Femtosecond-laser-written patterns at the surface of brittle materials may show at random times spontaneous alternations from regular to disordered structures and vice versa. Here, we show that these random transitions carry relevant statistical information, such as the Weibull parameters characterizing the fracture of brittle materials. The regular-erratic cycles of random lengths of the observed patterns suggests a phenomenological analogy with the idle and busy periods arising in queuing systems. This analogy enables us to establish experimentally that the random durations of the successive cycles are statistically independent. Based on these observations, we propose an experimental method bypassing the need for many specimens to build up statistically relevant ensembles of fracture tests. Our method is potentially generic, as it may apply to a broad number of brittle materials.