the seventies, a lot of work was done concerning surface association to points digitized with a Coordinate Measuring Machine (CMM). The function of minimization is based on the distance between the points Mi and the geometric element. It depends on the criterion of minimization. This function is nonlinear. A number of researchers have developed methods to speed up the calculations of diverse tasks and to simplify the displacement matrix. These methods imply conditions such as small displacements. An other condition is that every point has the same precision of measurement. In this paper a non-linear method is presented to calculate, the first (mean) and second (uncertainty) statistical moments of best fit surface parameters.