Advanced discrete simulation methods applied to repairable multistate systems

This implies that the state function S(t) is piecewise constant and right-continuous in t, with jumps at T1 < T2 < · · · .

The fact that a pure jump process is right-continuous and piecewise constant in t is convenient during simulations. Hence, in order to keep track of how the process evolves and update the value of the state function, only the points of time where the events happen need to be considered.