Abstract This paper presents the solutions to the stochastic differential equations which mathematically represent the machine tool workpiece system in BTA deep hole machining. The stochastic differential equations are derived assuming an appropriate model for the tool-workpiece interaction, and the machine tool work-piece system. The solutions to the non-parametric inhomogeneous differential equations are obtained using the Fokker-Planck equations. Based on these solutions, the true motion of the tool tip has been described using the maximum, average, and minimum error curves. Also, using the statistical description of the true motion, equations are derived which mathematically describe the CLA and RMS value of the surface produced. Based on these results, it is seen that the CLA and RMS value of the given surface vary 1n a given band depending upon certain machining paraj meters. The measurement of the surface texture of the specimens shows that the experimentally measured CLA values agree reasonably we...