Reliability Modelling Considering Self-Exciting Mechanisms of Shock Damage

Abstract

This study investigates reliability modelling and optimal preventive maintenance polices for engineering systems subject to shocks, considering two types of self-exciting mechanisms. Under trigger mechanism 1, if the accumulative number of δ—ineffective shocks reaches the trigger threshold k1 among the run of ineffective shocks, then the self-exciting mechanism will be activated, resulting in the accumulative number of effective shocks increasing by m1. Under trigger mechanism 2, if the consecutive number of δ—ineffective shocks reaches a fixed threshold K2 among the run of ineffective shocks, then the self-exciting mechanism will be triggered and the accumulative number of effective shocks will increase by m2. The system breaks down when the accumulative number of effective shocks exceeds the fixed threshold. Based on the established shock models, the reliability indices are obtained through the finite Markov chain imbedding approach. According to the operation of the system under different monitoring conditions, two types of preventive maintenance strategies are considered; then, optimization models are established, and the optimal preventive maintenance thresholds are determined. Finally, the proposed models are illustrated by numerical examples.