The Lognormal Life Distribution

The lognormal life distribution is one wherein the natural logarithms of the lifetime data, ln(t), form a normal distribution.  Consequently, the life data of a lognormal distribution will also form a straight line if plotted on a lognormal plot, i.e., a plot whose x- and y-axes stand for the cumulative % of failures and the logarithmic scale of time, respectively.  The failure rate curve l(t) of a lognormal life distribution starts at zero, rises to a peak, then asymptotically approaches zero again for all values of s. 

The lognormal distribution is formed by the multiplicative effects of random variables. Multiplicative interactions of variables are found in many natural processes, and are in fact observed in many frequently-encountered semiconductor failure mechanisms.  This characteristic of the lognormal distribution makes it a good choice for the analysis of the failure rates of many semiconductor failure mechanisms.

A notable characteristic of the lognormal distribution is the fact that its median time to failure, t_50%, or the time at which 50% of the samples fail, is equal to e^µ, where µ is the mean of the life data. Thus, t_50% = e^µ.