Piecewise deterministic Markov process for condition-based maintenance models — Application to critical infrastructures with discrete-state deterioration - Université de technologie de Troyes Access content directly
Journal Articles Reliability Engineering and System Safety Year : 2021

## Piecewise deterministic Markov process for condition-based maintenance models — Application to critical infrastructures with discrete-state deterioration

Anne Barros
Antoine Grall

#### Abstract

In recent decades, the technology and techniques for condition monitoring have experienced a rapid development. However, there is still a need for reducing unnecessary inspections and/or preventive maintenance actions and their associated cost, through optimal design of condition-based maintenance (CBM) strategies. Accordingly, mathematical modelling and optimization of CBM has become of interest for industry managers and researchers. This work explores on the application of a piecewise deterministic Markov process (PDMP) to encompass different modelling assumptions as non-negligible maintenance delays and inspection-based condition monitoring. These assumptions are relevant for many critical infrastructures in civil engineering or in oil & gas industry whose deterioration states are classified at a very high level of abstraction among a finite and small set of possible states. A formalism to model this type of problems is proposed in which the deterministic motion of the PDMP is reduced to a trivial differential equation to track the time elapsed between events. A numerical scheme for quantification, as an approximation of the Chapman–Kolmogorov equation, is presented. Later, an illustration case dealing with CBM of road bridges by the NPRA (Norwegian Public Roads Administration) is presented, guiding through the modelling and quantification approach.

#### Domains

Operations Research [math.OC]

### Dates and versions

hal-03273225 , version 1 (29-06-2021)

### Identifiers

• HAL Id : hal-03273225 , version 1
• DOI :

### Cite

Renny Arismendi, Anne Barros, Antoine Grall. Piecewise deterministic Markov process for condition-based maintenance models — Application to critical infrastructures with discrete-state deterioration. Reliability Engineering and System Safety, 2021, 212, pp.107540. ⟨10.1016/j.ress.2021.107540⟩. ⟨hal-03273225⟩

### Export

BibTeX XML-TEI Dublin Core DC Terms EndNote DataCite

52 View