Piecewise deterministic Markov process for condition-based imperfect maintenance models

Abstract

In this paper, a condition-based imperfect maintenance model based on piecewise deterministic Markov process (PDMP) is constructed. The degradation of the system includes two types: natural degradation and random shocks. The natural degradation is deterministic and can be nonlinear. The damage increment caused by a random shock follows a certain distribution, and its parameters are related to the degradation state. Maintenance methods include corrective maintenance and imperfect maintenance. Imperfect maintenance reduces the degradation degree of the system according to a random proportion. The maintenance action is delayed, and the system will suffer natural degradations and random shocks while waiting for maintenance. At each inspection time, the decision-maker needs to make a choice among planning no maintenance, imperfect maintenance and perfect maintenance, so as to minimize the total discounted cost of the system. The impulse optimal control theory of PDMP is used to determine the optimal maintenance strategy. A numerical study dealing with component coating maintenance problem is presented. Relationship with optimal threshold strategy is discussed. Sensitivity analyses on the influences of discount factor, observation interval and maintenance cost to the discounted cost and optimal actions are presented.

Optimisation of Maintenance by Piecewise Deterministic Markov Processes under Conditions of Population Heterogeneity

“…By allowing the process to jump randomly while remaining continuous between jumps, the PDMP model can accurately describe the processes of continuous and deterministic damage. Wang and Chen (2022) have made significant advances in the field of imperfect maintenance modeling by introducing a novel approach that incorporates a piecewise deterministic Markov process. This new model considers both random shocks and natural degradation and incorporates a physical formula to calculate the latter.…”