  We provide a framework to estimate the systematic uncertainties in chemical
freeze-out parameters extracted from $\chi^2$ analysis of thermal model, using
hadron multiplicity ratios in relativistic heavy-ion collision experiments.
Using a well known technique of graph theory, we construct all possible sets of
independent ratios from available hadron yields and perform $\chi^2$
minimization on each set. We show that even for ten hadron yields, one obtains
a large number ($10^8$) of independent sets which results in a distribution of
extracted freeze-out parameters. We analyze these distributions and compare our
results for chemical freeze-out parameters and associated systematic
uncertainties with previous results available in the literature.
