The lognormal distribution is the distribution of a random variable whose natural logarithm is distributed normally; in other words, it is the normal distribution with In t as the variate. The density function is

for t ≥ 0

where the mean is

and the standard deviation is

where μ and σ are the mean and standard deviation (SD) of In t.

The lognormal distribution is used in reliability analysis of semiconductors and fatigue life of certain types of mechanical components. However, its main application is really in maintainability analysis of time to repair data.

References:

1. MIL-HDBK-338, Electronic Reliability Design Handbook, 15 Oct 84
2. Bazovsky, Igor, Reliability Theory and Practice
3. O’Connor, Patrick, D. T., Practical Reliability Engineering
4. Birolini, Alessandro, Reliability Engineering: Theory and Practice