Lognormal Monte Carlo calculator
Drop in a median (point estimate) and an error factor (EF — the ratio of 95th percentile to median, the standard PRA way of expressing component-data uncertainty). The calculator samples 10,000 lognormal variates, returns the mean, 5th / 50th / 95th percentiles, and draws a histogram. Useful for fault-tree leaf uncertainty propagation when the analytical mean differs noticeably from the median.
Why lognormal?
Reliability data — failure rates, repair times, demand frequencies — are almost always non-negative and right-skewed. The lognormal distribution captures this naturally: log(X) is normally distributed, so X itself spans many orders of magnitude. Standard PRA component-data sources (NUREG/CR, IAEA, OREDA) publish median + EF rather than mean + std-dev because lognormals are easier to elicit and combine that way.
Conversion:
μ = ln(median) σ = ln(EF) / 1.645 ← because EF = P95/P50 = exp(1.645·σ) mean = exp(μ + σ²/2) ← always > median for σ > 0
How fault-tree quantification uses this
For a top event whose probability is dominated by a single cut set, the top-event distribution is approximately the product of the leaf lognormals — itself lognormal. For multi-cut-set top events, Monte Carlo propagation through the full tree is the standard approach (it's what FTA Studio Enterprise's Monte Carlo engine does). Run a one-shot calculation here for a single leaf to sanity-check what each component contributes; run the full tree in FTA Studio for the system-level distribution.