Application of modern mathematical methods

The monograph presents the research and optimization of resource-saving technological processes to increase machine reliability using modern mathematical methods, the results of which have been recognized internationally in scientific forums and journals. General and private methods for these studies are elaborated, which are implemented on specific examples. The methodologies incorporate modern mathematical methods such as probabilistic statistical modeling, queuing theory, designing and optimization of extreme experiments, the theory of similarity and dimensionality. The Kolmogorov, Pearson, Student, Fisher and Cochran criteria are used to check the adequacy of mathematical models. Similarity criteria for specific processes and adequate regression mathematical models are obtained to optimize technological processes using the steepest ascent (Box-Wilson) method and optimal regimes are developed. Technological processes for increasing machine reliability have been developed and investigated; the mechanical properties of metallic coatings have been studied. The monograph is destined for scientists, constructors, Master's and PhD students and specialists of machinery production.