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Cox processes in system degradation modelling

Bautista Bárcena Lucía, Torres Castro Inmaculada, Landesa Porras Luis

Safety and Reliability of Systems and Processes

2021

Summer Safety and Reliability Seminar 2021

7--16

Many systems are subject to multiple degradation processes, which reduce their capability for fulfilling their functions. Pitting corrosion, which consists of the appearance of different that evolve simultaneously in the system, is a classic example of this multiple degradation. It is assumed that the system fails when the pits are large enough that do not allow the system to perform its function, or, in other words, when the degradation level has exceeded a certain fixed threshold, which indicates whether the system is in a good condition. For a system to work properly, a maintenance is performed on it: periodic inspections, repairs, and replacements of the components. The search of the optimal maintenance strategy is a key challenge since we must bear in mind the different costs associated to each maintenance task and the different stochastic processes influencing the system condition: the arrival processes and the growth processes. In this work, we study a system subject to different degradation processes, in which the arrival of those processes is modelled using Cox processes, which are generalizations of the non-homogeneous Poisson process. Using their properties, the survival function, the expected number of arrivals and the expected intensity are obtained.