Stochastic comparisons of imperfect maintenance models for a gamma deteriorating system

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

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

This paper compares two imperfect repair models for a degrading system, with deterioration level modeled by a non homogeneous gamma process. Both models consider instantaneous and periodic repairs. The first model assumes that a repair reduces the degradation of the system accumulated from the last maintenance action. The second model considers a virtual age model and assumes that a repair reduces the age accumulated by the system since the last maintenance action. Stochastic comparison results between the two resulting processes are obtained. Furthermore, a specific case is analyzed, where the two repair models provide identical expected deterioration levels at maintenance times. Finally, two optimal maintenance strategies are explored, considering the two models of repair.

Mots clés: virtual age model; (increasing) convex order; non homogeneous gamma process; Reliability

Domaines: Probabilités [math.PR]

Sophie Mercier, I. T. Castro. Stochastic comparisons of imperfect maintenance models for a gamma deteriorating system. European Journal of Operational Research, 2019, 273 (1), pp.237-248. ⟨10.1016/j.ejor.2018.06.020⟩. ⟨hal-01812028⟩