Master thesis deals with a manufacturing process of the product with narrow tolerances. A problem of the machining process instability arose during the process. A measurement system analysis of the measuring system and a control of the system’s adequacy were made before the analysis of the machining process. After the examination and approval of the measuring system capability, the analysis of the machining process continued. A statistical process control on the existent machining process was performed. Low process capability coefficients showed that the machining process was not stable and was incapable. In order to stabilize the process an automatic correction system was integrated, followed by improvement of the machine precision. The stability and capability of the machining process increased but the problem of the roundness on the product was still present. The possible process parameters, which could affect the roundness problem, were examined with the design of the experiment method. The results showed that the clamping force has the largest effect on the problem. The lowest clamping force was achieved with the parameters optimization, but the problem was still present. Therefor a new clamping fixture was suggested to eliminate the roundness problem.