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Equation 19 · Part 5 · Ten Failure Modes That Define Production RAG

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Li≈λi τi ℓi,L_i \approx \lambda_i \, \tau_i \, \ell_i,
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What this part means

Approximately equal to; the equality is not exact.

Its job in the formula

Approximately equal to; the equality is not exact.

The passage around this formula

A catalogue is not a triage plan. The ten differ enormously in how much damage accrues before anyone notices, and instrumentation effort should follow that rather than follow which failure is most interesting to write about. For a mode i with arrival rate λi\lambda_i , mean time to detection τi\tau_i , and cost per undetected instance ℓi\ell_i , the loss accrued before intervention is approximately Li≈λi τi ℓiL_i \approx \lambda_i \, \tau_i \, \ell_i. and the marginal value of building a detector is whatever it removes from τi\tau_i . Written this way, the ranking departs sharply from intuition, because τi\tau_i spans several orders of magnitude across the ten while λi\lambda_i and ℓi\ell_i vary far less.

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