Road roughness is a broad term that incorporates everything from potholes and cracks to the random deviations that exist in a profile. To build a roughness index, road irregularities need to be measured first. Existing methods of gauging the roughness are based either on visual inspections or using one of a limited number of instrumented vehicles that can take physical measurements of the road irregularities. This paper presents used a quarter car model (passive suspension System in 206 Peugeot) in according road classification ISO 2631-1 is achieved road roughness interval in form of optimization method Gamma(4p) distribution as PSD function in constant speed of car 100 Km/h by using MATLAB Code. Then, frequency response of the pitman arm in a car moving has been analysed, its critical points determined to calculate the fatigue life of the part, and the amount of critical stress at the corner of connection between triangular suspension’s arm and pitman arm obtained based on von Misses criterion (348MPa). Finally, using finite element software, fatigue life of the pitman arm evaluated based on three methods of calculation (Dirlik, narrow-band, and a combination of both of them) in terms of the kilometres of the car travelled, and fatigue life of the part has been estimated in about 93000 km according to the conditions of applied load.