Inspection and maintenance optimisation of multicomponent systems
The present research proposes methodology and mathematical models for optimisation of inspection and maintenance in complex multicomponent systems with finite planning horizon. Components are classified by failure types: hard-type and soft-type. The systems analysed are composed of either multiple identical hidden soft-type components in k-out-of-n redundant configuration, or a combination of hard-type and hidden soft-type components. Failures of hard-type components cause system failures. Failures of components in k-out-of-n systems and soft-type component failures are hidden and not discoverable until an inspection, but reduce the system’s reliability and performance. The systems are inspected either periodically, or non-periodically. They are also inspected opportunistically at the times of system failure (occurring at (k – n + 1)st component failures in k-out-of-n systems, or at hard failures in the systems composed of hard-type and soft-type components). Inspections have negligible duration. All components may undergo minimal repair, or corrective replacement, with hard-type components also having a possibility of preventive replacement under periodic inspections. We only consider minimal repair and corrective replacement under non-periodic inspections.
We propose several models for joint optimisation of inspection and maintenance policies that result in the lowest total expected cost. Since soft failures are hidden, we generate expected values for the number of minimal repairs, number of replacements and downtime recursively. Due to multiple component interactions and system complexity, Monte Carlo simulation and genetic algorithms (GA) are used for optimisation. Using GA for optimisation allows to consider quasi-continuous inspection intervals due to improved computational efficiency compared to Monte Carlo simulation. Some of proposed models feature preventive component replacements and are applicable even for systems with hidden component failures.
For k-out-of-n systems, we apply periodic model to series and parallel systems and compare the results. We provide expressions for expected number of system failures in terms of cost ratio and component failure intensity. We also provide a simplified expression for system reliability. In addition, we derive a formula for finding the planning horizon length based on expected number of system failures. It may be useful for planning the system’s operating horizon, at the system design stage and when analysing its performance.