The paper presents a spectral formulation of surface profile irregularity in a wideband frequency range for roughness, waviness and shape components along the measured length. A unique distribution of roughness and waviness components is proposed, according to the nature of their origination in the course of machining with tools of defined cutting edge, as distinct from standard filtration in measurements of surface irregularities. Differences resulting from both formulations are outlined as well as the method of determining the frequency of component separation for surface roughness and waviness.

The paper describes the influence of the machining operation on a surface, which disturbs the projection of the tool profile in the form of its relative movements with respect to the object. The elements of the machine tool undergo constant wear during the machining process, it is therefore important to recognize the effects of their influence on the surface's irregularities. Amplitude-frequency analysis of lateral profiles has been used to evaluate and changes of turned lateral profiles. The results of simulation of radial and axial effects of the machine tool on surface and their spectral components were analyzed. Surfaces obtained in similar machining conditions on lathes operated in various time periods were analyzed spectrally. From the analysis of surface irregularity changes caused by disturbances in movements of the tool against the object, testifying the wear of main machine elements during its operation, the modulated, amplitude-frequency character of changes in surface irregularities of workpiece can be noticed.

When observations are autocorrelated, standard formulae for the estimators of variance, s2, and variance of the mean, s2 (x), are no longer adequate. They should be replaced by suitably defined estimators, s2a and s2a (x), which are unbiased given that the autocorrelation function is known. The formula for s2a was given by Bayley and Hammersley in 1946, this work provides its simple derivation. The quantity named effective number of observations neff is thoroughly discussed. It replaces the real number of observations n when describing the relationship between the variance and variance of the mean, and can be used to express s2a and s2a (x) in a simple manner. The dispersion of both estimators depends on another effective number called the effective degrees of freedom Veff. Most of the formulae discussed in this paper are scattered throughout the literature and not very well known, this work aims to promote their more widespread use. The presented algorithms represent a natural extension of the GUM formulation of type-A uncertainty for the case of autocorrelated observations.