Due to the increasing interest in Global Navigation Satellite Systems (GNSSs) for safety-critical applications, one of the major challenges to be solved is the provision of integrity to urban environments. In the past years, it has been noted that to do so, the integrity of the received signal must be analyzed with the aim of detecting any local effect disturbing the GNSS signal. Moreover, the detection of such disturbing effects must be done with a bounded delay. This is desirable because the presence of any local effect may cause large position errors. This work addresses the signal integrity problem as a transient change detection problem by proposing a stopping time based on a finite moving average. The statistical performance of this stopping time is investigated and compared, in the context of multipath detection relying on C/N0 monitoring, to different methods available in the literature. Numerical results are presented in order to assess their performance.