Non-periodic inspection of optimization of repairable systems

This study proposes models to find the optimal non-periodic inspection interval over a finite planning horizon for two types of multi-component repairable systems. The first system consists of hard-type and soft-type components, and the second system is a k-out-of-m system with m identical components. The failures of components in both systems follow a non-homogeneous Poisson process. The failure of soft-type components and the failure of components in a k-out-of-m system when the number of failed components is still less than m-k+1, are soft failures. Soft failures are revealed only at scheduled inspections or when an event of opportunistic inspection or a system failure occurs. The failures of hard-type components or the failure of (m-k+1)th failed component in a k-out-of-m system are hard failures, and cause the system to stop functioning. Hard failures are revealed immediately and the failed components are fixed. In this study, a failed component is either replaced or minimally repaired according to its age at failure time. To find the optimal inspection schedules for the systems, we minimize the total expected cost of the systems over a finite planning horizon. The total cost for the first type of system includes the costs of components’ minimal repairs, replacements, downtimes, and the scheduled inspections. The total cost of a k-out-of-m system has an additional penalty cost for system failures. We consider a binary variable for a possible scheduled inspection’s time, in which 1 indicates performing a planned inspection at that time, and 0 shows no inspection to be performed. Thus, our goal is to find the optimal vector of binary decision variables which results in the minimum total cost of the system. A recursive formula is developed to calculate the expected number of minimal repairs, replacements and downtime of soft-type components. However since obtaining the expected values from the mathematical formula is cumbersome, we develop a simulation model to obtain the total expected cost for a given non-periodic inspection scheme. We then integrate the simulation model with a genetic algorithm to obtain the optimal inspection scheme.