A condition-based imperfect replacement policy for a periodically inspected system with two dependent wear indicators
Résumé
A two-component system is considered, which is subject to accumulative deterioration. Because of common stress, the components are dependent. Their joint deterioration is modelled with a bivariate nondecreasing Lévy process. The deterioration level of both components is known only through perfect and periodic inspections. By an inspection, components with deterioration level beyond a specific threshold are instantaneously replaced by new ones (corrective or preventive replacements). Otherwise, they are left as they are. Between inspections, failures remain unrevealed. This replacement policy is classical in a univariate setting, with deterioration modelled by a Gamma process. In the bivariate case, it leads to imperfect repairs at the system level, which highly complicates the study. The replacement policy is assessed through cost functions on both finite and infinite horizons, which take into account some economical dependence between components. Markov renewal theory is used to study the behaviour of the system, in a continuous and bivariate setting. Numerical experiments illustrate the study, considering a specific Lévy process with univariate Gamma processes as margins. Although technical details are not provided here for the numerical computations, the paper shows that there is a technical gap between the traditional one-dimensional studies and the present two-dimensional one, especially for the computation of the asymptotic distribution of the underlying Markov chain. Hence, there is a need for further development in the bivariate (or multivariate) setting.
Origine : Fichiers produits par l'(les) auteur(s)
Loading...