Roles of noise in reliability problems: the view point of a mathematician and some application proposals

Noise is generally considered a disturbance in understanding systems dynamics and large efforts are devoted to filter its presence in observed data. In many instances the filtering helps the comprehension of involved phenomena but this cleaning can result in a distruction of important information. A set of examples, extracted from existing mathematical and applied literature, illustrate instances where the noise plays a positive role in determining the final dynamics of the system or allowing optimum values for signal detection. In this paper we will specifically focus on possible roles of noise when the underlining system presents non-linearities. Some of the discussed examples are toy examples useful to explain some unexpected result but we also consider the mathematical problem of determining the first passage times of stochastic processes through boundaries. These times have an immediate role in reliability theory, when alarms are tuned to prevent crashes.