$s_m$ provides the estimate of $s_\alpha$.

Sampling under the conditional probability {#operational_procedure}
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In practice batches of specimen are put under trial, each of them with a decreasing strength; this allows to target the tail of the distribution $\mathbb{P}$ iteratively.

![image](densR2.png) \[fatigue\]

In other words, in the first step, points are sampled in zone (I). Then in the following step, only specimen with strength in zone II are considered, and so on. In the final step, the specimen are sampled in zone IV. At level $s_{m}$, they have a very small probability to fail before $n_{0}$ cycles under $\mathbb{P}$, however under their own law of failure, which is $\mathbb{P}(\mathbf{.}\mid R\leq s_{m-1})$, they have a probability of failure of order 0.2.

In practice, sampling in the tail of the distribution is achieved by introducing flaws in the batches of specimens. The idea is that the strength of the material varies inversely with respect to the size of the incorporated flaws. The flaws are spherical and located inside the specimen (not on its surface). Thus, as the procedure moves on, the trials are performed on samples of materials incorporating flaws of greater diameter. This procedure is based on the hypothesis that there 