Lognormal Distribution Calculator
The lognormal distribution applies when the logarithm of life is normally distributed. It fits mechanisms driven by multiplicative degradation — crack propagation, semiconductor diffusion, corrosion — and is the standard distribution for repair times, which is why maintainability analysis leans on it.
Formula
Worked example
Repair times fit a lognormal with μ = 1.2 and σ = 0.6 (log-hours).
- Median repair time = e^1.2 = 3.32 hours
- MTTR = exp(1.2 + 0.6²/2) = exp(1.2 + 0.18) = exp(1.38) = 3.97 hours
- P(repair ≤ 8 h) = Φ[(ln 8 − 1.2)/0.6] = Φ[(2.0794 − 1.2)/0.6] = Φ(1.4657) = 0.9286
Half of repairs finish within 3.3 hours, the mean is 4.0 hours, and 92.9% complete within 8 hours. The gap between median and mean is the signature of a right-skewed distribution — planning crew shifts around the mean would leave roughly one repair in fourteen running past the shift.
Common mistakes
- Entering the mean of the raw times as μ. The parameters are in log space; μ = ln(median), not ln(mean).
- Choosing lognormal over Weibull purely on goodness of fit with small samples — the two are hard to distinguish below about 20 failures, and they extrapolate very differently in the lower tail.
- Using the mean to plan maintenance windows for a strongly skewed distribution.
Frequently asked questions
- Lognormal or Weibull — how do I choose?
- Prefer the one supported by the failure physics. Multiplicative degradation processes (fatigue crack growth, diffusion, corrosion) argue for lognormal; weakest-link processes argue for Weibull. When physics does not settle it and the fits are comparable, choose the one that is more conservative in the region you intend to extrapolate into.
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About Reliability Pro
Lognormal Solver is part of a suite of 126 reliability, maintenance and quality engineering tools covering life data analysis, accelerated testing, system reliability, FMEA and root cause, SPC, and design for reliability. It runs in the browser and as native iOS and Android apps, so the same calculation is available at a desk or in front of the asset.