This paper presents a maintenance strategy model of a system with a gamma deterioration process, regular inspection times, and intervention delay. Interventions are deemed necessary when the deterioration process is greater than an intervention level at inspection time. The objective is to determine the long-term mean costs of different maintenance strategies and to optimize these costs with respect to specific parameters, such as the intervention level or the inspection interval. Semi-regeneration properties at the inspection times and associated Markov renewal techniques are used in order to compute the long-term mean costs. This model is applied to the maintenance of railway tracks.
ZuckermanD.‘Optimal replacement policy for the case where the damage process is a one-sided Levy process’Stochastic Process. Appl.7 (1978): 141–151
3.
Abdel-HameedM‘Inspection and maintenance policies of devices subject to deterioration’Adv. Appl. Prob.19 (1987): 917–931
4.
van NoortwijkJ. M.KokMCookeR. M., ‘Optimal maintenance decisions for the seabed protection of the Eastern-Scheldt barrier’Engineering, probabilistic design and maintenance for flood protection (Dordrecht: Kluwer Academic Publishers1997): pp. 25–51 ch. 2.
5.
J.M van Noortwijk, H. E. Klatter, ‘Optimal inspection decisions for block models mats of the eastern-shield barrier’Reliab. Engng Syst. Saf.65 (1999): 203–211
6.
YangY.KlutkeG.-A‘Lifetime-characteristics and inspection schemes for Lévy processes’IEEE Trans. Reliab.49 (2000): 377–382
7.
GrallA.DieulleLBérenguerCRoussignolM‘Continuous – time predictive – maintenance scheduling for a deteriorating system’IEEE Trans. Reliab.51 (2002): 141–150
8.
BérenguerCGrallADieulleLRoussignolM‘Maintenance policy for a continuously monitored deteriorating system’Prob. Engng Informational Sci.17 (2003): 235–250
9.
DieulleL.BérenguerCGrallARoussignolM‘Sequential condition-based maintenance scheduling for a deteriorating system’Eur. J. Op. Res.150 (2003): 451–461
10.
Abdel-HameedM. S‘Optimal predictive maintenance policies for a deteriorating system: the total discounted cost and the long-run average cost case’Commun. Statist.33 (2004): 735–745
11.
CastanierB.GrallABérenguerC‘A condition-based maintenance policy with non-periodic inspections for a two-unit series system’Reliab. Engng Syst. Saf.87 (2005): 109–120
12.
GrallA.DieulleLBérenguerCRoussignolM‘Asymptotic failure rate of a continuously monitored system’Reliab. Engng Syst. Saf.91 (2006): 126–130
13.
LiaoH.ElsayedE. AChanL‘Maintenance of continuously monitored degrading systems’Eur. J. Op. Res.175 (2006): 821–835
14.
CrowderM.LawlessJ‘On a scheme for predictive maintenance’Eur. J. Op. Res.176 (2007): 1713–1722
15.
NicolaiR. PDekkerJ. R.van NoortwijkM.‘A comparison of models for measurable deterioration: An application to coatings on stell structures’Reliab. Engng Sys. Saf.92 (2007): 1635–1650
16.
PandeyM. DYuanX.-Xvan NoortwijkJ.M.‘The influence of temporal uncertainty of deterioration on life-cycle management of structures’Struct. Infrastruct. Engng5 (2009): 145–156
17.
J.M van Noortwijk, ‘Survey of the application of gamma processes in maintenance’Reliab. Engng Sys. Saf.94 (2009): 2–21
18.
Cocozza-ThiventCProcessus stochastiques et fiabilité des systèmes (Berlin: Springer1997)
19.
Meier-HirmerCModèles et techniques probabilistes pour l'optimisation des stratégies demaintenance. Application au domaine ferroviaire. PhD Thesis, Université de Marne-la-Vallée, 2007.
20.
AsmussenS.Applied probability and queues (UK: Wiley, Chichester1987)
21.
LeBihanA.‘Maintenance de la géométrie des voies à grande vitesse’LeRail116 (2005): 10–11
22.
Meier-HirmerCPoulignyPArdeoisJSibilleN‘Optimisation de l'utilisation des trains meuleur pour la maintenance des voies ferrées’ Actes du λμ 16, Avignon (Institut pour la Maitrise des Risques 2008): p. 148.
