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Advanced Modeling and Optimization Techniques for Repairable Systems Using GPIM and GRP

This document explores advanced modeling and optimization strategies for repairable systems, focusing on Generalized Proportional Intensity Models (GPIM) and General Repair Policies (GRP). We analyze the implications of various overhaul policies and present a comparative study of GPIM_PLP and GPIM_LLP based on existing literature. The methodology includes graphical analysis of log-likelihood functions alongside practical applications for predicting failure intensities. Key references are provided for further insights into modeling techniques pertinent to repairable system maintenance and optimization.

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Advanced Modeling and Optimization Techniques for Repairable Systems Using GPIM and GRP

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  1. 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

  2. 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.

  3. 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.

  4. REF 3:P_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).

  5. BASELINE MODELS

  6.  With the power-law intensity baseline functionLog Likelihood “ SIMPLE SYSTEM TYPE I ”PARTIAL REPAIR (CM  (PERCY) ,  (GUO) ,  (CALABRIA))

  7. GRAPHIQUE par CALCUL ANALYTIQUE du modèle P_PLP/PIM_PLPP_PLP[_,t_] = (-1/)*Log[(1-*λ*t^)]; = 3, λ = 0.001.  = Exp[-]

  8.  With the log-linear intensity baseline functionLog Likelihood “ SIMPLE SYSTEM TYPE I ”PARTIAL REPAIR (CM  (PERCY) ,  (GUO) ,  (CALABRIA))

  9. Log Likelihood “ MULTI- SYSTEMS TYPE I ” (1/2)PARTIAL REPAIR (CM  (GUO))

  10. Log Likelihood “ MULTI- SYSTEMS TYPE I ” (2/2)PARTIAL REPAIR (CM  (GUO))

  11. ESTIMATIONS

  12. GRAPHIQUES du C.I.F.

  13. OPTIMISATION du REMPLACEMENT

  14. OPTIMISATION du REMPLACEMENT

  15. OPTIMISATION du REMPLACEMENT

  16. INFLUENCE SURL’ OPTIMISATION

  17. VALIDATION d’un MODELE HPP

  18. VERIFICATION

  19. VALIDATION d’un MODELE GRP C ? ?

  20. RE-ANALYSE LK_HPP = - 152.85 AIC_HPP = 307.7 BIC_HPP = 309.52

  21. GENERALIZED PROPORTIONAL INTENSINTIES MODELSWhitout Covariates Log Likelihood “ SIMPLE SYSTEM ”GPIM ( CM  + PM  )

  22. 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.

  23. ESTIMATIONS

  24. ESTIMATIONS « AUTEURS »

  25. 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

  26. ESTIMATIONS

  27. ESTIMATIONS « AUTEURS »

  28. 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).

  29. ESTIMATIONS

  30. ESTIMATIONS « AUTEURS »

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