The incomplete block designs, especially balanced incomplete block designs, $BIBDs$, have many common uses. One of the important properties of balanced incomplete block designs is that the treatment differences have the same variance. But, these designs are not available for every parametric combination. Also, even if they exist for a given number of treatments and block size, it may require too many blocks. Due to the restriction on existing the BIBDs, a wider class of designs which are called partially balanced incomplete block designs with $m-$associate classes, $PBIBD(m)$ introduced.