  Mix-cumulants of conserved charge distributions are sensitive observables to
probe properties of the QCD medium and phase transition in heavy-ion
collisions. In order to perform a precise measurement, efficiency correction is
one of the most important steps. In this paper, we derive the proper efficiency
correction formulas for mutually exclusive and inclusive variables. UrQMD model
is applied to check the validity of those formulas for different types of
correlations. Further, we investigate the effect of the multiplicity loss and
contamination arising from the particle identifications. This study provides an
important step towards future measurements of mixed-cumulants in relativistic
heavy-ion collisions.
