The modified proportional hazard rates model, as one of the flexible families of distributions in reliability and survival analysis, and stochastic comparisons of (n-k+1) -out-of- n systems comprising this model have been introduced by Balakrishnan et al. (2018). In this paper, we consider the modified proportional hazard rates model with a  discrete baseline case and investigate ageing properties and preservation of the usual stochastic order, hazard rate order and likelihood ratio order in this family of distributions.