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The problem of estimating the probability $p=P\left(g\right(\mathbf{X})\le 0)$ is considered when $\mathbf{X}$ represents a multivariate stochastic input of a monotonic function $g$. First, a heuristic method to bound $p$, originally proposed by de Rocquigny (2009), is formally described, involving a specialized design of numerical experiments. Then a statistical estimation of $p$ is considered based on a sequential stochastic exploration of the input space. A maximum likelihood estimator of $p$ build from successive dependent Bernoulli data is defined...