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Equation 23 · Part 1 · Why Average Success Rate Hides the Failures That Matter Most

Symbol q_τ

qτ≲3nq_\tau \lesssim \frac{3}{n}
qτq_\tau

What this part means

q_τ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

q_τ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

…zero failures above the severity threshold τ\tau . It is tempting to read that as evidence the risk is negligible. It is not, and the size of the gap has a name: the rule of three. If the true failure probability is qτq_\tau , the probability of observing zero events in n independent trials is (1-qτq_\tau)^n ; setting that probability equal to 0.05 and solving gives n ln⁡(1−qτ)\ln(1-q_\tau) ≈\approx -3 , and for small qτq_\tau , where ln⁡(1−qτ)\ln(1-q_\tau) ≈\approx -qτq_\tau , this reduces to the boundary qτ≲3nq_\tau \lesssim \frac{3}{n}. as the 95…

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