  Bistable autonomous systems can be found inmany areas of science. When the
intrinsic noise intensity is large, these systems exhibits stochastic
transitions from onemetastable steady state to another. In electronic bistable
memories, these transitions are failures, usually simulated in a Monte-Carlo
fashion at a high CPU-time price. Existing closed-form formulas, relying on
near-stable-steady-state approximations of the nonlinear system dynamics to
estimate the mean transition time, have turned out inaccurate. Our contribution
is twofold. From a unidimensional stochastic model of overdamped autonomous
systems, we propose an extended Eyring-Kramers analytical formula accounting
for both nonlinear drift and state-dependent white noise variance, rigorously
derived from It\^o stochastic calculus. We also adapt it to practical system
engineering situations where the intrinsic noise sources are hidden and can
only be inferred from the fluctuations of observables measured in steady
states. First numerical trials on an industrial electronic case study suggest
that our approximate prediction formula achieve remarkable accuracy,
outperforming previous non-Monte-Carlo approaches.
