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Equation 26 · Part 3 · Why Average Success Rate Hides the Failures That Matter Most

Symbol q_τ

n≈kqτn \approx \frac{k}{q_\tau}
qτq_\tau

What this part means

q_τ occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Its job in the formula

q_τ occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

…is about the spread of a difference, not the rarity of an event. Bounding or estimating a rare catastrophic-failure rate is different in kind: the required sample size is inversely proportional to the rate itself. At qτq_\tau = 10^{-3} , getting even a rough twenty-event estimate needs on the order of twenty thousand trials. At qτq_\tau = 10^{-5} — the dangerous-failure probability ceiling regulated safety-critical software is held to under the SIL 4 standard, a bar Rabanser and colleagues cite alongside the FAA’s…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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