  We present a numerical analysis investigating the reliability of type Ia
supernova (SN~Ia) delay-time distributions recovered from individual host
galaxy star-formation histories. We utilize star-formation histories of mock
samples of galaxies generated from the IllustrisTNG simulation at two redshifts
to recover delay-time distributions. The delay-time distributions are
constructed through piecewise constants as opposed to typically employed
parametric forms such as power-laws or Gaussian or skew/log-normal functions.
The SN~Ia delay-time distributions are recovered through a Markov Chain Monte
Carlo exploration of the likelihood space by comparing the expected SN Ia rate
within each mock galaxy to the observed rate. We show that a reduced
representative sample of \emph{non-host} galaxies is sufficient to reliably
recover delay-time distributions while simultaneously reducing the
computational load. We also highlight a potential systematic between recovered
delay-time distributions and the mass-weighted ages of the underlying host
galaxy stellar population.
