  Various Monte Carlo programs, developed either by small groups or widely
available, have been used to calculate the effects of decays of radioactive
chains, from the original parent nucleus to the final stable isotopes. These
chains include uranium, thorium, radon, and others, and generally have
long-lived parent nuclei. Generating decays within these chains requires a
certain amount of computing overhead related to simulating unnecessary decays,
time-ordering the final results in post-processing, or both. We present a
combination analytic/stochastic algorithm for creating a time-ordered set of
decays with position and time correlations, and starting with an arbitrary
source age. Thus the simulation costs are greatly reduced, while at the same
time avoiding chronological post-processing. We discuss optimization methods
within the approach to minimize calculation time.
