  In this paper, we study network reliability in relation to a periodic
time-dependent utility function that reflects the system's functional
performance. When an anomaly occurs, the system incurs a loss of utility that
depends on the anomaly's timing and duration. We analyze the long-term average
utility loss by considering exponential anomalies' inter-arrival times and
general distributions of maintenance duration. We show that the expected
utility loss converges in probability to a simple form. We then extend our
convergence results to more general distributions of anomalies' inter-arrival
times and to particular families of non-periodic utility functions. To validate
our results, we use data gathered from a cellular network consisting of 660
base stations and serving over 20k users. We demonstrate the quasi-periodic
nature of users' traffic and the exponential distribution of the anomalies'
inter-arrival times, allowing us to apply our results and provide reliability
scores for the network. We also discuss the convergence speed of the long-term
average utility loss, the interplay between the different network's parameters,
and the impact of non-stationarity on our convergence results.
