The results of examining error evaluation of the coverage factor with approximate methods in indirect measurements have been presented in the paper. Basing on the method?s accuracy analysis, the scope of application of the approximate methods of the expanded uncertainty estimation has been presented; the criterion of not-exceeding a preset value of the error has been implemented. The knowledge of coverage factor characteristics for the convolution of three selected probability distributions was used for the examination.

In this paper a procedure to determine the uncertainty of thickness measurement of thin layer is presented. The spectrophotometer method uses the spectrum of light transmission and some dependences between interference extremes and thickness of thin layer. The final result has been achieved by using a method recommended by Guide to the Expression of Uncertainty in Measurement. The standard uncertainty has been estimated by approach, called type B, which is based on manufacturer?s specification of spectrophotometer, experience in reading of results on transmission spectrum and literature data.

Arithmetical operations performed on measurement results treated as intervals cause that the influence both errors distribution shape and errors correlation to the width of the resultant interval must be considered. The paper describes the use of reductive interval arithmetic in such a situation. Coherence coefficients which generally describe interdependence between intervals are interpreted as parameters of the error value set. The composition rule for two kinds of coefficients – those dependent on the shapes of the error distributions and those dependent on correlation between errors – is presented. Uncertainty calculation inaccuracy of the described method has been analysed in the paper, too.

The algorithms based on digital signal processing for impedance components’ evaluation in circuits with sampling transducer have been analysed. It is supposed that the voltage and current are sampled synchronously to the fundamental frequency of the generated sinusoidal signal. Two fitting sine wave algorithms, which are based on the least mean square (LMS) technique, have been described. The first one reconstructs indirect measurement method. The second algorithm estimates the unknown impedance components by direct method. The uncertainty’s propagation by described algorithms can be analysed by means of covariance matrix. The elements of covariance matrix are dependent on the phase angles of the measurement signals. It is shown that those algorithms provide minimization of uncertainty for selected number of samples and phase angles. The influence’s simulations of quantization error of the AD converter and jitters of sampling time for described algorithms on uncertainty processing results have been carried out.

Establishing the notion of equivalence, or indiscernibility, with the concept of attribute, precedes every measurement practice. The present paper proposes a formal theory of classification, and sheds a new light upon the notion of equivalence underlying nominal level of measurement. Assuming that each object is characterized by a set of predicates as a binary vector, whose components are 1 or 0 according as the object affirms a predicate or not, we first examine the relationship among objects in reference to the choice of predicates, or classifier, and formulate a formal theory of classification of objects by predicates. The formalization is perfectly symmetrical between the objects and the predicates, and allows us to consider a classification of predicates by objects. Based on this reciprocal view of classification we introduce a modified concept of equality between two groups of objects, propose a new approach to clustering, and discuss its merits by showing example.