ad σ 2 2 i = α i β i resectively. The comoet i fails as soo as its degradatio level exceeds a critical refixed threshold L i its failre time is the exressed by τ i = if { t Xi t Li}. Ths let Rτ i Xi t( xi be its coditioal reliability at time give its degradatio level at time t X = x it ca be comted as follows (va Noortwijk 2009 ( i i i i τ i X x i t i = P τi Xi t = xi = { xi< Li} Γ( αi ( t it i ( Γ( α ( t β ( L x R (2 where Γ ( α x = ( x α + e ddeotes the icomlete gamma fctio. 2.2 System level The cosidered system has kotof:f strctre i.e. it fails if ad oly if at least k of the comoets fail. Let τ s be the system failre time it is eqal to kth smallest vale amog the set of comoet failre times { τ τ 2 τ }. Ths the coditioal reliability of the system Rτ ( : : sx x t at time give the comoets degradatio level at time t x: ( x x 2 x is comted as (David ad Nagaraja 2003 k j τ X x: = P τs X: t = x: τ X xi Rτ X xi = R ( ( R ( ( (3 s : t il il t l il il t j j = 0 C l= l= j+ where Rτ ( i X x i t i is give from (2 C j icldig C =!( j!( j! terms deotes the sm over all ermtatios { τi τi2 τi } of the set of idices { 2 } for which i < i 2 < < i j ad ij+ < i j+ 2 < < i. 3. Reliabilitybased oortistic redictive maiteace We roose i this sectio a oortistic redictive maiteace strategy for the aforemetioed kotof:f deterioratig system. For this strategy maiteace decisiomakig is ot based o a classical coditio idex of degradatio level bt o the coditioal reliability give from Sectio 2. Its erformace is evalated throgh a mathematical cost model develoed o the basis of semiregeerative theory. j l ( 494
3 3. Maiteace assmtios We assme that the degradatio of each comoet i the system is hidde ad the comoet failre is otselfaocig. This reqires the isectio oeratios o the total system to reveal the degradatio level ad the failre/workig state of comoets. The isectio is assmed istataeos erfect odestrctive ad is icrred a cost ci. Two maiteace oeratios are available o each comoet: a revetive relacemet (cost c ci ad a corrective relacemet (cost cc c. Each relacemet oeratio ts the comoet back i the asgoodasew state. Moreover a relacemet (either revetive or corrective ca oly be istataeosly erformed at isectio times. Therefore a system dowtime may aear withi two sccessive isectio times hece a additioal cost is icrred from the system failre time til the ext relacemet time at a cost rate cd. Associated with a relacemet oeratios sch as dismatlig ad reassembly of the system sedig a maiteace team to the site etc. are eeded ad they icr a set cost c s. Ths ecoomic deedece amog comoets exists ad oe wold like erform maiteace joitly o several comoets to save set costs. 3.2 Maiteace strategy We aim at a oortistic maiteace strategy reresetig both CBM decisio ad ecoomic deedece. The CBM decisio is itegrated i the strategy throgh a re revetive relacemet threshold R of the comoet coditioal reliability while the ecoomic deedece is take ito accot by a oortistic revetive relacemet threshold R. More i detail a eriodic scheme with eriod ΔT is sed to isect the health state of comoets/system. At a isectio time Tm = m Δ T m = 2 we relace correctively the failed comoets ad revetively still srvivig comoets if their coditioal reliability at the ext isectio time give the actal detected degradatio level is less tha a threshold R (i.e. Rτ i Xi ( T Tm m +ΔT xi R for the comoet i i = 2. Whe a comoet is relaced (either revetively or correctively this is the oortity to relace other srvivig oes. More recisely if a relacemet is schedled o the comoet i we also oortistically relaced the comoet j i if its coditioal reliability at the ext isectio time give the actal detected degradatio level is less tha a threshold R (i.e. R < Rτ j X j Tm ( Tm +ΔT xj R. Ths for this strategy ΔT R ad R are the decisio arameters to be otimized. To ehace the imortace of the decisio arameters we call this strategy ( Δ TR R. Based o the ( Δ TR R strategy a degradatiobased oortistic maiteace strategy amely ( Δ TZ Z ca be easily give by relacig resectively the thresholds R ad R by degradatio thresholds Z ad Z. Oe ca remark that the ( Δ TZ Z strategy is less advatageos tha ( Δ TR R strategy whe the system is heterogeeos. I fact i a heterogeeos system a same reliability threshold for all comoets ca corresod to differet degradatio levels of differet comoets. Makig a maiteace decisio based o a reliability level is therefore more flexible tha based o a same degradatio level for all comoets. As a reslt the ( Δ TR R strategy is geerally more rofitable tha ( Δ TR R strategy. Of corse oe ca atrally thik abot a strategy with varios degradatio thresholds for differet comoets. However sch a strategy seems ifeasible i ractical alicatios becase it is relatively comlex. Moreover otimizig the strategy is really itractable becase of a large mber of decisio arameters. The ( Δ TR R strategy whose mber of decisio arameters is ivariat for all size of system is mch easier to be otimized. 3.3 Mathematical cost model To assess the erformace of the roosed maiteace strategy we focs o a widely sed asymtotic criterio which is the logr exected maiteace cost rate of the overall system (Béreger 2008 C ( E C t = lim t t where Ct ( deotes accmlated maiteace cost of the system to time t. Accordig to the strctre of the ( ΔTR R strategy Ct ( ca be give as Ct ( = c N ( t c ( h N ( t + ( c + c N ( t + ( c + c N ( t + c W( t (5 i Is s G h s i Prev c s i Corr d h= 2 i= i= where NIs( t is the isectios mber i [0t] N iprev ( t ad N icorr ( t are resectively the mber of revetive relacemets (i.e. either oortistic relacemets or re revetive relacemets ad corrective relacemets of the comoet i i [0t] ideedetly o oeratios erformed o other comoets NGh ( t is the mber of gros for which h comoets 2 h are relaced at the same time i [0t] ad W( t deotes the system dowtime i i [0t]. (4 495
4 A classical way to aalytically evalate (4 is to se the reewalreward theorem to exress the cost rate C o a reewal cycle of system (Tijms However i the reset case owig to very log reewal cycle i which too may scearios of maitaied system evoltio may aear alyig this aroach is almost imossible. To overcome the roblem we ca resort to semiregeerative theory to exress C o a semireewal cycle (Béreger Sch a cycle is mch shorter ad cotais simler maiteace scearios comared to the reewal cycle ad as a reslt it allows comtig more easily. I fact accordig to the ( Δ TR R strategy after a isectio at time Tm m = 2 the evoltio of every comoet ad hece of the system deeds oly o the revealed degradatio levels. So let s deote { X : t } t 0 the mltivariate rocess reresetig the evoltio of the maitaied system ( X : t = ( X t X 2 t X t ad X it is the degradatio level of the ith maitaied comoet at time t it is a semiregeerative rocess. The discrete time rocess describig the maitaied system states at isectio times { Y: m } m where Y : m = X : T m is the a embedded Markov chai of { X : t } t 0 with statioary law π = π( x :. Ths alyig the semiregeerative roerties of the maitaied system exressio (4 ca be rewritte as (Béreger 2008 ( Eπ C( T E [ ] E [ ] EC t C = lim = = ci Eπ NIs( T cs ( h π NG h( T t t π T π T E h= 2 + ( c + cs Eπ Ni Prev ( T + ( c + cs Eπ Ni Corr ( T + cd Eπ W ( T i= i= (6 where T is the first isectio time ad Eπ is the exectatio w.r.t. the statioary law π of { Y: m } m. Comtig the exectatio qatities i (6 is qite comlicated bt classical ad we omit it here becase of limit mber of ages. Istead we show the feasibility of (6 by givig a examle o a 2comoets series system. The followig set of arameters is sed: α = 2.25 β = 0.75 α 2 = β 2 = L = 0 L 2 = 0 ci = 0 cs = 5 c = cc = 00ad cd = 25. Figre illstrates the statioary law π ad the shae of the cost rate whe oe of decisio arameters is fixed at its otimal vale. I fact for the chose data set otimal decisio arameters are R ot = 7 R ot = 0.87 ad Δ Tot = 2.4 which corresod to the otimal cost rate ot =.692. R ot = 7 R ot = 0.87 ΔT ot = π (x x R ot = 7 ΔT ot = x x ΔT R R ot = 0.87 ΔT ot = 2.4 R ot = 0.87 R ot = ΔT 2 R R R 0.8 Figre : Shae of the statioary law π ad the logr exected maiteace cost rate comoets series system der ( Δ TR R strategy of a 2496
5 4. Performace ad robstess aalysis This sectio aims to aalyze more deely the erformace ad the robstess of the ( Δ TR R strategy throgh sesitivity stdies. For a simler aalysis the 2comoets series system i Sectio 3.3 is resed bt its characteristic arameters or maiteace costs ca be sccessively chaged deedig o differet case stdies. The ( Δ TZ Z strategy rereseted i Sectio 3.2 is sed as a bechmark. 4. Sesitivity to the maiteace costs We vary resectively oe of itervetio costs (i.e. ci cs cad cd fixe the others ad we ivestigate the evoltio of otimal cost rate of both ( Δ TR R strategy ad ( ΔTZ Z strategy. Figre 2 shows the reslts. We ca remark that the otimal cost rate of ( Δ TR R strategy is always lower tha the oe of ( ΔTZ Z strategy. This affirms the advatage of the coditioal reliability idex over the degradatio level i CBM decisiomakig i the cosidered case. However this advatage is decreased for smaller isectio cost ad dowtime cost rate or for higher set cost ad revetive relacemet cost c i c s c c d Figre 2: Evoltio of otimal maiteace cost rate w.r.t. the variatio of itervetio costs 4.2 Sesitivity to the system characteristics Here the degradatio seed m ad variace σ 2 of comoet are resectively varied other arameters are fixed ad we observe the otimal cost rate evoltio of the cosidered strategies. The ( ΔT R R strategy is still more rofitable tha the ( ΔTZ Z strategy (see Figre 3. However both strategies give almost the same rofit for a qasihomogeeos system (see left figre below or for a heterogeeos system whose degradatio variaces of differet comoets are too differet (see right figre below m 2 = α 2 /β 2 = 34 σ 2 2 = α 2 /β 2 2 = m 2 = α 2 /β 2 = σ 2 2 = α 2 /β 2 2 = m = α /β 27m σ 2 2 = α /β Figre 3: Evoltio of otimal maiteace cost rate w.r.t. the variatio of degradatio seed ad variace 4.3 Sesitivity to the errors made o maiteace strategy decisio arameters I may ractical alicatios the estimatio of system arameters may be imrecise becase of oisy measremets or the lack of data. This ca lead to errors i determiig the otimal decisio arameters of a maiteace strategy ad hece a loss i its erformace. This sectio therefore aims to examie the imact of sch a error o the erformace of ( Δ TR R strategy. For this ed we comte its 497
6 maiteace cost rate whe the decisio arameters vary arod theirs otimal vales ad we comare with the otimal cost rate of ( Δ TZ Z strategy. Figre 4 shows the reslts. Obviosly the erformace.4.2 Low degradatio variace: σ = α /β 2 = 3 R Error o R (R.6.5 High degradatio variace: σ = α /β 2 = 6 R Error o R (R ΔTZ Z C ot.4 ΔTZ Z C ot ΔTR R C ot.2. ΔTR R C ot.2 % 24% 8% 2% 6% 0% 6% 2% ε 6% 2% 8% 4% 0% 4% 7% ε Figre 4: Evoltio of otimal maiteace cost rate w.r.t. the variatio of decisio arameters error of the ( Δ TR R strategy decreases w.r.t. decisio arameters error. However it remais better tha the ( Δ TZ Z strategy whe the error is ot too high. This shows the robstess of the ( Δ TR R w.r.t. measremet errors. Moreover the strategy is more robst for smaller variace of degradatio rocess. 5. Coclsio ad ersectives We roose i this aer a reliabilitybased oortistic redictive maiteace model which ca characterize both asects of CBM decisio ad ecoomic deedece amog comoets of system. The merical reslts show that the roosed maiteace model is sitable for a kotof deterioratig system ad that sig coditioal reliability istead of degradatio level i maiteace decisiomakig ca make the model simle rofitable robst w.r.t. measremet errors ad easy to otimize. Desite these advatages the roosed maiteace strategy is still a semiblid strategy becase the global system health state is ot take ito accot i maiteace decisios. The ftre work therefore aims to develo a reliabilitybased oortistic maiteace strategy cosiderig the global system health. Moreover for a comlete stdy other tyes of iteractios amog comoets (i.e. stochastic deedece ad strctral deedece shold be itrodced ito the model. Refereces Béreger C O the mathematical coditiobased maiteace modellig for cotiosly deterioratig systems Iteratioal Joral of Materials ad Strctral Reliability Bovard K. Arts A. Béreger C. Cocqemot V. 20 Coditiobased dyamic maiteace oeratios laig & groig: Alicatio to commercial heavy vehicles Reliability Egieerig & System Safety Castaier B. Grall A. Béreger C A coditiobased maiteace olicy with oeriodic isectios for a twoit series system Reliability Egieerig & System Safety Cho D.I. Parlar M. 99 A srvey of maiteace models for mltiit systems Eroea Joral of Oeratioal Research David H.A. Nagaraja H.N Order statistics 3 rd ed Joh Wiley & Sos New Jersey Uited States. Dekker R. Wildema R.E. Va der Dy Shcote F.A. 997 A review of mlticomoet maiteace models with ecoomic deedece Mathematical Methods of Oeratios Research Jardie A.K.S. Li D. Bajevic D A review o machiery diagostics ad rogostics imlemetig coditiobased maiteace Mechaical Systems & Sigal Processig Tia Z. Liao H. 20 Coditiobased maiteace otimizatio for mlticomoet systems sig roortioal hazards model Reliability Egieerig & System Safety Tijms H.C A first corse i stochastic models Joh Wiley & Sos West Sssex Eglad. va Noortwijk J.M A srvey of gamma rocesses i maiteace Reliability Egieerig & System Safety Wag H A srvey of maiteace olicies of deterioratig systems Eroea Joral of Oeratioal research
BENCHMARK NEW PRODUCT DEVELOPMENT PROCESSES USING DEABASED MODULARIZED APPROACH
BENCHMARK NEW PRODUCT DEVELOPMENT PROCESSES USING DEABASED MODULARIZED APPROACH TzuA Chiag, Migchi Uiversity o Techology, tachiag@mail.mit.edu.tw Amy J.C. Traey, Natioal Taiei Uiversity o Techology,
More information3 Energy. 3.3. NonFlow Energy Equation (NFEE) Internal Energy. MECH 225 Engineering Science 2
MECH 5 Egieerig Sciece 3 Eergy 3.3. NoFlow Eergy Equatio (NFEE) You may have oticed that the term system kees croig u. It is ecessary, therefore, that before we start ay aalysis we defie the system that
More informationRF Engineering Continuing Education Introduction to Traffic Planning
RF Egieerig otiuig Educatio Itroductio to Traffic Plaig Queuig Systems Figure. shows a schematic reresetatio of a queuig system. This reresetatio is a mathematical abstractio suitable for may differet
More informationEvaluation of Coupling Development for Regional LogisticsEconomic System
Sed Orders for Reprits to reprits@bethamsciece.ae 2642 The Ope Cyberetics & Systemics Joral, 205, 9, 26422646 Ope Access Evalatio of Coplig Developmet for Regioal LogisticsEcoomic System Yaow Wag ad
More informationOn the L p conjecture for locally compact groups
Arch. Math. 89 (2007), 237 242 c 2007 Birkhäuser Verlag Basel/Switzerlad 0003/889X/0302376, ublished olie 2007080 DOI 0.007/s0003007993x Archiv der Mathematik O the L cojecture for locally comact
More informationA MixedInteger Optimization Model for Compressor Selection in Natural Gas Pipeline Network System Operations
Joural of virometal Iformatics 3 () 334 (2004) 04JI00025 726235/6848799 2004 ISIS www.iseis.org/jei A MixedIteger Otimizatio Model for Comressor Selectio i Natural as Pielie Network System Oeratios
More informationRisk contributions of trading and nontrading hours: Evidence from commodity futures markets
Risk cotributios of tradig ad otradig hours: Evidece from commodity futures markets Qigfu Liu Istitute for Fiacial Studies Fuda Uiversity, Shaghai, Chia Yubi A 1 Odette School of Busiess Uiversity of
More informationIn nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008
I ite Sequeces Dr. Philippe B. Laval Keesaw State Uiversity October 9, 2008 Abstract This had out is a itroductio to i ite sequeces. mai de itios ad presets some elemetary results. It gives the I ite Sequeces
More informationA markovian study of no claim discount system of Insurance Regulatory and Development Authority and its application
Thailad Statisticia July 214; 12(2): 223236 htt://statassoc.or.th Cotributed aer A markovia study of o claim discout system of Isurace Regulatory ad Develomet Authority ad its alicatio Dili C. Nath* [a]
More informationOn the Throughput Scaling of Cognitive Radio Ad Hoc Networks
O the Throughut Scalig of Cogitive Radio Ad Hoc Networks Chegzhi Li ad Huaiyu Dai Deartmet of Electrical ad Comuter Egieerig North Carolia State Uiversity, Raleigh, NC email: {cli3, hdai}@csu.edu Abstract
More information4.1 Sigma Notation and Riemann Sums
0 the itegral. Sigma Notatio ad Riema Sums Oe strategy for calculatig the area of a regio is to cut the regio ito simple shapes, calculate the area of each simple shape, ad the add these smaller areas
More informationModified Line Search Method for Global Optimization
Modified Lie Search Method for Global Optimizatio Cria Grosa ad Ajith Abraham Ceter of Excellece for Quatifiable Quality of Service Norwegia Uiversity of Sciece ad Techology Trodheim, Norway {cria, ajith}@q2s.tu.o
More informationAnalyzing Longitudinal Data from Complex Surveys Using SUDAAN
Aalyzig Logitudial Data from Complex Surveys Usig SUDAAN Darryl Creel Statistics ad Epidemiology, RTI Iteratioal, 312 Trotter Farm Drive, Rockville, MD, 20850 Abstract SUDAAN: Software for the Statistical
More informationAbstract. 1. Introduction. Wei Li. Bo Zhou. Science and Technologies, Zhejiang University Hangzhou, China bzhou@zju.edu.cn
Model Based Load Testig of Web Applicatios Xige Wag Departmet of Compter Sciece ad Techologies, Zhejiag Uiersity Hagzho, Chia ewroot@zj.ed.c Bo Zho Departmet of Compter Sciece ad Techologies, Zhejiag Uiersity
More informationAutomatic Tuning for FOREX Trading System Using Fuzzy Time Series
utomatic Tuig for FOREX Tradig System Usig Fuzzy Time Series Kraimo Maeesilp ad Pitihate Soorasa bstract Efficiecy of the automatic currecy tradig system is time depedet due to usig fixed parameters which
More informationKey Ideas Section 81: Overview hypothesis testing Hypothesis Hypothesis Test Section 82: Basics of Hypothesis Testing Null Hypothesis
Chapter 8 Key Ideas Hypothesis (Null ad Alterative), Hypothesis Test, Test Statistic, Pvalue Type I Error, Type II Error, Sigificace Level, Power Sectio 81: Overview Cofidece Itervals (Chapter 7) are
More informationMonitoring Frequency of Change By Li Qin
Monitoring Frequency of Change By Li Qin Abstract Control charts are widely used in rocess monitoring roblems. This aer gives a brief review of control charts for monitoring a roortion and some initial
More informationTaking DCOP to the Real World: Efficient Complete Solutions for Distributed MultiEvent Scheduling
Taig DCOP to the Real World: Efficiet Complete Solutios for Distributed MultiEvet Schedulig Rajiv T. Maheswara, Milid Tambe, Emma Bowrig, Joatha P. Pearce, ad Pradeep araatham Uiversity of Souther Califoria
More informationGregory Carey, 1998 Linear Transformations & Composites  1. Linear Transformations and Linear Composites
Gregory Carey, 1998 Liear Trasformatios & Composites  1 Liear Trasformatios ad Liear Composites I Liear Trasformatios of Variables Meas ad Stadard Deviatios of Liear Trasformatios A liear trasformatio
More informationGovernment intervention in credit allocation: a collective decision making model. Ruth BenYashar and Miriam Krausz* BarIlan University, Israel
Govermet itervetio i credit allocatio: a collective decisio makig model Ruth BeYashar ad Miriam Krausz* BarIla Uiversity, Israel Abstract The urose of this study is to address the imortat issue of govermet
More informationInfinite Sequences and Series
CHAPTER 4 Ifiite Sequeces ad Series 4.1. Sequeces A sequece is a ifiite ordered list of umbers, for example the sequece of odd positive itegers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29...
More informationAutomated Trust Negotiation Model based on Dynamic Game of Incomplete Information
2668 JOURNAL OF SOFTWARE, VOL 8, NO 10, OCTOBER 2013 Automated Trust Negotiatio Model based o Dyamic Game of Icomlete Iformatio Hogwei Che, Shuig Wag, Hui Xu, Zhiwei Ye,*Chuzhi Wag School of Comuter Sciece,
More information2.7 Sequences, Sequences of Sets
2.7. SEQUENCES, SEQUENCES OF SETS 67 2.7 Sequeces, Sequeces of Sets 2.7.1 Sequeces Defiitio 190 (sequece Let S be some set. 1. A sequece i S is a fuctio f : K S where K = { N : 0 for some 0 N}. 2. For
More informationOption Pricing: A Simplified Approach
Otio Pricig: A Simlified Aroach Joh C. Cox Massachusetts Istitute of Techology ad Staford Uiversity Stehe A. Ross Yale Uiversity Mark Rubistei Uiversity of Califoria, Berkeley March 1979 revised July 1979
More informationThe analysis of the Cournot oligopoly model considering the subjective motive in the strategy selection
The aalysis of the Courot oligopoly model cosiderig the subjective motive i the strategy selectio Shigehito Furuyama Teruhisa Nakai Departmet of Systems Maagemet Egieerig Faculty of Egieerig Kasai Uiversity
More information5 Boolean Decision Trees (February 11)
5 Boolea Decisio Trees (February 11) 5.1 Graph Coectivity Suppose we are give a udirected graph G, represeted as a boolea adjacecy matrix = (a ij ), where a ij = 1 if ad oly if vertices i ad j are coected
More informationChapter 7 Methods of Finding Estimators
Chapter 7 for BST 695: Special Topics i Statistical Theory. Kui Zhag, 011 Chapter 7 Methods of Fidig Estimators Sectio 7.1 Itroductio Defiitio 7.1.1 A poit estimator is ay fuctio W( X) W( X1, X,, X ) of
More informationNonlife insurance mathematics. Nils F. Haavardsson, University of Oslo and DNB Skadeforsikring
Nolife isurace mathematics Nils F. Haavardsso, Uiversity of Oslo ad DNB Skadeforsikrig Mai issues so far Why does isurace work? How is risk premium defied ad why is it importat? How ca claim frequecy
More informationHypothesis testing. Null and alternative hypotheses
Hypothesis testig Aother importat use of samplig distributios is to test hypotheses about populatio parameters, e.g. mea, proportio, regressio coefficiets, etc. For example, it is possible to stipulate
More informationMAGNT Research Report (ISSN. 14448939) Vol.3 (2). PP: 189198
MAGNT Research Reort (ISSN. 14448939) Vol.3 (2). PP: 189198 Exlaiig the Model of the Imact of Demograhic Variables with kowledge ad Collaborative Accordig to the Moderatig Role of Orgaizatioal Culture
More informationDifferential Quartet, A Novel Circuit Building Block for High Slew Rate Differential Amplification
4th WSEAS Iteratioal Coferece o ELECTRONICS, CONTROL ad SIGNAL PROCESSING, Miami, Florida, USA, 79 November, 5 (.666 Differetial Quartet, A Novel Circuit Buildig Block for High Slew Rate Differetial
More informationEstimating Probability Distributions by Observing Betting Practices
5th Iteratioal Symposium o Imprecise Probability: Theories ad Applicatios, Prague, Czech Republic, 007 Estimatig Probability Distributios by Observig Bettig Practices Dr C Lych Natioal Uiversity of Irelad,
More informationECE606: Solid State Devices Lecture 16 pn diode AC Response
ECE66: Solid State Devices Lecture 16  diode C esose Gerhard Klimeck gekco@urdue.edu Klimeck ECE66 Fall 1 otes adoted from lam Toic Ma Equilibrium DC Small sigal Large Sigal Circuits Diode Schottky Diode
More informationEntropy of bicapacities
Etropy of bicapacities Iva Kojadiovic LINA CNRS FRE 2729 Site école polytechique de l uiv. de Nates Rue Christia Pauc 44306 Nates, Frace iva.kojadiovic@uivates.fr JeaLuc Marichal Applied Mathematics
More informationAmendments to employer debt Regulations
March 2008 Pesios Legal Alert Amedmets to employer debt Regulatios The Govermet has at last issued Regulatios which will amed the law as to employer debts uder s75 Pesios Act 1995. The amedig Regulatios
More informationbstract The aer ivestigates the imact of fiacial itegratio o asset retur, risk diversificatio ad breadth of fiacial markets. We aalyse a threecoutry macroecoomic model i which (i) the umber of fiacial
More informationMeasures of Spread and Boxplots Discrete Math, Section 9.4
Measures of Spread ad Boxplots Discrete Math, Sectio 9.4 We start with a example: Example 1: Comparig Mea ad Media Compute the mea ad media of each data set: S 1 = {4, 6, 8, 10, 1, 14, 16} S = {4, 7, 9,
More informationCOMPARISON OF THE EFFICIENCY OF SCONTROL CHART AND EWMAS 2 CONTROL CHART FOR THE CHANGES IN A PROCESS
COMPARISON OF THE EFFICIENCY OF SCONTROL CHART AND EWMAS CONTROL CHART FOR THE CHANGES IN A PROCESS Supraee Lisawadi Departmet of Mathematics ad Statistics, Faculty of Sciece ad Techoology, Thammasat
More informationRegression with a Binary Dependent Variable (SW Ch. 11)
Regressio with a Biary Deedet Variable (SW Ch. 11) So far the deedet variable (Y) has bee cotiuous: districtwide average test score traffic fatality rate But we might wat to uderstad the effect of X o
More informationI. Chisquared Distributions
1 M 358K Supplemet to Chapter 23: CHISQUARED DISTRIBUTIONS, TDISTRIBUTIONS, AND DEGREES OF FREEDOM To uderstad tdistributios, we first eed to look at aother family of distributios, the chisquared distributios.
More informationInstallment Joint Life Insurance Actuarial Models with the Stochastic Interest Rate
Iteratioal Coferece o Maagemet Sciece ad Maagemet Iovatio (MSMI 4) Istallmet Joit Life Isurace ctuarial Models with the Stochastic Iterest Rate NiaNia JI a,*, Yue LI, DogHui WNG College of Sciece, Harbi
More informationPENSION ANNUITY. Policy Conditions Document reference: PPAS1(7) This is an important document. Please keep it in a safe place.
PENSION ANNUITY Policy Coditios Documet referece: PPAS1(7) This is a importat documet. Please keep it i a safe place. Pesio Auity Policy Coditios Welcome to LV=, ad thak you for choosig our Pesio Auity.
More informationDAME  Microsoft Excel addin for solving multicriteria decision problems with scenarios Radomir Perzina 1, Jaroslav Ramik 2
Itroductio DAME  Microsoft Excel addi for solvig multicriteria decisio problems with scearios Radomir Perzia, Jaroslav Ramik 2 Abstract. The mai goal of every ecoomic aget is to make a good decisio,
More information4 n. n 1. You shold think of the Ratio Test as a generalization of the Geometric Series Test. For example, if a n ar n is a geometric sequence then
SECTION 2.6 THE RATIO TEST 79 2.6. THE RATIO TEST We ow kow how to hadle series which we ca itegrate (the Itegral Test), ad series which are similar to geometric or pseries (the Compariso Test), but of
More informationIncremental calculation of weighted mean and variance
Icremetal calculatio of weighted mea ad variace Toy Fich faf@cam.ac.uk dot@dotat.at Uiversity of Cambridge Computig Service February 009 Abstract I these otes I eplai how to derive formulae for umerically
More informationThe Stable Marriage Problem
The Stable Marriage Problem William Hut Lae Departmet of Computer Sciece ad Electrical Egieerig, West Virgiia Uiversity, Morgatow, WV William.Hut@mail.wvu.edu 1 Itroductio Imagie you are a matchmaker,
More informationProperties of MLE: consistency, asymptotic normality. Fisher information.
Lecture 3 Properties of MLE: cosistecy, asymptotic ormality. Fisher iformatio. I this sectio we will try to uderstad why MLEs are good. Let us recall two facts from probability that we be used ofte throughout
More informationReview for 1 sample CI Name. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Review for 1 sample CI Name MULTIPLE CHOICE. Choose the oe alterative that best completes the statemet or aswers the questio. Fid the margi of error for the give cofidece iterval. 1) A survey foud that
More informationMTOMTS Production Systems in Supply Chains
NSF GRANT #0092854 NSF PROGRAM NAME: MES/OR MTOMTS Productio Systems i Supply Chais Philip M. Kamisky Uiversity of Califoria, Berkeley Our Kaya Uiversity of Califoria, Berkeley Abstract: Icreasig cost
More information*The most important feature of MRP as compared with ordinary inventory control analysis is its time phasing feature.
Itegrated Productio ad Ivetory Cotrol System MRP ad MRP II Framework of Maufacturig System Ivetory cotrol, productio schedulig, capacity plaig ad fiacial ad busiess decisios i a productio system are iterrelated.
More informationLesson 15 ANOVA (analysis of variance)
Outlie Variability betwee group variability withi group variability total variability Fratio Computatio sums of squares (betwee/withi/total degrees of freedom (betwee/withi/total mea square (betwee/withi
More informationHow to read A Mutual Fund shareholder report
Ivestor BulletI How to read A Mutual Fud shareholder report The SEC s Office of Ivestor Educatio ad Advocacy is issuig this Ivestor Bulleti to educate idividual ivestors about mutual fud shareholder reports.
More informationAn EnergyEfficient Communication Scheme in Wireless Cable Sensor Networks
This fll text aer was eer reiewed at the direction of IEEE Commnications Society sbject matter exerts for blication in the IEEE ICC 11 roceedings An EnergyEfficient Commnication Scheme in Wireless Cable
More informationSupply Chain Network Design with Preferential Tariff under Economic Partnership Agreement
roceedigs of the 2014 Iteratioal oferece o Idustrial Egieerig ad Oeratios Maageet Bali, Idoesia, Jauary 7 9, 2014 Suly hai Network Desig with referetial ariff uder Ecooic artershi greeet eichi Fuaki Yokohaa
More informationSubject CT5 Contingencies Core Technical Syllabus
Subject CT5 Cotigecies Core Techical Syllabus for the 2015 exams 1 Jue 2014 Aim The aim of the Cotigecies subject is to provide a groudig i the mathematical techiques which ca be used to model ad value
More informationSection 11.3: The Integral Test
Sectio.3: The Itegral Test Most of the series we have looked at have either diverged or have coverged ad we have bee able to fid what they coverge to. I geeral however, the problem is much more difficult
More informationActa Acad. Paed. Agriensis, Sectio Mathematicae 29 (2002) 77 87. ALMOST SURE FUNCTIONAL LIMIT THEOREMS IN L p( ]0, 1[ ), WHERE 1 p <
Acta Acad. Paed. Agriesis, Sectio Mathematicae 29 22) 77 87 ALMOST SUR FUNCTIONAL LIMIT THORMS IN L ], [ ), WHR < József Túri Nyíregyháza, Hugary) Dedicated to the memory of Professor Péter Kiss Abstract.
More informationComponent Reliability in Fault Diagnosis DecisionMaking based on Dynamic Bayesian Networks
Compoet Reliability i Fault Diagosis DecisioMakig based o Dyamic Bayesia Networks Philippe Weber, Didier Theilliol, Christophe Aubru To cite this versio: Philippe Weber, Didier Theilliol, Christophe Aubru.
More informationConfidence Intervals for Two Proportions
PASS Samle Size Software Chater 6 Cofidece Itervals for Two Proortios Itroductio This routie calculates the grou samle sizes ecessary to achieve a secified iterval width of the differece, ratio, or odds
More informationEkkehart Schlicht: Economic Surplus and Derived Demand
Ekkehart Schlicht: Ecoomic Surplus ad Derived Demad Muich Discussio Paper No. 200617 Departmet of Ecoomics Uiversity of Muich Volkswirtschaftliche Fakultät LudwigMaximiliasUiversität Müche Olie at http://epub.ub.uimueche.de/940/
More information9.8: THE POWER OF A TEST
9.8: The Power of a Test CD91 9.8: THE POWER OF A TEST I the iitial discussio of statistical hypothesis testig, the two types of risks that are take whe decisios are made about populatio parameters based
More informationUniversal coding for classes of sources
Coexios module: m46228 Uiversal codig for classes of sources Dever Greee This work is produced by The Coexios Project ad licesed uder the Creative Commos Attributio Licese We have discussed several parametric
More informationConfidence Intervals for One Mean
Chapter 420 Cofidece Itervals for Oe Mea Itroductio This routie calculates the sample size ecessary to achieve a specified distace from the mea to the cofidece limit(s) at a stated cofidece level for a
More informationTheorems About Power Series
Physics 6A Witer 20 Theorems About Power Series Cosider a power series, f(x) = a x, () where the a are real coefficiets ad x is a real variable. There exists a real oegative umber R, called the radius
More informationChapter 6: Variance, the law of large numbers and the MonteCarlo method
Chapter 6: Variace, the law of large umbers ad the MoteCarlo method Expected value, variace, ad Chebyshev iequality. If X is a radom variable recall that the expected value of X, E[X] is the average value
More information1 Computing the Standard Deviation of Sample Means
Computig the Stadard Deviatio of Sample Meas Quality cotrol charts are based o sample meas ot o idividual values withi a sample. A sample is a group of items, which are cosidered all together for our aalysis.
More informationOptimal Parallel Algorithms for Computing the Sum, the Prefixsums, and the Summed Area Table on the Memory Machine Models
IEICE TRANS. INF. & SYST., VOL.Exx??, NO.xx XXXX x 1 PAPER Secial Sectio o Secial Sectio o Parallel ad Distributed Comutig ad Netorkig Otimal Parallel Algorithms for Comutig the Sum, the Prefixsums, ad
More information4.1.4 Electrical Characterisation of MOVPE Grown n and pngaas Nanowires
3 BiAual Reort 28/29  SolidState Electroics Deartmet 4.1.4 Electrical Characterisatio of MOVPE Grow  ad GaAs Naowires Scietist: C. Gutsche, I. Regoli, A. Lysov Itroductio Recetly, we reseted a cotrolled
More informationDomain 1: Configuring Domain Name System (DNS) for Active Directory
Maual Widows Domai 1: Cofigurig Domai Name System (DNS) for Active Directory Cofigure zoes I Domai Name System (DNS), a DNS amespace ca be divided ito zoes. The zoes store ame iformatio about oe or more
More informationOutput Analysis (2, Chapters 10 &11 Law)
B. Maddah ENMG 6 Simulatio 05/0/07 Output Aalysis (, Chapters 10 &11 Law) Comparig alterative system cofiguratio Sice the output of a simulatio is radom, the comparig differet systems via simulatio should
More information0.7 0.6 0.2 0 0 96 96.5 97 97.5 98 98.5 99 99.5 100 100.5 96.5 97 97.5 98 98.5 99 99.5 100 100.5
Sectio 13 KolmogorovSmirov test. Suppose that we have a i.i.d. sample X 1,..., X with some ukow distributio P ad we would like to test the hypothesis that P is equal to a particular distributio P 0, i.e.
More informationQuaderni di Dipartimento. A note on the Exclusion Principle. Paolo Bertoletti (University of Pavia) # 179 (1205)
Quaderi di Diartimeto A ote o te xclusio Pricile Paolo Bertoletti Uiersity of Paia # 7905 Diartimeto di ecoomia olitica e metodi quatitatii Uiersità degli studi di Paia Via Sa Felice 5 I700 Paia Dicembre
More informationNr. 2. Interpolation of Discount Factors. Heinz Cremers Willi Schwarz. Mai 1996
Nr 2 Iterpolatio of Discout Factors Heiz Cremers Willi Schwarz Mai 1996 Autore: Herausgeber: Prof Dr Heiz Cremers Quatitative Methode ud Spezielle Bakbetriebslehre Hochschule für Bakwirtschaft Dr Willi
More informationThe second difference is the sequence of differences of the first difference sequence, 2
Differece Equatios I differetial equatios, you look for a fuctio that satisfies ad equatio ivolvig derivatives. I differece equatios, istead of a fuctio of a cotiuous variable (such as time), we look for
More informationDepartment of Computer Science, University of Otago
Departmet of Computer Sciece, Uiversity of Otago Techical Report OUCS200609 Permutatios Cotaiig May Patters Authors: M.H. Albert Departmet of Computer Sciece, Uiversity of Otago Micah Colema, Rya Fly
More informationNPTEL STRUCTURAL RELIABILITY
NPTEL Course O STRUCTURAL RELIABILITY Module # 0 Lecture 1 Course Format: Web Istructor: Dr. Aruasis Chakraborty Departmet of Civil Egieerig Idia Istitute of Techology Guwahati 1. Lecture 01: Basic Statistics
More informationSpam Detection. A Bayesian approach to filtering spam
Spam Detectio A Bayesia approach to filterig spam Kual Mehrotra Shailedra Watave Abstract The ever icreasig meace of spam is brigig dow productivity. More tha 70% of the email messages are spam, ad it
More informationEvery manufacturer is confronted with the problem
HOW MANY PARTS TO MAKE AT ONCE FORD W. HARRIS Prodction Engineer Reprinted from Factory, The Magazine of Management, Volme 10, Nmber 2, Febrary 1913, pp. 135136, 152 Interest on capital tied p in wages,
More informationQUANTIFYING THE PERFORMANCE OF A TOPDOWN NATURAL VENTILATION WINDCATCHER. Benjamin M. Jones a,b and Ray Kirby b, *
QUANTFYNG TH PRFORMANC OF A TOPDOWN NATURAL VNTLATON WNDCATCHR Benjamin M. Jones a,b and Ray Kirby b, * a Monodraght Ltd. Halifax Hose, Halifax Road, Cressex Bsiness Park High Wycombe, Bckinghamshire,
More informationA RANDOM PERMUTATION MODEL ARISING IN CHEMISTRY
J. Appl. Prob. 45, 060 070 2008 Prited i Eglad Applied Probability Trust 2008 A RANDOM PERMUTATION MODEL ARISING IN CHEMISTRY MARK BROWN, The City College of New York EROL A. PEKÖZ, Bosto Uiversity SHELDON
More informationAnnuities Under Random Rates of Interest II By Abraham Zaks. Technion I.I.T. Haifa ISRAEL and Haifa University Haifa ISRAEL.
Auities Uder Radom Rates of Iterest II By Abraham Zas Techio I.I.T. Haifa ISRAEL ad Haifa Uiversity Haifa ISRAEL Departmet of Mathematics, Techio  Israel Istitute of Techology, 3000, Haifa, Israel I memory
More informationLecture 2: Karger s Min Cut Algorithm
priceto uiv. F 3 cos 5: Advaced Algorithm Desig Lecture : Karger s Mi Cut Algorithm Lecturer: Sajeev Arora Scribe:Sajeev Today s topic is simple but gorgeous: Karger s mi cut algorithm ad its extesio.
More informationModule 4: Mathematical Induction
Module 4: Mathematical Iductio Theme 1: Priciple of Mathematical Iductio Mathematical iductio is used to prove statemets about atural umbers. As studets may remember, we ca write such a statemet as a predicate
More informationDefinition. A variable X that takes on values X 1, X 2, X 3,...X k with respective frequencies f 1, f 2, f 3,...f k has mean
1 Social Studies 201 October 13, 2004 Note: The examples i these otes may be differet tha used i class. However, the examples are similar ad the methods used are idetical to what was preseted i class.
More informationResearch Article Sign Data Derivative Recovery
Iteratioal Scholarly Research Network ISRN Applied Mathematics Volume 0, Article ID 63070, 7 pages doi:0.540/0/63070 Research Article Sig Data Derivative Recovery L. M. Housto, G. A. Glass, ad A. D. Dymikov
More informationData Analysis and Statistical Behaviors of Stock Market Fluctuations
44 JOURNAL OF COMPUTERS, VOL. 3, NO. 0, OCTOBER 2008 Data Aalysis ad Statistical Behaviors of Stock Market Fluctuatios Ju Wag Departmet of Mathematics, Beijig Jiaotog Uiversity, Beijig 00044, Chia Email:
More informationLEASEPURCHASE DECISION
Public Procuremet Practice STANDARD The decisio to lease or purchase should be cosidered o a caseby case evaluatio of comparative costs ad other factors. 1 Procuremet should coduct a cost/ beefit aalysis
More informationConvention Paper 6764
Audio Egieerig Society Covetio Paper 6764 Preseted at the 10th Covetio 006 May 0 3 Paris, Frace This covetio paper has bee reproduced from the author's advace mauscript, without editig, correctios, or
More informationThis chapter considers the effect of managerial compensation on the desired
Chapter 4 THE EFFECT OF MANAGERIAL COMPENSATION ON OPTIMAL PRODUCTION AND HEDGING WITH FORWARDS AND PUTS 4.1 INTRODUCTION This chapter cosiders the effect of maagerial compesatio o the desired productio
More informationLecture 4: Cauchy sequences, BolzanoWeierstrass, and the Squeeze theorem
Lecture 4: Cauchy sequeces, BolzaoWeierstrass, ad the Squeeze theorem The purpose of this lecture is more modest tha the previous oes. It is to state certai coditios uder which we are guarateed that limits
More informationSignal Reconstruction from Noisy Random Projections
Sigal Recostructio from Noisy Radom Projectios Jarvis Haut ad Robert Nowak Deartmet of Electrical ad Comuter Egieerig Uiversity of WiscosiMadiso March, 005; Revised February, 006 Abstract Recet results
More informationSequences and Series
CHAPTER 9 Sequeces ad Series 9.. Covergece: Defiitio ad Examples Sequeces The purpose of this chapter is to itroduce a particular way of geeratig algorithms for fidig the values of fuctios defied by their
More informationRISK TRANSFER FOR DESIGNBUILD TEAMS
WILLIS CONSTRUCTION PRACTICE IBEAM Jauary 2010 www.willis.com RISK TRANSFER FOR DESIGNBUILD TEAMS DesigbuilD work is icreasig each quarter. cosequetly, we are fieldig more iquiries from cliets regardig
More informationThe following example will help us understand The Sampling Distribution of the Mean. C1 C2 C3 C4 C5 50 miles 84 miles 38 miles 120 miles 48 miles
The followig eample will help us uderstad The Samplig Distributio of the Mea Review: The populatio is the etire collectio of all idividuals or objects of iterest The sample is the portio of the populatio
More informationErik Ottosson & Fredrik Weissenrieder, 19960301 CVA. Cash Value Added  a new method for measuring financial performance.
CVA Cash Value Added  a ew method for measurig fiacial performace Erik Ottosso Strategic Cotroller Sveska Cellulosa Aktiebolaget SCA Box 7827 S103 97 Stockholm Swede Fredrik Weisserieder Departmet of
More informationEstimating the Mean and Variance of a Normal Distribution
Estimatig the Mea ad Variace of a Normal Distributio Learig Objectives After completig this module, the studet will be able to eplai the value of repeatig eperimets eplai the role of the law of large umbers
More informationProject Deliverables. CS 361, Lecture 28. Outline. Project Deliverables. Administrative. Project Comments
Project Deliverables CS 361, Lecture 28 Jared Saia Uiversity of New Mexico Each Group should tur i oe group project cosistig of: About 612 pages of text (ca be loger with appedix) 612 figures (please
More informationDesigning Incentives for Online Question and Answer Forums
Desigig Icetives for Olie Questio ad Aswer Forums Shaili Jai School of Egieerig ad Applied Scieces Harvard Uiversity Cambridge, MA 0238 USA shailij@eecs.harvard.edu Yilig Che School of Egieerig ad Applied
More informationMaximum Likelihood Estimators.
Lecture 2 Maximum Likelihood Estimators. Matlab example. As a motivatio, let us look at oe Matlab example. Let us geerate a radom sample of size 00 from beta distributio Beta(5, 2). We will lear the defiitio
More informationVladimir N. Burkov, Dmitri A. Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT
Keywords: project maagemet, resource allocatio, etwork plaig Vladimir N Burkov, Dmitri A Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT The paper deals with the problems of resource allocatio betwee
More information