Gamma-ray bursts (GRBs) are transients associated with the formation of compact objects. It had long been theorised that mergers of two neutron stars leading to the formation of a heavier neutron star or a black hole are the progenitors of the so-called `short' GRBs. The merger is associated with the emission of gravitational waves (GWs) that are detectable on earth, and this association was proved empirically with the detection of a short GRB and other electromagnetic emission of the GW source 170817. It is important to make statistical predictions of the number of sGRBs detectable by a GRB monitor in the sky. Here I present predictions of the event rate of the $\textit{AstroSat}$-CZTI via careful studies of the luminosity function of short GRBs. Using the maximum distance to which the GW networks are sensitive in the past, present and future runs, stringent lower limits are placed on the rate of binary neutron star mergers (BNSMs). It is shown that the number will go up significantly in the next observing runs of aLIGO/VIRGO. Comparison of the short GRB rate with the BNSM rate calculated independently from the single source statistics of GW170817 reveals the presence of a slight tension that can have significant implications on the physics of the merger ejecta; however the scenario that each BNSM indeed produces a short GRB, cannot be ruled out.