Evaluating dependability metrics of critical systems: Monte ... - iaria

Work-normalized properties
Variance is not all, generation time is important (figure of merit).
Let σ 2 n(ǫ) and t n (ǫ) be the variance and generation time t n (ǫ) for a
sample of size n.
When t n (ǫ) is strongly dependent on ǫ, any behavior is possible:
increasing or decreasing to 0 as ǫ → 0.
Work-normalized versions of the above properties:
◮ The estimator verifies work-normalized relative variance if
σ 2 n(ǫ)t n (ǫ)
µ 2 (ǫ)
is upper-bounded whatever the rarity, and is therefore a
work-normalized version of the bounded relative error property.
◮ The estimator verifies work-normalized asymptotic optimality if
ln t n (ǫ) + lnσ
lim
n(ǫ)
2 = 2.
ǫ→0 lnµ(ǫ)
G. Rubino (INRIA) Monte Carlo DEPEND 2010 34 / 72