Precision dimensional inspection of diameters of circular reflecting cylinders

A method for measuring diameters of circular reflecting cylinders is discussed. The method consists in processing a diffraction pattern that is formed in the near-field zone by illuminating the object edges by a plane monochromatic beam. An equivalent mathematical model of forming a diffraction field is developed and experimentally validated. The model makes it possible to obtain analytical functions describing the distribution of the field from the circular reflecting cylinder. The influence of the cylinder reflecting surface on the diffraction pattern parameters is studied. A highly accurate algorithm is proposed for calculating the diameter of the cylindrical article by its Fresnel diffraction pattern with an error under 1 μm. Original Russian Text ? Yu.A. Lemeshko, Yu.V. Chugui, A.K. Yarovaya, 2007, published in Avtometriya, 2007, Vol. 43, No. 3, pp. 112–121.     

Peculiarities of measurements in scanning electrical-conductivity microscopy

Functional capabilities of the scanning electrical-conductivity microscopy (SECM) in determining the electrical conductivity of nano-sized elements, studying the nanostructure of conductive coating materials, and evaluating the conductivity of nano-objects are described. The applicability of the SECM to finding imperfections in the multilevel metallization of integrated circuits with a nano-sized topology is demonstrated.     

Application and power of criteria for testing the homogeneity of variances. Part II. Nonparametric criteria

The distributions and power of nonparametric tests of the homogeneity of dispersion characteristics (Ansari–Bradley, Mood, Siegel–Tukey, Capon, and Klotz) are studied. A comparative analysis is made of their power relative to the classical tests for the homogeneity of variance (Fisher, Bartlett, Cochran, Hartley, Levene). Tables of percentage points for the Cochran test are given for non-normal distributions.     

Solving problems of using some nonparametric goodness-of-fit tests

Estimates are given of the power of the Kuiper and Watson goodness-of-fit tests and three Zhang tests with the Z _A , Z _C , and Z _K statistics with respect to some pairs of competing laws in testing simple and composite hypotheses. The powers of these tests are compared with the powers of the Kolmogorov, Cramer-von Mises-Smirnov, and Anderson-Darling tests. Statistic distribution models and tables of percentage points are constructed which allow the Kuiper and Watson goodness-of-fit tests to be used to test composite hypotheses about the goodness of fit of samples against various parametric distribution laws. An interactive simulation method is proposed that allows constructing and using distributions of test statistics in solving problems of statistical analysis.     

Errors and Incorrect Procedures When Utilizing χ2 Fitting Criteria

It is shown that the practice of using ² criteria is accompanied by errors of two types. Firstly, those associated with the checking of complex hypotheses and with the use of a ² _k–m–1 distribution as the limiting law when estimating the m parameters of the law from point samples. Errors of this type result in an increase in the probability of errors of the first kind. Secondly, those associated with incorrect procedures involving the choice of the number of intervals and the grouping method. It is asserted that the choice of the number of intervals and of the method of dividing the domain of definition into intervals should be made on the basis of the maximum criterion power for the close alternatives.     

Errors When Using Nonparametric Fitting Criteria

It is shown that the mistakes most frequently made when utilizing nonparametric fitting criteria of the Kolmogorov and ² and ² Mises type are associated with the use of classical results for testing complex hypotheses or with undervaluing the factors influencing the distributions of the statistics of the criteria.