Development of a comprehensive rock fragmentation model has long been a complicated task because several parameters can affect the rock fragment size of blasted rocks. The role of delay factor has not yet been clear enough to use in the empirical rock fragmentation model. In this study, first a simple new flexible delay function (Df) was found to evaluate the impact of delay factor (Δt) on the rock fragmentation. Then, the effect of in-situ rock mass properties, blasthole parameters, powder factor and delay factor on the rock fragment size were analyzed. After using the new delay function in the combination of the parameters affecting the rock fragment size, the correlation considerably increased. At the end, new empirical models were developed with high correlation of determination (R2), less root mean square error (RMSE) and less coefficient of variation (CV) with actual large scale results.