Curso Mantenimiento Predictivo

CONFIABILIDAD DE COMPONENTES Y SISTEMAS

Relator: Rodrigo Huenumn Rojas

FACULTAD DE INGENIERAUNIVERSIDAD DE ATACAMA

2Contenidos:Funciones ConfiabilidadAnlisis SistemasAnlisis DisponibilidadAnlisis de RedundanciaOptimizacin del MantenimientoFunciones de confiabilidadFACULTAD DE INGENIERAUNIVERSIDAD DE ATACAMA

4Definicin de ConfiabilidadConfiabilidad de un elemento es la probabilidad de que dicho elemento funcione sin fallas durante un tiempo "t" determinado bajo condiciones ambientales dadas.

Para cuantificarla es necesario que :Sea fijado en forma inequvoca el criterio que determina si el elemento funciona o no.Sean establecidas exactamente las condiciones ambientales y de utilizacin.Sea definido el intervalo de tiempo durante el cual se requiere que el elemento funcione.5Indicadores de Confiabilidad- Tiempo medio de funcionamiento entre dos fallas sucesivas MTBF (Mean Time Between Failure).- Tiempo medio de funcionamiento entre dos intervenciones sucecivas de mantencin. MTBM (Mean Time Between Maintenance).

Indicadores de Mantenibilidad.- Tiempo medio tcnico de intervencin de mantencin MTTR (Mean Time To Repair).- tiempo medio total fuera de servicio, suma de MTTR y de tiempos de reparacin y de espera (logsticos). MDT (Mean Down Time).

Confiabilidad y MantenibilidadIndicadores 6Funciones de Confiabilidad

f(t): funcin de densidad de falla.F(t): funcin acumulada de falla.R(t): Confiabilidad.6La funcin de densidad de falla representa la frecuencia relativa de fallas como funcin del tiempo.El rea total bajo la funcin de densidad de falla debe ser 1 (todos los casos posibles).La funcin acumulada de falla representa la medida de la probabilidad que un equipo falle entre 0 y t.La funcin acumulada de falla vara entre O y 1 a medida que la variable tiempo se incrementa desde su valor ms pequeo al mayor.Es as como si t --- infinito el valor de la funcin acumulada de falla tiende a 1.Base Conceptual 7Tasa de falla Es la probabilidad de tener una falla del sistema o del elemento entre los instantes t y (t+Dt) a condicin de que el sistema haya sobrevivido hasta el tiempo "t". Tasa de fallas de una poblacin homognea en funcin de su edadDesgasteVida tilRodaje (t)ltl()()()tiftiRti=73Base Conceptual 8Funciones de ConfiabilidadProbabilidad de falla instantnea :Confiabilidad :Probabilidad de fallas acumulada :ftiti()DFti()Rti()82Base Conceptual 9Funciones de Confiabilidad

NotacinNo : Nmero de elementos buenos al instante to (instante inicial)Ni : Nmero de elementos buenos al instante tini : Nmero de elementos que fallaron entre ti y t(i+1), equivalente a DNi.Dti: Intervalo de tiempo observado igual a t(i+1) - ti.Donde :9Base Conceptual 10Confiabilidad a Nivel Continuo

Por hiptesis :Integrando :

104Base Conceptual 11Confiabilidad a Nivel Continuo

Formalizando :Aplicando exponencial :115Base Conceptual 12Modelos de Confiabilidad

EXPONENCIAL NEGATIVA128Base Conceptual 13Modelos de Confiabilidad

NORMALmf(t)0t0(t)lt139Base Conceptual 14Modelos de Confiabilidad : Weibull

14Base Conceptual 15Confiabilidad A Nivel Continuo MTTF (Mean Time To Failure)

MTBF (Mean Time Between Failures)

Perodo en el ciclo de vida de sistemas reparablesM.T.B.FM.T.T.R.156Base Conceptual 16Mantenibilidad es la probabilidad de que la intervencin de mantenimiento se lleve a cabo dentro del tiempo definido tr.La distribucin normal logartmica es la que mejor representa la aleatoriedad de tr. Su explicacin ms cientfica se basa en la separacin del proceso de reparacin individual en dos tiempos en esencia distintos:Tiempo asociado a factores accidentales en la reparacin.Tiempo usual de la reparacin propiamente tal

Mantenibilidad16Base Conceptual 17trm(tr)Distribucin normal logartmica para trMantenibilidad17ANLISIS DE SISTEMASFACULTAD DE INGENIERAUNIVERSIDAD DE ATACAMA

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para i = cte : Configuracin en Serie

20Efecto de Sistemas en Serie

0.99990.9990.990.980.950.90R(n)N de Componentes (n)21Un circuito electrnico simple consiste en 6 transistores, cada uno con una tasa de falla de 10-6 f/hr, 3 Capacitadores cada uno con tasa de falla de 0.5 x 10-6 f/hr, 10 resistencias cada una con tasa de falla de 5 x 10-6 f/hr y 2 switches con tasas de falla de 2 x 10-6 f/hr. Considerando que los cables son 100% confiables evale la probabilidad de que el sistema funcione a las 1.000 hrs y 10.000 hrs de operacin.Ejemplo Configuracin en Serie2122Un circuito electrnico simple consiste en 6 transistores, cada uno con una tasa de falla de 10-6 f/hr, 3 Capacitadores cada uno con tasa de falla de 0.5 x 10-6 f/hr, 10 resistencias cada una con tasa de falla de 5 x 10-6 f/hr y 2 switches con tasas de falla de 2 x 10-6 f/hr. Considerando que los cables son 100% confiables evale la probabilidad de que el sistema funcione a las 1.000 hrs y 10.000 hrs de operacin.Ejemplo Configuracin en Serie

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Caso 2 equipos:Configuracin en Paralelo24Efecto de Sistemas en Paralelo

Anlisis de Confiabilidad Anlisis de Impacto25Reconsidere el ejemplo anterior y evale la probabilidad de sobrevivir 1.000 hrs y 10.000 hrs si dos circuitos idnticos como los descritos anteriormente son utilizados en paralelo y se asume que el sistema opera exitosamente si slo uno de los circuitos est operativo.Ejemplo Configuracin en Paralelo26Reconsidere el ejemplo anterior y evale la probabilidad de sobrevivir 1.000 hrs y 10.000 hrs si dos circuitos idnticos como los descritos anteriormente son utilizados en paralelo y se asume que el sistema opera exitosamente si slo uno de los circuitos est operativo.Ejemplo Configuracin en Paralelo

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Comparacin de Subsistemas28Eq FallaRsResultado0Ra*Rb*Rc11-(a)(1-Ra)*Rb*Rc11-(b)Ra*(1-Rb)*Rc11-(c)Ra*Rb*(1-Rc)12-(b,c)Ra*(1-Rb)*(1-Rc)12-(a.c)(1-Ra)*Rb*(1-Rc)12-(a,b)(1-Ra)*(1-Rb)*Rc13-(a,b,c)(1-Ra)*(1-Rb)*(1-Rc)0

Paralelo Event Space Method29

Configuracin Stand-bypara a = b cte : 30Compare la confiabilidad de un subsistema de 2 componentes cada uno con una tasa de falla de 0.02 f/hr a un tiempo de operacin de 10 hrs si se encuentran A) en paralelo y B) en configuracin Standby con un conmutador 100% confiable. Tambin compare los MTBFs de los dos sistemas.Ejemplo Configuracin Stand By31Compare la confiabilidad de un subsistema de 2 componentes cada uno con una tasa de falla de 0.02 f/hr a un tiempo de operacin de 10 hrs si se encuentran A) en paralelo y B) en configuracin Standby con un conmutador 100% confiable. Tambin compare los MTBFs de los dos sistemas.

B)

Ejemplo Configuracin Stand By

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Comparacin de Subsistemas33

Configuracin en Redundancia Parcial34Eq FallaRsResultado0Ra*Rb*Rc11-(a)(1-Ra)*Rb*Rc11-(b)Ra*(1-Rb)*Rc11-(c)Ra*Rb*(1-Rc)12-(b,c)Ra*(1-Rb)*(1-Rc)02-(a,c)(1-Ra)*Rb*(1-Rc)02-(a,b)(1-Ra)*(1-Rb)*Rc03-(a,b,c)(1-Ra)*(1-Rb)*(1-Rc)0

Ejemplo k=2 y N=3, Event Space MethodEjercicio:La instalacin de tres generadores elctricos cada uno con la mitad de la capacidad del requerimiento total. Esto es una redundancia de tres sobre dos. Los generadores son de las misma marca y el tiempo de modelo, y su tasa de falla es 9*10^-6 (1/h) en la etapa de madurez. Calcular todos los elementos de confiabilidad a un ao de operacin.36Configuracin en fraccionamiento

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Reduccin: Ejemplo 138

Reduccin: Ejemplo 139

R1=0.850R2=0.820R3=0.920R4=0.750R6=0.910R5=0.870R7=0.900R8=0.986R1=0.850R8=0.939R7=0.900R7=0.900R10=0.787R11=0.9792/3Reduccin: Ejemplo 240

Diagrama de Bloques de Confiabilidad (RBD) Cada equipo es representado por un bloque. Determinar el Impacto de la Falla de cada equipo. Las fallas de los equipos son independientes. El comportamiento del sistema se obtiene conectando los bloques.Existen distintos modelos que permiten representar los diagramas de bloques:

1.Serie. 2.Paralelo. 3.Stand by. 4.Redundancia Parcial. 5.Fraccionamiento. Serie: Dependencia total del equipo. Si falla se cae el sistema. Redundancia Total (paralelo): Caso especial de Redundancia Parcial. Cada equipo que compone el sistema es capaz de tomar de forma independiente el 100% de la carga del proceso. Por lo general operan los n equipos a un fraccin de la carga total. (ptimo) No se puede operar si no es al 100%. (n sobre 1).Stand by: Cada equipo que compone el sistema es capaz de tomar de forma independiente el 100% de la carga. Slo funciona un equipo al 100% de la carga total (capacidad ptima). Fraccionamiento: n equipos se reparten de forma proporcional o no la carga de trabajo. Pueden tener capacidad ociosa. Se puede operar a una fraccin de la carga total. Redundancia Parcial: Se requiere de una fraccin del total de equipos para operar a la carga total. No se puede operar si no es al 100%. (n sobre r)

Diagrama de Bloques de Confiabilidad (RBD)

Configuracin sistmica

Serie

Configuracin sistmica Stand by

Configuracin sistmica Redundancia parcial

Configuracin sistmica Redundancia total

Configuracin sistmica Fraccionamiento

47Ejercicio de Diseo Lgico

El proceso comienza con un buzn de finos y alimentadores, que cumplen la funcin de almacenar y repartir el material a 12 lneas de procesos, cada una compuesta por tres alimentadores, una correa, un molino, una bomba y un hidrocicln. Posterior a la molienda unitaria sigue el proceso de Flotacin.

Segn lo informado, de los tres alimentadores disponibles, se utilizan slo dos

Caso Planta Molienda unitariaDiseo Lgico RBD

El sistema posee 12 lneas idnticas, a excepcin de las lneas 6 y 8.

Caso Planta Molienda unitariaDiseo Lgico RBDLos dos grupos de lneas completan el sistema total en una configuracin de fraccionamiento. ANLISIS DE DISPONIBILIDADFACULTAD DE INGENIERAUNIVERSIDAD DE ATACAMA

51Disponibilidad :

UT (up-time) representa el tiempo en que el sistema est realmente disponible para el funcionamiento.DT (down-time) representa el tiempo fuera de servicio imputable a causas tcnicas.

Disponibilidad Histrica

52Disponibilidad Sistema en Serie Ejemplo Disponibilidad Histrica (Serie)

Time53Disponibilidad Sistema en Paralelo Ejemplo Disponibilidad Histrica (Paralelo)

Time54 MTTF (Mean Time To Failure)

MTBF (Mean Time Between Failures) Perodo en el ciclo de vida de sistemas reparablesM.T.B.FM.T.T.R.Disponibilidad Probabilstica

55Disponibilidad :

MTBF es la esperanza en tiempo de buen funcionamiento.MTTR es la esperanza en tiempo de mantencin.

Disponibilidad Probabilstica56Donde :

Ni : El nmero de partes componentes del tipo i-simo.ti : El tiempo medio de reparacin de la parte i-sima.ai : El nmero medio de fallas por unidad de tiempo, siempre para la parte i-sima.MTBFRtdt=()0MTTRNiiiNii=ataDisponibilidad ProbabilsticaANLISIS DE REDUNDANCIAFACULTAD DE INGENIERAUNIVERSIDAD DE ATACAMA

58Mejorar el diseo de los equiposRedundanciaAumentar la mantenibilidadAumentar la disponibilidadesperadaQue pasa con los costos globales?Alternativas de mejoramiento59Los costos de la falta

Donde:Cf= Costos de la falta F= Facturacin perdidaCv= Costos variablesCf = F- CvCostos de Falta60Impacto en losCostosAumentar laredundanciaInversinFaltaConceptos

C Globales: Cfa + PMTNomenclatura:As: Disponibilidad del Sistema.Cfa: Costo de falta anual.Cf: Costo de falta horario.T: Tiempo de operacin anual.PMT: Payment (cuota anual).i:tasa de descuento.

Cf: (Facturacin C. Variables)/T61Ejemplo paraleloInv=$500.000 ; 4 aosT.dcto=10%

Facturacin anual= $10.000.000.Horas de operacin = 5.000 (hrs/ao).Impacto C. Variables = 20%.

Caso original:MTTRs = 20 hrs.MTBFs = 200 hrs.As = 200 / 220 =90.9%.Cfa= $727.272Cglobal = $727.272.Caso con redundancia:MTTRs = 20 hrs.MTBFs = 338,9 hrs.As = 338,9/358,9 =94.4%.Cfa = $445.820.PMT = $157.735.Cglobal = $603.556.Ci=$1,600/hr

OPTIMIZACION DEL MANTENIMIENTOFACULTAD DE INGENIERAUNIVERSIDAD DE ATACAMA

63Una de las aplicaciones interesantes de la teora de confiabilidad en el mbito de la gestin tiene relacin con la definicin de planes de mantencin.Planificacin de Actividades64Modelo - Costos

65Para que las actividades planificadas de mantencin preventiva sean econmicamente convenientes se deben satisfacer dos condiciones:La tasa de fallas debe ser creciente.Los costos de la intervencin de emergencia deben ser mayores que la intervencin preventiva.Modelo - Restricciones66Con este tipo de mantencin se dispone que el componente se sustituya cuando falla o cuando alcanza cierta edad TCE : Costo total de reparacin en emergenciaCP : Costo total de intervencin preventivaR(T): Confiabilidad al tiempo TF(T): Probabilidad de falla altiempo TEdad ConstanteEC = [CE F(T) + CP R(T)]/ MTBFT67EC = [CE F(T) + CP R(T)]/ MTBFTDonde:

TiempoEctpEdad Constante68Un equipo en etapa de desgaste tiene una curva de confiabilidad determinada por una distribucin Weibull con parmetros alfa = 100 y beta = 2. El costo de mantencin preventiva del equipo es de $10,000 mientras que el costo de mantencin de emergencia es de $100,000. Evale, desde el punto de vista de los costos, la programacin ptima de mantencin para el equipo.Ejemplo: Edad constante

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Ejemplo: Edad constante

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Ejemplo: Edad constante71

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Programa de Inspecciones

Frecuencia de inspeccionesMinimizacin del costo globalFuente: A.K.S. Jardine, A. Tsang, Maintenance, Replacement and Reliability,Taylor & Francis, 2006.

Grfico10.99990.9990.990.980.950.90.999800010.9980010.98010.96040.90250.810.999700030.9970029990.9702990.9411920.8573750.7290.999600060.9960059960.960596010.922368160.814506250.65610.99950010.995009990.95099004990.90392079680.77378093750.590490.999400150.994014980.94148014940.88584238090.73509189060.5314410.999300210.9930209650.93206534790.86812553320.69833729610.47829690.99920027990.99202794410.92274469440.85076302260.66342043130.430467210.99910035990.99103591610.91351724750.83374776210.63024940970.3874204890.99900044990.99004488020.9043820750.81707280690.59873693920.34867844010.99890054980.98905483530.89533825430.80073135070.56880009230.31381059610.99880065980.98806578050.88638487170.78471672370.54036008770.28242953650.99870077970.98707771470.8775210230.76902238930.51334208330.25418658280.99860090960.9860906370.86874581280.75364194150.48767497910.22876792450.99850104950.98510454640.86005835460.73856910260.46329123020.20589113210.99840119940.98411944180.85145777110.72379772060.44012666870.18530201890.99830135930.98313532240.84294319340.70932176620.41812033520.1667718170.99820152920.98215218710.83451376150.69513533090.39721431850.15009463530.9981017090.98117003490.82616862380.68123262420.37735360250.13508517180.99800189890.98018886480.81790693760.66760797180.35848592240.12157665460.99790209870.9792086760.80972786820.65425581230.34056162630.10941898910.99780230850.97822946730.80163058950.64117069610.3235335450.09847709020.99770252820.97725123780.79361428360.62834728220.30735686770.08862938120.9976027580.97627398660.78567814080.61578033650.29198902430.07976644310.99750299770.97529771260.77782135940.60346472980.27738957310.07178979880.99740324740.97432241490.77004314580.59139543520.26352009450.06461081890.99730350710.97334809250.76234271430.57956752650.25034408970.0581497370.99720377670.97237474440.75471928720.5679761760.23782688530.05233476330.99710405630.97140236960.74717209430.55661665240.2259355410.0471012870.99700434590.97043096730.73970037340.54548431940.21463876390.04239115830.99690464550.96946053630.73230336970.5345746330.20390682570.03815204240.9968049550.96849107580.7249803360.52388314030.19371148450.03433683820.99670527450.96752258470.71773053260.51340547750.18402591020.03090315440.9966056040.96655506210.71055322730.5031373680.17482461470.02781283890.99650594350.9655885070.7034476950.49307462060.1660833840.0250315550.99640629290.96462291850.6964132180.48321312820.15777921480.02252839950.99630665220.96365829560.68944908590.47354886560.1498902540.02027555960.99620702160.96269463730.6825545950.46407788830.14239574130.01824800360.99610740090.96173194270.67572904910.45479633060.13527595430.01642320330.99600779010.96077021070.66897175860.4457004040.12851215660.01478088290.99590818940.95980944050.6622820410.43678639590.12208654870.01330279460.99580859850.95884963110.65565922060.4280506680.11598222130.01197251520.99570901770.95789078150.64910262840.41948965460.11018311020.01077526370.99560944680.95693289070.64261160210.41109986150.10467395470.00969773730.99550988580.95597595780.63618548610.40287786430.0994402570.00872796360.99541033480.95501998180.62982363120.3948203070.09446824410.00785516720.99531079380.95406496180.62352539490.38692390080.08974483190.00706965050.99521126270.95311089690.61729014090.37918542280.08525759030.00636268540.99511174160.9521577860.61111723950.37160171440.08099471080.00572641690.99501223040.95120562820.60500606710.36416968010.07694497530.00515377520.99491272920.95025442260.59895600650.35688628650.07309772650.00463839770.99481323790.94930416810.59296644640.34974856080.06944284020.00417455790.99471375660.9483548640.58703678190.34275358950.06597069820.00375710210.99461428520.94740650910.58116641410.33589851770.06267216330.00338139190.99451482380.94645910260.575354750.32918054740.05953855510.00304325270.99441537230.94551264350.56960120250.32259693640.05656162740.00273892740.99431593080.94456713090.56390519050.31614499770.0537335460.00246503470.99421649920.94362256370.55826613850.30982209780.05104686870.00221853120.99411707750.94267894120.55268347720.30362565580.04849452520.00199667810.99401766580.94173626220.54715664240.29755314270.0460697990.00179701030.99391826410.9407945260.5416850760.29160207980.0437663090.00161730930.99381887220.93985373140.53626822520.28577003820.04157799360.00145557830.99371949030.93891387770.5309055430.28005463750.03949909390.00131002050.99362011840.93797496380.52559648750.27445354470.03752413920.00117901850.99352075640.93703698890.52034052270.26896447380.03564793230.00106111660.99342140430.93609995190.51513711740.26358518440.03386553560.0009550050.99332206220.93516385190.50998574620.25831348070.03217225890.00085950450.993222730.93422868810.50488588880.25314721110.03056364590.0007735540.99312340770.93329445940.49983702990.24808426680.02903546360.00069619860.99302409540.93236116490.49483865960.24312258150.02758369040.0006265787

Hoja10.99990.9990.990.980.950.910.99990.9990.990.980.950.920.999800010.9980010.98010.96040.90250.8130.999700030.9970029990.9702990.9411920.8573750.72940.999600060.9960059960.960596010.922368160.814506250.656150.99950010.995009990.95099004990.90392079680.77378093750.5904960.999400150.994014980.94148014940.88584238090.73509189060.53144170.999300210.9930209650.93206534790.86812553320.69833729610.478296980.99920027990.99202794410.92274469440.85076302260.66342043130.4304672190.99910035990.99103591610.91351724750.83374776210.63024940970.387420489100.99900044990.99004488020.9043820750.81707280690.59873693920.3486784401110.99890054980.98905483530.89533825430.80073135070.56880009230.3138105961120.99880065980.98806578050.88638487170.78471672370.54036008770.2824295365130.99870077970.98707771470.8775210230.76902238930.51334208330.2541865828140.99860090960.9860906370.86874581280.75364194150.48767497910.2287679245150.99850104950.98510454640.86005835460.73856910260.46329123020.2058911321160.99840119940.98411944180.85145777110.72379772060.44012666870.1853020189170.99830135930.98313532240.84294319340.70932176620.41812033520.166771817180.99820152920.98215218710.83451376150.69513533090.39721431850.1500946353190.9981017090.98117003490.82616862380.68123262420.37735360250.1350851718200.99800189890.98018886480.81790693760.66760797180.35848592240.1215766546210.99790209870.9792086760.80972786820.65425581230.34056162630.1094189891220.99780230850.97822946730.80163058950.64117069610.3235335450.0984770902230.99770252820.97725123780.79361428360.62834728220.30735686770.0886293812240.9976027580.97627398660.78567814080.61578033650.29198902430.0797664431250.99750299770.97529771260.77782135940.60346472980.27738957310.0717897988260.99740324740.97432241490.77004314580.59139543520.26352009450.0646108189270.99730350710.97334809250.76234271430.57956752650.25034408970.058149737280.99720377670.97237474440.75471928720.5679761760.23782688530.0523347633290.99710405630.97140236960.74717209430.55661665240.2259355410.047101287300.99700434590.97043096730.73970037340.54548431940.21463876390.0423911583310.99690464550.96946053630.73230336970.5345746330.20390682570.0381520424320.9968049550.96849107580.7249803360.52388314030.19371148450.0343368382330.99670527450.96752258470.71773053260.51340547750.18402591020.0309031544340.9966056040.96655506210.71055322730.5031373680.17482461470.0278128389350.99650594350.9655885070.7034476950.49307462060.1660833840.025031555360.99640629290.96462291850.6964132180.48321312820.15777921480.0225283995370.99630665220.96365829560.68944908590.47354886560.1498902540.0202755596380.99620702160.96269463730.6825545950.46407788830.14239574130.0182480036390.99610740090.96173194270.67572904910.45479633060.13527595430.0164232033400.99600779010.96077021070.66897175860.4457004040.12851215660.0147808829410.99590818940.95980944050.6622820410.43678639590.12208654870.0133027946420.99580859850.95884963110.65565922060.4280506680.11598222130.0119725152430.99570901770.95789078150.64910262840.41948965460.11018311020.0107752637440.99560944680.95693289070.64261160210.41109986150.10467395470.0096977373450.99550988580.95597595780.63618548610.40287786430.0994402570.0087279636460.99541033480.95501998180.62982363120.3948203070.09446824410.0078551672470.99531079380.95406496180.62352539490.38692390080.08974483190.0070696505480.99521126270.95311089690.61729014090.37918542280.08525759030.0063626854490.99511174160.9521577860.61111723950.37160171440.08099471080.0057264169500.99501223040.95120562820.60500606710.36416968010.07694497530.0051537752510.99491272920.95025442260.59895600650.35688628650.07309772650.0046383977520.99481323790.94930416810.59296644640.34974856080.06944284020.0041745579530.99471375660.9483548640.58703678190.34275358950.06597069820.0037571021540.99461428520.94740650910.58116641410.33589851770.06267216330.0033813919550.99451482380.94645910260.575354750.32918054740.05953855510.0030432527560.99441537230.94551264350.56960120250.32259693640.05656162740.0027389274570.99431593080.94456713090.56390519050.31614499770.0537335460.0024650347580.99421649920.94362256370.55826613850.30982209780.05104686870.0022185312590.99411707750.94267894120.55268347720.30362565580.04849452520.0019966781600.99401766580.94173626220.54715664240.29755314270.0460697990.0017970103610.99391826410.9407945260.5416850760.29160207980.0437663090.0016173093620.99381887220.93985373140.53626822520.28577003820.04157799360.0014555783630.99371949030.93891387770.5309055430.28005463750.03949909390.0013100205640.99362011840.93797496380.52559648750.27445354470.03752413920.0011790185650.99352075640.93703698890.52034052270.26896447380.03564793230.0010611166660.99342140430.93609995190.51513711740.26358518440.03386553560.000955005670.99332206220.93516385190.50998574620.25831348070.03217225890.0008595045680.993222730.93422868810.50488588880.25314721110.03056364590.000773554690.99312340770.93329445940.49983702990.24808426680.02903546360.0006961986700.99302409540.93236116490.49483865960.24312258150.02758369040.0006265787

Hoja1

Hoja2

Hoja3

Hoja1ParaleloSerie01.00E+001.00E+0019.96E-019.39E-0129.86E-018.82E-010.000062615974.440894568739.71E-018.29E-0149.51E-017.78E-0159.28E-017.31E-0169.02E-016.87E-0178.74E-016.45E-0188.45E-016.06E-0198.14E-015.69E-01107.84E-015.35E-01117.52E-015.02E-01127.21E-014.72E-01136.90E-014.43E-01146.59E-014.16E-01156.29E-013.91E-01166.00E-013.67E-01175.71E-013.45E-01185.43E-013.24E-01195.16E-013.04E-01204.90E-012.86E-01214.65E-012.69E-01224.41E-012.52E-01234.18E-012.37E-01243.96E-012.23E-01253.74E-012.09E-01263.54E-011.96E-01273.35E-011.84E-01283.17E-011.73E-01292.99E-011.63E-01302.82E-011.53E-01312.67E-011.44E-01322.52E-011.35E-01332.37E-011.27E-01342.24E-011.19E-01352.11E-011.12E-01361.99E-011.05E-01371.88E-019.86E-02381.77E-019.27E-02391.67E-018.70E-02401.57E-018.18E-02411.48E-017.68E-02421.39E-017.21E-02431.31E-016.78E-02441.23E-016.36E-02451.16E-015.98E-02461.09E-015.62E-02471.03E-015.27E-02489.66E-024.95E-02Rs(1.000)Rs(10.000)MTBFs (hrs)499.09E-024.65E-02Serie93.93%53.47%15,974508.55E-024.37E-02Paralelo99.63%78.35%23,962518.04E-024.11E-02527.57E-023.86E-02537.12E-023.62E-02546.69E-023.40E-02556.29E-023.20E-02565.92E-023.00E-02575.56E-022.82E-02585.23E-022.65E-02594.92E-022.49E-02604.62E-022.34E-02614.34E-022.20E-02624.08E-022.06E-02633.84E-021.94E-02643.61E-021.82E-02653.39E-021.71E-02663.19E-021.61E-02672.99E-021.51E-02682.81E-021.42E-02692.64E-021.33E-02702.48E-021.25E-02

Hoja110.99631783160.98615151670.97068386460.95093302090.92777339050.9019540050.874114640.84479995370.81447188320.78352050940.75227357460.72100481580.68994125690.65926958540.62914172580.59967970690.57097990910.54311676760.51614599830.49010740540.46502732080.44092072370.41779307670.39564191670.37445822910.35422763440.33493140910.31654736320.29905059260.28241412080.26660944750.25160701190.23737658620.22388760530.21110944270.199011640.18756409560.17673721820.16650205120.15683037040.14769476060.13906867230.13092646360.12324342740.11599580840.1091608090.10271658870.09664225610.09091785540.08552434870.0804435950.07565832610.07115212020.06690937480.06291527720.05915577550.05561754860.05228797590.0491551080.04620763670.0434348660.04082668380.03837353420.03606639010.03389672780.0318565010.02993811680.02813441240.02643863240.0248444076

ParaleloSeriet (miles hrs)Rs(t)

Hoja2

Hoja3

Ser-ParParaleloSerie01.00E+001.00E+0019.96E-019.39E-0129.86E-018.82E-010.000062615974.440894568739.71E-018.29E-0149.51E-017.78E-0159.28E-017.31E-0169.02E-016.87E-0178.74E-016.45E-0188.45E-016.06E-0198.14E-015.69E-01107.84E-015.35E-01117.52E-015.02E-01127.21E-014.72E-01136.90E-014.43E-01146.59E-014.16E-01156.29E-013.91E-01166.00E-013.67E-01175.71E-013.45E-01185.43E-013.24E-01195.16E-013.04E-01204.90E-012.86E-01214.65E-012.69E-01224.41E-012.52E-01234.18E-012.37E-01243.96E-012.23E-01253.74E-012.09E-01263.54E-011.96E-01273.35E-011.84E-01283.17E-011.73E-01292.99E-011.63E-01302.82E-011.53E-01312.67E-011.44E-01322.52E-011.35E-01332.37E-011.27E-01342.24E-011.19E-01352.11E-011.12E-01361.99E-011.05E-01371.88E-019.86E-02381.77E-019.27E-02391.67E-018.70E-02401.57E-018.18E-02411.48E-017.68E-02421.39E-017.21E-02431.31E-016.78E-02441.23E-016.36E-02451.16E-015.98E-02461.09E-015.62E-02471.03E-015.27E-02489.66E-024.95E-02Rs(1.000)Rs(10.000)MTBFs (hrs)499.09E-024.65E-02Serie93.93%53.47%15,974508.55E-024.37E-02Paralelo99.63%78.35%23,962518.04E-024.11E-02527.57E-023.86E-02537.12E-023.62E-02546.69E-023.40E-02556.29E-023.20E-02565.92E-023.00E-02575.56E-022.82E-02585.23E-022.65E-02594.92E-022.49E-02604.62E-022.34E-02614.34E-022.20E-02624.08E-022.06E-02633.84E-021.94E-02643.61E-021.82E-02653.39E-021.71E-02663.19E-021.61E-02672.99E-021.51E-02682.81E-021.42E-02692.64E-021.33E-02702.48E-021.25E-02

Ser-Par

ParaleloSeriet (miles hrs)Rs(t)

Par-SbytParaleloS bySerie011150.9909440830.99532115980.904837418100.96714146010.98247690370.8187307531150.93282480530.96306368690.7408182207200.8913111280.93844806440.670320046250.84518187830.90979598960.6065306597Rs(10)MTBFs (hrs)300.79642906030.87809861780.5488116361Stand By98.25%100350.74657364360.84419501640.4965853038Paralelo96.71%75400.69676141020.80879213540.4493289641Serie81.87%50450.64784043130.77248235350.4065696597500.60042359910.73575888230.3678794412550.5549390090.69902927580.3328710837600.51167047050.66262726620.3011942119650.47079000790.6268231240.272531793700.43238386530.59183271350.2465969639750.39647325190.55782540040.2231301601800.3630308320.52493094680.201896518850.33199377810.49324551490.1826835241900.3032740540.4628368870.1652988882950.27676646660.43374899570.14956861921000.25235492760.40600584970.13533528321050.22991727970.37961492760.12245642831100.20932897680.35457010680.11080315841150.19046585170.33085418430.10025884371200.17320615950.30844104120.09071795331250.15743205020.28729749520.08208499861300.1430305920.26738488160.07427357821350.12989444450.24866039710.06720551271400.11792226150.2310782380.06081006261450.10701888540.21459055820.05502322011500.09709538460.19914827350.04978706841550.08806897420.18470172980.04504920241600.07986285070.17120125670.0407622041650.07240596680.15859761980.03688316741700.06563276480.14684238780.033373271750.05948288490.13588822540.03019738341800.05390085910.12568912330.0273237224

Par-Sby1110.9909440830.99532115980.9048374180.96714146010.98247690370.81873075310.93282480530.96306368690.74081822070.8913111280.93844806440.6703200460.84518187830.90979598960.60653065970.79642906030.87809861780.54881163610.74657364360.84419501640.49658530380.69676141020.80879213540.44932896410.64784043130.77248235350.40656965970.60042359910.73575888230.36787944120.5549390090.69902927580.33287108370.51167047050.66262726620.30119421190.47079000790.6268231240.2725317930.43238386530.59183271350.24659696390.39647325190.55782540040.22313016010.3630308320.52493094680.2018965180.33199377810.49324551490.18268352410.3032740540.4628368870.16529888820.27676646660.43374899570.14956861920.25235492760.40600584970.13533528320.22991727970.37961492760.12245642830.20932897680.35457010680.11080315840.19046585170.33085418430.10025884370.17320615950.30844104120.09071795330.15743205020.28729749520.08208499860.1430305920.26738488160.07427357820.12989444450.24866039710.06720551270.11792226150.2310782380.06081006260.10701888540.21459055820.05502322010.09709538460.19914827350.04978706840.08806897420.18470172980.04504920240.07986285070.17120125670.0407622040.07240596680.15859761980.03688316740.06563276480.14684238780.033373270.05948288490.13588822540.03019738340.05390085910.12568912330.0273237224

ParaleloStand bySeriet (horas)Rs(t)

Hoja3

Hoja1Cp10000Ce100000Alfa100Beta2tR(t)F(t)MTBF(t)EcCostos (b=0,8)Costos(b=0,5)Costos (b=1)Costos (b=2)Costos (b=5)01.0000.0000.00010,00010,00010,00010,00010,00011.0000.0002.0005,0056,1939,7465,4755,0055,00021.0000.0003.0003,3464,7247,8863,9673,3463,33330.9990.0013.9992,5213,9456,7283,2132,5212,50040.9980.0024.9972,0303,4585,9362,7602,0302,00050.9980.0025.9951,7063,1215,3582,4591,7061,66760.9960.0046.9911,4772,8724,9132,2431,4771,42970.9950.0057.9861,3072,6814,5592,0821,3071,25080.9940.0068.9801,1782,5284,2691,9561,1781,11190.9920.0089.9721,0762,4024,0261,8561,0761,000100.9900.01010.9629942,2973,8201,773994909110.9880.01211.9509272,2083,6411,705927833120.9860.01412.9358732,1313,4851,647873769130.9830.01713.9198272,0633,3471,597827715140.9810.01914.8997882,0043,2241,554788667150.9780.02215.8777561,9513,1131,517756625160.9750.02516.8527281,9033,0131,483728589170.9720.02817.8237051,8602,9221,454705556180.9680.03218.7916851,8212,8391,428685527190.9650.03519.7566681,7852,7631,404668501200.9610.03920.7176531,7532,6921,382653478210.9570.04321.6736411,7222,6271,363641456220.9530.04722.6266301,6942,5661,345630437230.9480.05223.5756211,6682,5101,329621419240.9440.05624.5196131,6442,4571,314613403250.9390.06125.4586071,6222,4071,300607388260.9350.06526.3936021,6002,3611,287602374270.9300.07027.3225981,5802,3171,275598362280.9250.07528.2475941,5622,2751,264594350290.9190.08129.1665921,5442,2361,254592340300.9140.08630.0805901,5272,1991,244590330310.9080.09230.9895891,5112,1631,235589321320.9030.09731.8915881,4962,1301,226588312330.8970.10332.7885881,4822,0981,219588305340.8910.10933.6795891,4682,0671,211589298350.8850.11534.5645901,4552,0381,204590291360.8780.12235.4425911,4432,0101,197591285370.8720.12836.3145921,4311,9841,191592280380.8660.13437.1805941,4191,9581,185594275390.8590.14138.0395971,4081,9331,179597271400.8520.14838.8915991,3981,9101,174599267410.8450.15539.7366021,3881,8871,168602263420.8380.16240.5746051,3781,8651,163605260430.8310.16941.4066081,3691,8441,159608258440.8240.17642.2306121,3601,8241,154612256450.8170.18343.0466161,3511,8041,150616254460.8090.19143.8556191,3431,7851,146619253470.8020.19844.6576231,3351,7671,142623252480.7940.20645.4526271,3271,7491,138627251490.7870.21346.2386321,3201,7321,135632251500.7790.22147.0176361,3121,7161,131636252510.7710.22947.7886411,3051,7001,128641252520.7630.23748.5516451,2981,6841,125645254530.7550.24549.3066501,2921,6691,121650255540.7470.25350.0536551,2851,6541,118655257550.7390.26150.7926591,2791,6401,116659260560.7310.26951.5236641,2731,6261,113664263570.7230.27752.2456691,2671,6131,110669266580.7140.28652.9606741,2611,5991,108674269590.7060.29453.6666791,2561,5871,105679273600.6980.30254.3636841,2501,5741,103684278610.6890.31155.0536901,2451,5621,100690283620.6810.31955.7346951,2401,5501,098695288630.6720.32856.4067001,2351,5391,096700294640.6640.33657.0707051,2301,5281,094705300650.6550.34557.7257101,2251,5171,092710307660.6470.35358.3727161,2211,5061,090716314670.6380.36259.0117211,2161,4961,088721321680.6300.37059.6407261,2121,4861,086726329690.6210.37960.2627321,2071,4761,084732338700.6130.38760.8747371,2031,4661,083737346710.6040.39661.4787421,1991,4561,081742356720.5950.40562.0747481,1951,4471,079748365730.5870.41362.6617531,1911,4381,078753375740.5780.42263.2397581,1871,4291,076758386750.5700.43063.8097641,1831,4201,075764397760.5610.43964.3707691,1791,4121,073769408770.5530.44764.9237741,1761,4031,072774420780.5440.45665.4677791,1721,3951,070779432790.5360.46466.0037851,1691,3871,069785444800.5270.47366.5307901,1651,3791,068790457810.5190.48167.0497951,1621,3721,066795471820.5100.49067.5598001,1591,3641,065800484830.5020.49868.0618051,1561,3571,064805498840.4940.50668.5558101,1521,3491,063810512850.4860.51469.0418151,1491,3421,061815527860.4770.52369.5188211,1461,3351,060821541870.4690.53169.9878261,1431,3281,059826556880.4610.53970.4488311,1401,3221,058831572890.4530.54770.9018361,1381,3151,057836587900.4450.55571.3468401,1351,3081,056840603910.4370.56371.7838451,1321,3021,055845619920.4290.57172.2128501,1291,2961,054850635930.4210.57972.6338551,1271,2901,053855651940.4130.58773.0468601,1241,2841,052860667950.4060.59473.4528651,1211,2781,051865683960.3980.60273.8508691,1191,2721,050869699970.3900.61074.2408741,1161,2661,049874715980.3830.61774.6238781,1141,2601,049878731990.3750.62574.9988831,1121,2551,0488837471000.3680.63275.3668881,1091,2491,0478887631010.3610.63975.7268921,1071,2441,0468927781020.3530.64776.0808961,1051,2381,0458967941030.3460.65476.4269011,1021,2331,0449018091040.3390.66176.7659051,1001,2281,0449058241050.3320.66877.0979091,0981,2231,0439098391060.3250.67577.4229141,0961,2181,0429148531070.3180.68277.7409181,0941,2131,0429188671080.3110.68978.0529221,0921,2081,0419228811090.3050.69578.3569261,0901,2031,0409268941100.2980.70278.6559301,0871,1981,0409309071110.2920.70878.9469341,0851,1941,0399349201120.2850.71579.2329381,0841,1891,0389389321130.2790.72179.5119421,0821,1851,0389429431140.2730.72779.7839461,0801,1801,0379469541150.2660.73480.0509501,0781,1761,0369509641160.2600.74080.3109531,0761,1711,0369539741170.2540.74680.5649571,0741,1671,0359579841180.2480.75280.8139611,0721,1631,0359619931190.2430.75781.0569641,0711,1591,0349641,0011200.2370.76381.2929681,0691,1551,0339681,0091210.2310.76981.5249711,0671,1501,0339711,0161220.2260.77481.7499751,0651,1461,0329751,0231230.2200.78081.9709781,0641,1421,0329781,0291240.2150.78582.1859811,0621,1391,0319811,0351250.2100.79082.3949851,0601,1351,0319851,0401260.2040.79682.5999881,0591,1311,0309881,0451270.1990.80182.7989911,0571,1271,0309911,0501280.1940.80682.9929941,0561,1231,0299941,0541290.1890.81183.1829971,0541,1201,0299971,0581300.1850.81583.3661,0001,0531,1161,0281,0001,0611310.1800.82083.5461,0031,0511,1131,0281,0031,0641320.1750.82583.7211,0061,0501,1091,0281,0061,0671330.1710.82983.8921,0091,0481,1061,0271,0091,0691340.1660.83484.0581,0121,0471,1021,0271,0121,0711350.1620.83884.2191,0151,0451,0991,0261,0151,0731360.1570.84384.3761,0171,0441,0951,0261,0171,0741370.1530.84784.5301,0201,0421,0921,0251,0201,0761380.1490.85184.6781,0231,0411,0891,0251,0231,0771390.1450.85584.8231,0251,0401,0851,0251,0251,0781400.1410.85984.9641,0281,0381,0821,0241,0281,0791410.1370.86385.1011,0301,0371,0791,0241,0301,0801420.1330.86785.2341,0331,0361,0761,0231,0331,0801430.1290.87185.3641,0351,0341,0731,0231,0351,0811440.1260.87485.4891,0371,0331,0701,0231,0371,0811450.1220.87885.6121,0401,0321,0671,0221,0401,0821460.1190.88185.7301,0421,0311,0641,0221,0421,08250.0010.00000031251470.1150.88585.8451,0441,0291,0611,0221,0441,082100.0020.0000051480.1120.88885.9571,0461,0281,0581,0211,0461,082150.0030.00002531251490.1090.89186.0661,0481,0271,0551,0211,0481,083200.0040.000081500.1050.89586.1711,0501,0261,0521,0211,0501,083250.0050.00019531251510.1020.89886.2741,0521,0251,0491,0201,0521,083300.0060.0004051520.0990.90186.3731,0541,0231,0461,0201,0541,083350.0070.00075031251530.0960.90486.4691,0561,0221,0431,0201,0561,083400.0080.001281540.0930.90786.5621,0581,0211,0411,0191,0581,083450.0090.00205031251550.0900.91086.6531,0601,0201,0381,0191,0601,083500.010.0031251560.0880.91286.7411,0621,0191,0351,0191,0621,083550.0110.00457531251570.0850.91586.8261,0641,0181,0331,0181,0641,083600.0120.006481580.0820.91886.9081,0651,0171,0301,0181,0651,083650.0130.00892531251590.0800.92086.9881,0671,0161,0271,0181,0671,083700.0140.0120051600.0770.92387.0651,0691,0141,0251,0181,0691,083750.0150.01582031251610.0750.92587.1401,0701,0131,0221,0171,0701,083800.0160.020481620.0720.92887.2121,0721,0121,0201,0171,0721,083850.0170.02610031251630.0700.93087.2831,0731,0111,0171,0171,0731,083900.0180.0328051640.0680.93287.3501,0751,0101,0151,0171,0751,083950.0190.04072531251650.0660.93487.4161,0761,0091,0121,0161,0761,0831000.020.051660.0640.93687.4801,0781,0081,0101,0161,0781,0831050.0210.06077531251670.0610.93987.5411,0791,0071,0071,0161,0791,0831100.0220.0732051680.0590.94187.6011,0801,0061,0051,0151,0801,0831150.0230.08745031251690.0570.94387.6581,0821,0051,0021,0151,0821,0831200.0240.103681700.0560.94487.7141,0831,0041,0001,0151,0831,0831250.0250.12207031251710.0540.94687.7681,0841,0039981,0151,0841,0831300.0260.1428051720.0520.94887.8191,0861,0029951,0151,0861,0831730.0500.95087.8701,0871,0029931,0141,0871,0831740.0480.95287.9181,0881,0019911,0141,0881,0831750.0470.95387.9651,0891,0009891,0141,0891,0831760.0450.95588.0101,0909999861,0141,0901,0831770.0440.95688.0531,0919989841,0131,0911,0831780.0420.95888.0961,0929979821,0131,0921,0831790.0410.95988.1361,0939969801,0131,0931,0831800.0390.96188.1751,0949959781,0131,0941,0831810.0380.96288.2131,0959949751,0131,0951,0831820.0360.96488.2501,0969949731,0121,0961,0831830.0350.96588.2851,0979939711,0121,0971,0831840.0340.96688.3191,0989929691,0121,0981,0831850.0330.96788.3511,0999919671,0121,0991,0831860.0310.96988.3831,0999909651,0121,0991,0831870.0300.97088.4131,1009899631,0111,1001,0831880.0290.97188.4421,1019899611,0111,1011,0831890.0280.97288.4701,1029889591,0111,1021,0831900.0270.97388.4971,1029879571,0111,1021,0831910.0260.97488.5231,1039869551,0111,1031,0831920.0250.97588.5481,1049869531,0101,1041,0831930.0240.97688.5721,1059859511,0101,1051,0831940.0230.97788.5961,1059849491,0101,1051,0831950.0220.97888.6181,1069839481,0101,1061,0831960.0210.97988.6391,1069839461,0101,1061,0831970.0210.97988.6601,1079829441,0101,1071,0831980.0200.98088.6801,1089819421,0091,1081,0831990.0190.98188.6991,1089809401,0091,1081,0832000.0180.98288.7171,1099809381,0091,1091,083

Hoja1000000000000000

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MTBF=(90;840)Beta=2Beta=1

Hoja3

Opt=(33;588)