A general inspection and replacement policy for protection systems subject to shocks with state dependent effect

This paper proposes a new maintenance policy for protection systems which fail due to competing causes: internal deterioration and fatal external shocks. The study is motivated by a real problem in a power distribution company, in which a circuit breaker is designed to protect an electrical network from critical events such as overloads and short circuits. The failure of the system is hidden and can lead to a disaster if it is not replaced before a demand is received. So, to improve its readiness, we have developed a new two-phase (inspection & replacement) policy for a protection system with a heterogeneous population. Heterogeneity reflects factors such as variability in the quality of spare parts or in the installation of the components, which can be poorly or properly executed, resulting in some having a short life, while others may achieve a long life. Inspections are imperfect, which induces misclassification. The deterioration process is modeled via the delay-time concept. Furthermore, the shock rate depends upon the state of the system and follows a non-homogeneous Poisson process. Thus, using a numerical approach, the objective of this study is to determine the number of inspections during the first phase, the interval between consecutive inspections, and the age for scheduled preventive replacement. We compared this policy to two other classical policies via a case study and found that it has significant cost-saving potential. Generally, our results indicate when inspections should be prioritized over age-preventive replacement, and vice versa. Multi-phase policies are particularly effective for components with different characteristic lives, with inspections being crucial for maintaining readiness, often requiring investment in quality assurance to prevent misclassification. Conversely, age-based policies are more advantageous for strong (long-lived) components or when the probability of misclassification is high.