This shows that for getting the age ranked discharges for any time, \(t\), we need the values of \(s_f\left(T\right)\ \ \ \forall T\) . Please also observe that, for any \(t\ \ge t_c+\Delta t\),- it is \(\left(s_f(T)-s_f(T-\Delta t)\right)\ =0\) and therefore \(q\left(t,t-T\right)\equiv0\), as expected. To illustrate better the topic let's rework Figure 1 into Figure 3 below.