  Mathematically, it takes an infinite amount of time for the transient
solution of a diffusion equation to transition from initial to steady state.
Calculating a \textit{finite} transition time, defined as the time required for
the transient solution to transition to within a small prescribed tolerance of
the steady state solution, is much more useful in practice. In this paper, we
study estimates of finite transition times that avoid explicit calculation of
the transient solution by using the property that the transition to steady
state defines a cumulative distribution function when time is treated as a
random variable. In total, three approaches are studied: (i) mean action time
(ii) mean plus one standard deviation of action time and (iii) a new approach
derived by approximating the large time asymptotic behaviour of the cumulative
distribution function. The new approach leads to a simple formula for
calculating the finite transition time that depends on the prescribed tolerance
$\delta$ and the $(k-1)$th and $k$th moments ($k \geq 1$) of the distribution.
Results comparing exact and approximate finite transition times lead to two key
findings. Firstly, while the first two approaches are useful at characterising
the time scale of the transition, they do not provide accurate estimates for
diffusion processes. Secondly, the new approach allows one to calculate finite
transition times accurate to effectively any number of significant digits,
using only the moments, with the accuracy increasing as the index $k$ is
increased.
