Template:Lognormal distribution mean

The Mean or MTTF
The mean of the lognormal distribution, $$\mu $$, is given by [18]:


 * $$\mu ={{e}^{{\mu }'+\tfrac{1}{2}\sigma _^{2}}}$$

The mean of the natural logarithms of the times-to-failure, $$\mu'$$, in terms of $$\bar{T}$$  and  $${{\sigma }_{T}}$$  is givgen by:


 * $${\mu }'=\ln \left( {\bar{T}} \right)-\frac{1}{2}\ln \left( \frac{\sigma _{T}^{2}}+1 \right)$$