In the paper, there are discussed the backgrounds of unified approach to the analysis and statistical synthesis of optimal (best in the given conditions) analogue- digital measurement systems (MS), working in a presence of noises, random disturbances and observation errors. Methods of derivation of equations and algorithms for optimal estimation of measurands and for adaptive control the measurement experiment are presented. Apart from optimal software, the obtained results determine optimal structure, characteristics, the way of functioning and locked interaction of the main elements of analogue and digital parts of the MS. The approach enables effective mathematical support of the MS design at the most responsible, initial phase of design. It may also serve as a basis for development of more efficient, mathematically argued computer – aided methods of the MS design.

RNS arithmetic has received great attention in the literature and its advantages have been clearly pointed out but practical applications are, until now, very poor. This fact is related to different reasons but the most important is the need of a complex conversion from analog or binary quantities to RNS representation (input conversion) and to the necessary final conversion from RNS representation to the classical binary one (output conversion). Recently, some authors have faced the input conversion problem, introducing the MRNS and giving a first hardware implementation for the conversion from analog quantities to RNS. Starting from this proposal, the present paper gives an alternative solution using traditional RNS representation and an architecture that can avoid, under some suitable hypotheses, the crucial problem of the conversion errors. The error conversion handling is of fundamental importance because this conversion leads to a non-positional representation.

The reliability of machining operations is an essential requirement of modern automatic manufacturing system. In the machining operations, in which unbroken chips are the major obstacles for automation, reliability implies chip control as a major aspect. To improve chip control is necessity for automated machining. In turning operation chip control is difficult especially for mild steel because chips are continuous. Chip control is closely related to the chip flow and it plays also a predominant role in the effective control of chip formation and chip breaking for the easy and safe disposal of chips, as well as for protecting the surface-integrity of the workpiece. Although the chip flow direction plays an important role in the chip control and a way to calculate the chip flow angle in a wide range of cutting conditions has been subjected in some papers by several researchers, it has not been established satisfactorily yet. Obviously, to predict the chip flow direction is becoming an important subject for the development of suitable chip breakers and the automation of turning operations. In this study, using different indexable inserts and cutting conditions for turning of mild steel, the chip flow directions were measured and a new empirical formula for prediction of the chip flow direction in term of the tool cutting edge geometry and cutting conditions was obtained by using of mathematical statistics.

Flow curves of metals to be formed must be known if we want to calculate the forces for metal-forming processes. If we can not find flow curve for the material to be formed, we have to carry out an experiment to get flow curve for this material. Instead of expensive and long-time experimental work, flow curve can be determined by using statistical methods. This paper presents determination of flow curves by using multi- regression analysis based on few experimental points of torsion test.

Two-parameters double exponential distribution is presented. Maximum likelihood method is applied to estimate the parameters of the distribution. It seems that the maximum likelihood estimates of the double exponential distribution exist only for rather specific collections of data.