PARTIE II

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PARTIE II

• Introduction à la Modélisation
• à l Optimisation
• Modèle GPIM vs GRP
• Optimisation  Overhaul Policy B-H 
• Antinomie selon le REX pour la modélisation
  MC/MP GPIM_PLP vs GPIM_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 repairable units .By R.CALABRIA G.
PULCINI. International Journal OF Reliability,
Quality and Safety Engineering (1999) Vol.6,
N.4, 361-382.
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REF 3P_PLP ? cf.Practical Methods for Modeling
Repairable Systems with Time Trends and Repair
Effects. by H. GUO, W. ZHAO A. METTAS.
IEEE(2006).L_LLP ? cf.A New Stochastic Model for
Systems Under General Repair. by H. GUO, W. ZHAO
A. METTAS. IEEE(2007).
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BASELINE MODELS
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? With the power-law intensity baseline
functionLog Likelihood SIMPLE SYSTEM TYPE I
PARTIAL REPAIR (CM ?? (PERCY) , ? (GUO) , ?
(CALABRIA))
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GRAPHIQUE par CALCUL ANALYTIQUE du modèle
P_PLP/PIM_PLPP_PLP?_,t_ (-1/?)Log(1-??t?
)? 3, ? 0.001.
? Exp-?
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? With the log-linear intensity baseline
functionLog Likelihood SIMPLE SYSTEM TYPE I
PARTIAL REPAIR (CM ?? (PERCY) , ? (GUO) , ?
(CALABRIA))
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Log Likelihood MULTI- SYSTEMS TYPE I
(1/2)PARTIAL REPAIR (CM ? ? (GUO))
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Log Likelihood MULTI- SYSTEMS TYPE I
(2/2)PARTIAL REPAIR (CM ? ? (GUO))
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ESTIMATIONS
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GRAPHIQUES du C.I.F.
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OPTIMISATION du REMPLACEMENT
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OPTIMISATION du REMPLACEMENT
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OPTIMISATION du REMPLACEMENT
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INFLUENCE SUR L OPTIMISATION
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VALIDATION dun MODELE HPP
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VERIFICATION
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VALIDATION dun MODELE GRP
C
?
?
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RE-ANALYSE
LK_HPP - 152.85 AIC_HPP 307.7 BIC_HPP 309.52
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GENERALIZED PROPORTIONAL INTENSINTIES
MODELSWhitout Covariates Log Likelihood
SIMPLE SYSTEM GPIM ( CM ? ? PM ? ? )
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EXAMPLE I ? SIMPLE SYSTEM (General Repair)cf.
Scheduling preventive maintenance for oil pumps
using generalized proportional intensities models
by D.F. PERCY B.M. ALKALI. International
Transactions in Operational Research. 14 (2007)
547-563.
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ESTIMATIONS
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ESTIMATIONS  AUTEURS 
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EXAMPLE I I ? SIMPLE SYSTEM (General
Repair)Cf. A pratical method of predicting the
failure intensity of hydropower generating
units.By X. QIAN Y. WUIEEE 2011
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ESTIMATIONS
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ESTIMATIONS  AUTEURS 
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EXAMPLE III ? SIMPLE SYSTEM (General
Repair)Cf. Bayesian Prediction of the Overhaul
Effect on a Repairable Systemwith Bounded
Failure Intensity.(International Journal of
Quality, Statistics and Reliability 2010).

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ESTIMATIONS
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ESTIMATIONS  AUTEURS 
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OPTIMISATION de la M.P.
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GPIM_PLP ? LK_V - 28.4311 ? 1.13678e-14, ?
7.68063, ?c 0.291656, ?p 0.432698

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GPIM_PLP ? LK_V - 28.4311 ? 1.13678e-14, ?
7.68063, ?c 0.291656, ?p 0.432698

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SIMULATION MONTE-CARLO DU MODELE GPIM_PLP
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