Performance modelling and maintenance planning of repairable structural systems subject to multiple deterioration modes

In this paper, we present a new deterioration-reduction model for performance evaluation and maintenance planning of structural systems. In contrast to existing models, our approach models the joint effect of multiple deterioration phenomena. The underlying deterioration process is the squared norm of an n-dimensional Wiener process with drift. Maintenance effects are assumed to be imperfect, modelled through applying the idea of the Arithmetic Reduction of Deterioration (ARD₁) model. As such, in this paper, to model maintenance decisions, we characterize the deterioration reduction model as a mixture of stochastic motions and a random number of load cycles. Then, using the local features of the characterized model as a decision rule and the average cost rate as a measure of policy, we propose an optimal joint policy of periodic repair and replacement. The latter is determined by the optimal number of imperfect repairs and random load cycles. A numerical example is provided to demonstrate the effectiveness of the proposed approach and examine the behavior of optimal solutions as the model parameters change. It is also demonstrated the proposed model outperforms several models emerging as special cases. Finally, the sensitivity analysis of optimal solutions with respect to three variants of the cost model has been carried out, and the implications are discussed in detail.