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2 Safety and Reliability of Systems and Processes

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Imperfect maintenance in correlated bivariate Wiener model

Bautista Lucía, Castro Inma T., Bérenguer Christophe, Gaudoin Olivier, Doyen Laurent

Safety and Reliability of Systems and Processes

2023

Summer Safety and Reliability Seminar 2023

7--17

A two-unit system subject to imperfect maintenance is analyzed in this chapter. The deterioration of the system follows a bivariate Wiener degradation process. This process is built from the trivariate reduction method by sharing a common noise that describes the dependence between both units. This dependence is measured through the Pearson’s correlation coefficient between both degradation trajectories of the bivariate Wiener process at time t. A maintenance strategy consisting of periodic inspections in which the accumulated deterioration of the system is reduced by a certain quantity is implemented. Some results on the monotonicity of the Pearson’s correlation coefficient in different scenarios are obtained.

Degradation model for system incorporating heterogeneities

Bautista Lucía, Castro Inmaculada Torres, Landesa Porras Luis

Safety and Reliability of Systems and Processes

2022

Summer Safety and Reliability Seminar 2022

7--16

A system subject to several deteriorationprocesses is studiem. These processes arrive to the system following a Cox process and they grow according to a homogeneous gamma process. The system is failed when a degradation process exceeds a certain failure threshold. The maintenance strategy implemented on the system is condition-based maintenance, the deterioration state of the system is checked, and replacements are performer if necessary. A random effects model is considered to dealwith the heterogeneities between processes, in particular, a uniform distribution is used to model the inverse of the scale parameter of the gamma process. Finally, the analytic cost model is obtained and analysed through some numerical examples.