One pillar of modern material's design is density functional theory (DFT). In many circumstances DFT's calculations are as important as experimental results. Although in first principle or ab initio calculations, everything starts with few physical principles, in practice there are several approximations in order to make the calculations possible. Beside, several methods have been proposed to tackle Kohn-Sham equations. Each of these methods has its own advantages and disadvantages. Site centered methods such as EMTO, LMTO and KKR plus coherent potential approximation (CPA) is a standard tool to treat alloy disorder in metals. Due to above mentioned approximation, there remain some systems which cannot be accurately treated by current status of the methods. One can name materials such as cemented carbide, nitride and oxide which are of interests for industries. For such systems, it is possible to use plane-wave methods but still it is difficult to treat alloy disorder in plane-wave methods. The main purpose of this project is to make use of accurate Exact muffin-tin orbital method (EMTO). New modules have been added to the code. Performing calculations are of great importance and interest for mentioned systems. Two industrially important alloys have been chosen to study namely pseudobinary Ti(O,C) and Zr(O,C). Since usually these carbide are made of its corresponding oxides, even in carbide there remains amount of oxygen in material. With newly developed method, these materials will be studied and effect of oxygen on thermodynamic stability of defects will be considered.