A system subject to degradation is considered. The degradation is modelled by a gamma process. A condition-based maintenance policy with perfect corrective and an imperfect preventive actions is proposed. The maintenance cost is derived considering a Markov-renewal process. The statistical inference of the degradation and maintenance parameters by the maximum likelihood method is investigated. A sensibility analysis to different parameters is carried out and the perspectives are detailed.
BordesLMercierSRemyE, et al. Partially observed competing degradation processes: modeling and inference. Appl Stoch Models Bus Ind2016; 32(5): 677–696.
2.
GiorgioMGuidaMPulciniG. A condition-based maintenance policy for deteriorating units. An application to the cylinder liners of marine engine. Appl Stoch Models Bus Ind2015; 31(3): 339–348.
3.
van NoortwijkJM. A survey of the application of gamma processes in maintenance. Reliab Eng Syst Saf2009; 94(1): 2–21.
4.
BarkerCTNewbyMJ. Optimal non-periodic inspection for a multivariate degradation model. Reliab Eng Syst Saf2009; 94: 33–43.
5.
KahleWMercierSParoissinC. Degradation processes in reliability. John Wiley & Sons, 2016.
6.
ChristerAHWangW. A simple condition monitoring model for a direct monitoring process. Eur J Oper Res1995; 82: 258–269.
7.
GrallADieulleLBerenguerC, et al. Continuous-time predictive-maintenance scheduling for a deteriorating system. IEEE Trans Reliab2002; 51(2): 141–150.
8.
KallenMJvan NoortwijkJM. Optimal maintenance decisions under imperfect inspection. Reliab Eng Syst Saf2005; 90: 177–185.
9.
KumarDWestbergU. Maintenance scheduling under age replacement policy using proportional hazards model and TTT-plotting. Eur J Oper Res1997; 99: 507–515.
SpeijkerLJPvan NoortwijkJMKokM, et al. Optimal maintenance decisions for dikes. Probab Eng Inf Sci2000; 14: 101–121.
12.
WangH. A survey of maintenance policies of deteriorating systems. Eur J Oper Res2002; 139: 469–489.
13.
NicolaiRPFrenkJBDekkerR. Modelling and optimizing imperfect maintenance of coatings on steel structures. Struct Saf2009; 31: 234–244.
14.
ShuYFengQCoitDW. Life distribution analysis based on lévy subordinators for degradation with random jumps. Nav Res Logist2015; 62(6): 483–492.
15.
WangYPhamH. A multi-objective optimization of imperfect preventive maintenance policy for dependent competing risk systems with hidden failure. IEEE Trans Reliab2011; 60(4): 770–781.
16.
KlutkeGA. Lifetime-characteristics and inspection-schemes for Levy degradation processes. IEEE Trans Reliab2000; 49(4): 377–382.
17.
KijimaMNakagawaT. A cumulative damage shock model with imperfect preventive maintenance. Nav Res Logist1991; 38: 145–156.
18.
KijimaMNakagawaT. Replacement policies of a shock model with imperfect preventive maintenance. Eur J Oper Res1992; 57: 100–110.
19.
MaH-GWuJ-PLiX-Y, et al. Condition-based maintenance optimization for multicomponent systems under imperfect repair—based on RFAD model. IEEE Trans Fuzzy Syst2019; 27(5): 917–927.
20.
KahleW. Imperfect repair in degradation processes: a Kijima-type approach. Appl Stoch Models Bus Ind2019; 35(2): 211–220.
21.
CastanierBBérenguerCGrallA. A sequential condition-based repair/replacement policy with non-periodic inspections for a system subject to continuous wear. Appl Stoch Models Bus Ind2003; 19(4): 327–347.
22.
VanPDBérenguerC. Condition-based maintenance with imperfect preventive repairs for a deteriorating production system. Qual Reliab Eng Int2012; 28(6): 624–633.
23.
LeMDTanCM. Optimal maintenance strategy of deteriorating system under imperfect maintenance and inspection using mixed inspection scheduling. Reliab Eng Syst Saf2013; 113: 21–29.
24.
NiknamSAAcosta-AmadoRKobzaJE. A value-based maintenance strategy for systems under imperfect repair and continuous degradation. In: 2017 Annual reliability and maintainability symposium (RAMS), Orlando, FL, USA, 23–26 January 2017, pp.1–6. New York, NY: IEEE.
25.
WangZ-QHuC-HSiX-S, et al. Remaining useful life prediction of degrading systems subjected to imperfect maintenance: application to draught fans. Mech Syst Signal Process2018; 100: 802–813.
26.
ZhangMGaudoinOXieM. Degradation-based maintenance decision using stochastic filtering for systems under imperfect maintenance. Eur J Oper Res2015; 245(2): 531–541.
27.
PonchetAFouladiradMGrallA. Maintenance policy on a finite time span for a gradually deteriorating system with imperfect improvements. Proc IMechE, Part O: J Risk and Reliability2011; 225(2): 105–116.
28.
MercierSCastroIT. On the modelling of imperfect repairs for a continuously monitored gamma wear process through age reduction. J Appl Probab2013; 50(4): 1057–1076.
29.
MercierSCastroIT. Stochastic comparisons of imperfect maintenance models for a gamma deteriorating system. Eur J Oper Res2019; 273(1): 237–248.
30.
MartinodRMBistorinOCastañedaLF, et al. Maintenance policy optimisation for multi-component systems considering degradation of components and imperfect maintenance actions. Comput Ind Eng2018; 124: 100–112.
31.
ShahrakiAFYadavOPVogiatzisC. Selective maintenance optimization for multi-state systems considering stochastically dependent components and stochastic imperfect maintenance actions. Reliab Eng Syst Saf2020; 196: 106738.
32.
PanZFengJSunQ. Lifetime distribution and associated inference of systems with multiple degradation measurements based on gamma processes. Eksploatacja i Niezawodność2016; 18: 307–313.
33.
PanZBalakrishnanN. Reliability modeling of degradation of products with multiple performance characteristics based on gamma processes. Reliab Eng Syst Saf2011; 96(8): 949–957.
34.
BalakrishnanNTsaiC-CLinC-T. Gamma degradation models: inference and optimal design. Statistical Modeling for Degradation Data2017; 171–191.
35.
HuCPeiHWangZ, et al. A new remaining useful life estimation method for equipment subjected to intervention of imperfect maintenance activities. Chin J Aeronaut2018; 31(3): 514–528.
36.
SallesGMercierSBordesL. Semiparametric estimate of the efficiency of imperfect maintenance actions for a gamma deteriorating system. J Stat Plan Inference2020; 206: 278–297.
37.
ChuangCNingyunLBinJ, et al. Condition-based maintenance optimization for continuously monitored degrading systems under imperfect maintenance actions. J Syst Eng Electronics2020; 31(4): 841–851.
38.
KamranfarHFouladiradMBalakrishnanN. Inference for a gradually deteriorating system with imperfect maintenance. Commun Stat Simul Comput2021; 1–19.
39.
MadsenRWIsaacsonDL. Strongly ergodic behavior for non-stationary Markov Processes. Ann Prob1973; 1: 329–335.
40.
LiêuBDorelM. Sur le comportement asymptotique de processus de Markov non homogènes. Stud Matem1967; 28(3): 253–274.