Oxygen-free high conductivity (OFHC) Cu is a pure form of Cu with 99.99% Cu and is widely used in electrical applications such as cryogenic shunts, X-ray storage ring, and various other industries for different applications (Mahto and Kumar, 2008; Yang and Chen, 2001; Zhang, Chen, and Kirby, 2007).

Presently, the demand for good quality of finished OFHC Cu material (like a mirror finish surface) is increasing at a brisk pace for its use in various sectors, like manufacturing, electrical, electronics, nuclear, and medical science (Mahto and Kumar, 2008; Yang and Chen, 2001; Zhang et al. 2007). To achieve a good quality of surface finished products, the selection of proper process parameters are important and essential (Yang and Chen, 2001). Among the several metal cutting operations, end milling has been a vital, common, and widely used process for machining parts in numerous applications including aerospace, automotive, and several manufacturing industries (Mahto and Kumar, 2008; Zhang et al. 2007).

It is well known that the surface roughness is an important parameter in the machining process (Makadia and Nanavati, 2013). Usually, the product quality is measured by its surface roughness. Minimizing the surface roughness results in a product with good surface finish of the final machined part. Thus, researchers have directed their attention toward developing models and quantifying the relationship between roughness and its parameters. The determination of this relationship is for the advancement in manufacturing machines, materials technology, and the availability of modeling techniques. The different methods include that confined in this approach response surface method (RSM), factorial designs, and Taguchi methods (Lin, 1994). Recently, these are the most popular methods used by researchers that tend to reduce the effort of a machinist and minimize the machining time and cost which was not possible by the old experimental approach that includes single factor at a time or “trial-and-error” approach (Lin, 1994). Among the various approaches used to predict the surface roughness, the present article demands a brief review of roughness modeling using RSM.

Alauddin et al. (Alauddin, El Baradie, and Hashmi, 1996) presented their work on optimizing the surface finish of Inconel 718 in end milling. They used uncoated carbide inserts under dry operating conditions. The RSM was used to develop a first- and second-order models, and based on the results, it was concluded that with the increase in feed surface roughness, increases cutting speed but increasing speed results in a decrease in the surface roughness. Suresh et al. (Suresh, Rao, and Deshmukh, 2002) proposed a model dependent on the machining parameters for measuring the surface roughness of material and later optimized the parameters using a generic algorithm. Routara et al. (Routara, Bandyopadhyay, and Sahoo, 2009) proposed a roughness model for end milling of three different materials: Al 6061-T4, AISI 1040 steel, and medium-leaded brass UNS C34000. The study included five roughness parameters, and for each behavior, a second-order response surface equation was developed. Benadros et al. (Benardos and Vosniakos, 2002) presented a review for surface roughness prediction in the machining process. The different approaches reviewed were based on machining, experimental design and investigation, and artificial intelligence. Colak et al. (Colak, Kurbanoglu, and Kayacan, 2007) optimized roughness parameters using a generic algorithm for generating end milled surface. A linear equation was proposed for the estimation of the surface roughness that was in terms of parameters such as cutting speed, feed, and depth of cut. Lakshmi et al. (Lakshmi and Subbaiah, 2012) used RSM for modeling and optimization of the end milling process parameters. Average surface roughness for the EN24 grade steel stands for CNC vertical machining center. In addition, the second-order model was developed based on the feed, depth of cut, and the speed of cutting. It was shown that the predicted value from the model was in close agreement with the experimental values for *R*_{a}. Jeyakumar et al. (Jeyakumar and Marimuthu, 2013) used RSM to predict the tool wear, cutting force, and surface roughness of Al6061/SiC composite in end milling operation. The developed model was further used to investigate the synergistic effect of machining parameters on the tool wear. Ozcelik et al. (Ozcelik and Bayramoglu, 2006) developed a statistical model to predict the surface roughness in high-speed flat end milling of AISI 1040 steel. The experiments were performed under wet cutting conditions using step over, spindle speed, feed rate, and depth of cut. It was found that *R*^{2}_{adj} increases from 87.9 to 94% by adding total machining time as a new variable. Mansour and Abdalla (Mansour and Abdalla, 2002) studied the roughness (*R*_{a}) in end milling of EN 32 steel using RSM. Wang et al. (Wang and Chang, 2004) studied the effect of micro-end-milling cutting conditions on the roughness of a brass surface using RSM. Reddy and Rao (Reddy and Rao, 2005) developed a mathematical model using RSM to calculate surface roughness during end milling of medium carbon steel.

Based on the literature presented above, it reflects that there are mainly four machining parameters that effect on the surface roughness of end milled parts. Thus, in the present study, two roughness parameters viz. roughness average (*R*_{a}) and mean roughness depth (*R*_{z}) was considered as responses for generating stata istical predictive model in terms of machining parameters.