Forced Monte Carlo simulation strategy for the design of maintenance plans with multiple inspections

A maintenance problem can be regarded as an optimization task, where the solution is a trade-off between the costs associated with inspection and repair activities and the benefits related to the faultless operation of the infrastructure. The optimization aims at minimizing the total cost while tuning some parameters, such as the number, time, and quality of inspections. Due to the unavoidable uncertainties, the expected cost of maintenance and failure can only be estimated by assessing the reliability of the system. The problem is, therefore, formulated as a time-variant reliability-based optimization, where both objective and constraint functions require the assessment of reliability with time. This paper proposes an efficient general numerical technique to solve this problem by means of just one single reliability analysis, while explicitly taking the diverse forms of uncertainty into account. The technique is generally applicable to any problem where the ageing or damage propagation process is known by means of input-output relationships, which apply to a great number of the cases. This technique exploits a Monte Carlo strategy derived from the concept of forced simulation, which significantly increases the efficiency of computing the optimal solution. The efficiency and accuracy of the proposed approach is shown by means of an example involving a fatigue-prone weld in a bridge girder.