PARTIE II
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Transcript of PARTIE II
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PARTIE IIPARTIE IIIntroduction à la Introduction à la
ModélisationModélisation & &
à l’ Optimisationà l’ Optimisation
Modèle GPIM Modèle GPIM vsvs GRP GRP Optimisation « Overhaul Policy B-H »Optimisation « Overhaul Policy B-H » Antinomie selon le REX pour la Antinomie selon le REX pour la
modélisationmodélisation MC/MP MC/MP GPIM_PLP GPIM_PLP vs vs GPIM_LLPGPIM_LLP
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REF 1 : cf.Generalized proportional intensities models for repairable systems.
By D.F. PERCY & B.M. ALKALI. Journal of Management Mathematics(2006) 17,171-185.
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REF 2 : cf. Discontinuous point processes for the analysis of REF 2 : cf. Discontinuous point processes for the analysis of repairable units .repairable units .
By R.CALABRIA & G. PULCINI. By R.CALABRIA & G. PULCINI. International Journal OF Reliability, Quality and Safety International Journal OF Reliability, Quality and Safety
Engineering (1999) Engineering (1999) Vol.6, N°.4, 361-382.Vol.6, N°.4, 361-382.
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REF 3:P_PLP REF 3:P_PLP cf.Practical Methods for Modeling Repairable cf.Practical Methods for Modeling Repairable Systems with Time Trends and Repair Effects. Systems with Time Trends and Repair Effects.
by H. GUO, W. ZHAO & A. METTAS. IEEE(2006).by H. GUO, W. ZHAO & A. METTAS. IEEE(2006).L_LLP L_LLP cf.A New Stochastic Model for Systems Under cf.A New Stochastic Model for Systems Under
General Repair. General Repair. by H. GUO, W. ZHAO & A. METTAS. IEEE(2007).by H. GUO, W. ZHAO & A. METTAS. IEEE(2007).
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BASELINE MODELSBASELINE MODELS
)1(** t
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With the power-law intensity baseline functionWith the power-law intensity baseline functionLog Likelihood “ SIMPLE SYSTEM TYPE I ”Log Likelihood “ SIMPLE SYSTEM TYPE I ”
PARTIAL REPAIR (CM PARTIAL REPAIR (CM (PERCY) , (PERCY) , (GUO) , (GUO) , (CALABRIA)) (CALABRIA))
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GRAPHIQUE par CALCUL ANALYTIQUE du modèle GRAPHIQUE par CALCUL ANALYTIQUE du modèle P_PLP/PIM_PLPP_PLP/PIM_PLP
P_PLP[P_PLP[_,t_] = (-1/_,t_] = (-1/)*Log[(1-)*Log[(1-**λλ*t^*t^)];)]; = 3, λ = 0.001. = 3, λ = 0.001.
= Exp[-]
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With the log-linear intensity baseline functionWith the log-linear intensity baseline functionLog Likelihood “ SIMPLE SYSTEM TYPE I ”Log Likelihood “ SIMPLE SYSTEM TYPE I ”
PARTIAL REPAIR (CM PARTIAL REPAIR (CM (PERCY) , (PERCY) , (GUO) , (GUO) , (CALABRIA)) (CALABRIA))
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Log Likelihood “ MULTI- SYSTEMS TYPE I ” Log Likelihood “ MULTI- SYSTEMS TYPE I ” (1/2)(1/2)
PARTIAL REPAIR (CM PARTIAL REPAIR (CM (GUO)) (GUO))
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Log Likelihood “ MULTI- SYSTEMS TYPE I ” Log Likelihood “ MULTI- SYSTEMS TYPE I ” (2/2)(2/2)
PARTIAL REPAIR (CM PARTIAL REPAIR (CM (GUO)) (GUO))
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ESTIMATIONSESTIMATIONS
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GRAPHIQUES du C.I.F.GRAPHIQUES du C.I.F.
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OPTIMISATION du OPTIMISATION du
REMPLACEMENTREMPLACEMENT
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OPTIMISATION du OPTIMISATION du REMPLACEMENTREMPLACEMENT
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OPTIMISATION du OPTIMISATION du REMPLACEMENTREMPLACEMENT
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INFLUENCE SURINFLUENCE SUR L’ OPTIMISATIONL’ OPTIMISATION
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VALIDATION d’un MODELE HPPVALIDATION d’un MODELE HPP
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VERIFICATIONVERIFICATION
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VALIDATION d’un MODELE VALIDATION d’un MODELE GRPGRP
C
?
?
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RE-ANALYSERE-ANALYSE
CUMULATIF TIME ( hours )
MCF
4003002001000
50
40
30
20
10
0
Parameter, MLEMTBF
8,32612
Mean Cumulative Function " TUBER MACHINE "
LK_HPP = - 152.85
AIC_HPP = 307.7BIC_HPP = 309.52
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GENERALIZED PROPORTIONAL INTENSINTIES GENERALIZED PROPORTIONAL INTENSINTIES MODELSMODELS
Whitout Covariates Whitout Covariates Log Likelihood “ SIMPLE SYSTEM ”Log Likelihood “ SIMPLE SYSTEM ”
GPIM GPIM ( CM ( CM + PM + PM ) )
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EXAMPLE I : EXAMPLE I : SIMPLE SYSTEM (General SIMPLE SYSTEM (General Repair)Repair)
cf. Scheduling preventive maintenance for oil pumps using cf. Scheduling preventive maintenance for oil pumps using generalized proportional intensities models by D.F. PERCY & generalized proportional intensities models by D.F. PERCY &
B.M. ALKALI.B.M. ALKALI. International Transactions in Operational Research. 14 International Transactions in Operational Research. 14
(2007) 547-563.(2007) 547-563.
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ESTIMATIONSESTIMATIONS
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ESTIMATIONS « AUTEURS »ESTIMATIONS « AUTEURS »
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EXAMPLE I I : EXAMPLE I I : SIMPLE SYSTEM (General SIMPLE SYSTEM (General Repair)Repair)
Cf. A pratical method of predicting the failure intensity of hydropower Cf. A pratical method of predicting the failure intensity of hydropower generating units.generating units.
By X. QIAN & Y. WUBy X. QIAN & Y. WUIEEE 2011IEEE 2011
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ESTIMATIONSESTIMATIONS
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ESTIMATIONS « AUTEURS »ESTIMATIONS « AUTEURS »
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EXAMPLE III : EXAMPLE III : SIMPLE SYSTEM (General SIMPLE SYSTEM (General Repair)Repair)
Cf. Bayesian Prediction of the Overhaul Effect on a Repairable Cf. Bayesian Prediction of the Overhaul Effect on a Repairable SystemSystem
with Bounded Failure Intensity.with Bounded Failure Intensity.(International Journal of Quality, Statistics and Reliability (International Journal of Quality, Statistics and Reliability
2010).2010).
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ESTIMATIONSESTIMATIONS
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ESTIMATIONS « AUTEURS »ESTIMATIONS « AUTEURS »
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OPTIMISATION de la M.P.OPTIMISATION de la M.P.
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GPIM_PLP GPIM_PLP LK_V = LK_V = - 28.4311- 28.4311 = 1.13678e-14, = 1.13678e-14, = 7.68063, = 7.68063, c = 0.291656, c = 0.291656,
p = 0.432698p = 0.432698
0 50 100 150 200 250Tu.t 0.00
0.05
0.10
0.15
INTENSITY u.tINTENSITY FUNCTION GPIM_PLP vs ARAinfAGAN
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GPIM_PLP GPIM_PLP LK_V = LK_V = - 28.4311- 28.4311 = 1.13678e-14, = 1.13678e-14, = 7.68063, = 7.68063, c = 0.291656, c = 0.291656,
p = 0.432698p = 0.432698
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SIMULATION MONTE-CARLO SIMULATION MONTE-CARLO DU MODELE DU MODELE GPIM_PLPGPIM_PLP
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