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Tool · Uncertainty propagation

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.

e.g. 1e-5 /h for a typical electronic component λ.
P95 / P50. Typical: 3 (well-known) to 10 (poor data).
10,000 is plenty for 5/50/95 stability.
Mean
P5 (5th)
P50 (median)
P95 (95th)
Click "Run Monte Carlo" to draw the distribution

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.

Privacy The Monte Carlo runs entirely in your browser. Your inputs and the 10,000 samples never leave your device. Use it for sensitive component data without the procurement conversations that cloud-hosted tools demand.