Drilling operations constitute the major part of the exploration costs. Drill bits are the primary part required to be changed frequently due to its quick wearing nature. In order to reduce the drilling cost, rate of bit penetration (ROP) must be estimated or optimized by using several drilling parameters. One of the most commonly used methods for estimating the optimum penetration rate is Bourgoyne and Young Method (BYM) that is eight-parameter model. However, mathematically speaking, minimum of thirty different sets of data zones, which must be taken from uniform-lithology sections (particularly shales) are needed to get accurate results. To construct the functional relationship with the data, a multiple regression analysis is performed. When there is not enough data, the accuracy of BYM decreases.