Collective effective dose

The collective effective dose, $S$, due to individual effective dose values between $E_1$ and $E_2$ from a specified source within a specified time period $\Delta T$ is defined as:
$S(E_1, E_2, \Delta T) = \int\limits_{E_1}^{E_2} E [ \frac{dN}{dE} ]_{\Delta T}\ dE$
It can be approximated as $S = \sum_i E_i N_i$ where $E_i$ is the average effective dose for a subgroup i, and $N_i$ is the number of individuals in this subgroup. The time period and number of individuals over which the effective doses are summed should always be specified. The unit of the collective effective dose is joule per kilogram (J kg-1) and its special name is man Sievert (man Sv).