This work studies the reliability function of K-out-of-N systems with a general repair time distribution and a single repair facility. It introduces a new repair mechanism using an effort function, described by a nonlinear ordinary differential equation. Three theoretical results are obtained: regularity properties preventing simultaneous failures and repairs, derivation of a Kolmogorov forward system for micro-state and macro-state probabilities, and comparison of reliability functions of two K-out-of-N systems. An additional hypothesis on the model’s parameters allows us to obtain an ordering relation between the reliability functions. A numerical example demonstrates the model’s practical application and confirms the theoretical results.
