ITPEC FE Morning April 2023 Question 48
In the error embedding method, when the number of embedded errors is S, the number of discovered errors from the embedded errors is m, the number of latent errors before the start of testing not including embedded errors is T, and the total number of discovered errors is n, which of the following expresses the relationship of S, T, m, and n?
Explanation
Detection rate of embedded errors = detection rate of latent errors — the method assumes testing finds seeded and genuine errors at the same rate.
Of the n errors found, m are embedded ones, so n − m are genuine latent errors. If testing found the fraction m ÷ S of the embedded errors, it should have found the same fraction of the T latent errors:
mS = n − mT
Solving for the unknown gives T = S × (n − m) ÷ m. For example, 20 errors embedded, 10 of them found and 30 errors found in total: T = 20 × 20 ÷ 10 = 40 latent errors.
Answer (a)
Why not others:
- •(b) — the right-hand ratio is upside down: T ÷ (n − m) is latent errors per genuine error found, not a detection rate
- •(c) — uses all n errors found as if they were genuine, although n includes the m embedded ones
- •(d) — both inverts the right-hand ratio and counts the embedded errors in n
Key rule: Compare like with like, found over total for each kind, and subtract the seeded errors from the total found before estimating the genuine ones.
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