O & M Cost O & M Cost

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1 5/5/008 Turbie Reliabiliy, Maieace ad Faul Deecio Zhe Sog, Adrew Kusiak 39 Seamas Ceer Iowa Ciy, Iowa Tel: Fax: hp:// Oulie Iroducio Basic reliabiliy models Faul deecio O & M Cos O & M Cos Average O&M Coss for Available Daa Years from , by Las Year of Equipme

2 5/5/008 O & M Cos Average O&M Coss for Available Daa Years from , by Projec Size O & M Cos Aual Average O&M Coss, by Projec Age ad Las Year of Equipme Isallaio Reliabiliy Defiiio: reliabiliy is he probabiliy ha a compoe or sysem will perform a required fucio for a give period of ime whe used uder saed operaig codiios Reliabiliy, Some Theories Reliabiliy fucio R () = Pr( T ) T, ime o failure R ( ) is he probabiliy ha he ime o failure is greaer ha or equal o F () = R () F ( ) is he probabiliy ha a failure occurs before ime

3 5/5/008 Probabiliy Desiy Fucio Mea Time o Failure df() = d f () ' ' F() = f( ) d 0 MTTF = E( T ) = f ( ) d 0 ' ' R() = f( ) d MTTF = 0 R() d Failure Rae Fucio Bahub Curve λ () = f () R() ' ' R() = exp λ( ) d 0. Icreasig failure rae (IFR). Decreasig failure rae (DFR) 3. Cosa failure rae (CFR) 3

4 5/5/008 Reliabiliy of Sysems Maiaiabiliy Serial cofiguraio R () R () A B Parallel cofiguraio ( R ( )) ( R ( )) A B ' ' Pr{ T } = H( ) = h( ) d T, ime o repaire a failed ui MTTR = h() d 0 0 Reducig Maieace Cos Develop logisics pla Ideify opporuiies for redudacy Improve raiig Improve maiaiabiliy Impleme codiio moiorig Some Recommedaios Quaify O&M coss over ime Develop compoe reliabiliy Ideify high-risk compoes ad udersad failure modes Re-evaluae desig sadards 4

5 5/5/008 Faul Deecio Saisical mehod, qualiy corol Sigle variable Two variables Cluserig Residual approach Low bed emperaure Wid urbie power curve x+ x x x = X Bar Char for he Mea x + x + + x x = m... m { } { } R = max x, x,..., x mi x, x,..., x R + R + + R R = m... m UCL = x + A R CeerLie = x LCL = x A R R Bar Char for he Variaio UCL = D R 4 CeerLie = R LCL = D R 3 R + R + + R R = m... m Two Variables Each variable seems o be ormal Lookig a hem ogeher geeraes fauls 5

6 5/5/008 Two Variables wih Correlaio How o moior wo variables if hey have correlaio Joi Normal Regios x = x x x... H Char ' S = ( xi x)( xi x) i= χ σ ( μ ) σ ( μ ) σ ( μ )( μ ) σ σ σ 0 = x + x x x Too may variables Large daa se Daa seams No ormal disribuios Cluserig χ α, Chi-square saisics 0 >, χ χ α No ormal, ou of corol 6

7 5/5/008 -Dimesio Example 3-Dimesio Example ri = ( P ci) m i P Ci Residual Approach No fixed mea No obvious paers, e.g. clusers Uderlyig process model ca be cosruced Daa miig algorihms, liear regressio, pricipal compoe aalysis yˆ f( x) Residual How o Ge Residual y = f ( x) real = Ideified process model ε = ŷ y Prediced Observed 7

8 5/5/008 Low Bed Temperaure Example A combusio process A sesor is isalled o measure he low bed emperaure of a boiler How o deec he sesor failures Low Bed Temperaure Example Process variables yˆ = f y ( xv, ) Wha is he Model s Performace Samplig Tes Daa Pois μ g = ( y yˆ ) Trai i i g i= Mea raiig error μ = ( y yˆ ) Tes g+ i g+ i i= Mea es error σ g = (( y yˆ ) μ ) Trai i i Trai g i= Sd of he raiig error σ = (( y yˆ ) μ ) Tes g+ i g+ i Tes i= Sd of he es error 8

9 5/5/008 σ UCL = μtrai + 3 CeerLie = μ Trai Corol Limis Trai Moior he mea es error σ LCL = μtrai 3 Trai σtrai UCL Moior he es error s sd CeerLie LCL = χ = 0 = σ α, Trai No Temperaure Sesor Failures Bias Temperaure Sesor Failures Variaio Temperaure Sesor Failures 9

10 5/5/008 Wid Turbie Power Curve Moiorig Ideify a power curve fucio based o ormal raiig daa pois Calculae he power curve model s performace i erms of mea raiig error ad sd of he raiig error Cosruc corol limis for moiorig mea es error ad sd of he es error Power Curve Moiorig Ideified Abormaliies Power Curve Profile Moiorig Use parameric models o ideify a power curve, he moior he parameers + me y = f ( x, θ ) = a + e x / τ x / τ Noliear 0, v< vcu _ i f() v = λv+ η, vcu i v v Praed, v > vraed raed Liear 0

11 5/5/008 Liear Sceario 0, v< vcu _ i f() v = λv+ η, vcu i v v Praed, v > vraed ( λ, η) Moior his wo parameers by usig T char? raed Summary Reliabiliy models Collec failure Esimae pdf Desig logisic plas Faul deecio Sigle variable Muliple variables