On the modelling of imperfect repairs for a continuously monitored gamma wear process through age reduction

Sophie Mercier (1) , I. T. T Castro (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 Departamento de Matemáticas - Universidad de Extremadura

A continuously monitored system is considered, which is subject to accumulating deterioration modelled as a gamma process. The system fails when its degradation level exceeds a limit threshold. At failure, a delayed replacement is performed. To shorten the down period, a condition-based maintenance strategy is applied, with imperfect repair. Mimicking virtual age models used for recurrent events, imperfect repair actions are assumed to lower the system degradation through a first-order arithmetic reduction of age model. Under these assumptions, Markov renewal equations are obtained for several reliability indicators. Numerical examples illustrate the behaviour of the system.

Mots clés: imperfect maintenance; delay time; maintenance policy; gamma process; ARA1; Markov renewal process; Markov renewal equation

Domaines: Probabilités [math.PR]

Sophie Mercier, I. T. T Castro. On the modelling of imperfect repairs for a continuously monitored gamma wear process through age reduction. Journal of Applied Probability, 2013, 50 (4), pp.1057-1076. ⟨10.1239/jap/1389370099⟩. ⟨hal-00984773⟩