In some application domains (e.g., mission-critical systems), proactive detection of reliability threats or prompt fault containment are mandatory to avoid or limit the malfunctioning of electronic systems as an effect of the onset of permanent faults at runtime. As an essential milestone for the design of these systems, this paper presents a distributed and lightweight control framework for the built-in self-testing of networks-on-chip (NoCs) in the background while applications are running. The main idea of this concurrent online testing framework consists of modularizing the NoC into communication channels, of selectively taking them offline for non-concurrent testing, and of reconfiguring the NoC routing function to route packets around the temporary blockages to preserve network availability.