On the convergence rate for queueing and reliability models described by regenerative process
Convergence rates in total variation are established for some models of queueing theory and reliability theory. Analysis is based on renewal technique and asymptotic results for the renewal function. It is shown that convergence rate has an exponential asymptotics when distribution function of regeneration period satisfies Cramer's condition. Results concerning polynomial convergence are also obtained.
Many electronic devices operate in a cyclic mode. This should be considered when forecastingreliability indicators at the design stage.The accuracy of the prediction and the planning for the event to ensure reliability depends on correctness of valuation and accounting greatest possiblenumber of factors. That in turn will affect the overall progress of the design and, in the end,result in the quality and competitiveness of products
The considered model of the failure rate of CMOS VHSIC design proposed in the article Piskun G.A., Alekseev V.F., "Improvement of mathematical models calculating of CMOS VLSIC taking into account features of impact of electrostatic discharge", published in the first issue of the journal "Technologies of electromagnetic compatibility" for the year 2016. It is shown that the authors claim that this model "...will more accurately assess the reliability of CMOS VHSIC design" is fundamentally flawed and its application will inevitably lead to inadequate results. Alternatively, the proposed model of the failure rate of CMOS VHSIC design, which also allows to take into account the views of ESD, but based on the use of resistance characteristics of CMOS VHSIC to the effects of ESD.
The article considers the questions assessing the reliability of mechanical components used in the electronic equipment in the early stages of design. The calculations of failure rates springs shock absorbers according to various methods. It is shown that the use of models failure rates of mechanical elements, taking into account the peculiarities of their structural and technological performance, not only allows us to solve the problem of calculating, but also to ensure the required level of reliability and mechanical components, and containing electronic equipment.
The monograph presents results by professor Dr. A. Shalumov’s Research School of Modeling, Information Technology and Automated Systems (Russia). The program, ASONIKA, developed by the school is reviewed here regarding reliability and quality of devices for simulation of electronics and chips during harmonic and random vibration, single and multiple impacts, linear acceleration and acoustic noise, and steady-state and transient thermal effects. Calculations are done for thermal stress during changes in temperature and power in time. Calculations are done for number of cycles to fatigue failure under mechanical loads as well as under cyclic thermal effects. Simulation results for reliability analysis are taken into account. Models, software interface, and simulation examples are presented.
For engineers and scientists involved in design automation of electronics.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.
The basic influencing the factor defining its reliability are temperature influences at which speed of chemical reaction of materials a part REE increases. It is represented the equation which has been received by the Swedish chemist Svante Arreniusom from thermodynamic reasons
The monograph contents totaled the many years results of Scientific school «The Automated System for Ensuring of Reliability and Quality of Equipment - ASONIKA» National research University «Higher school of Economics» (scientific supervisor of the Scientific school - academician of RANS, doctor of technical sciences, professor YU. Kofanov) and long-term cooperation with the scientists of Kiev Institute of mathematical machines and systems problems of the Ukrainian National Sciences Academy (Deputy Director on science, doctor of technical sciences V.P. Strelnikov). The final structure of the monograph had been formed in the discussion of modern problems of reliability aerospace electronic equipment at the XVII International scientific-technical conference «Systemic problems of reliability, quality, mathematical modelling, information and infocommunication technologies in innovation projects». This conference was dedicated to the 20th anniversary of the HSE. The book outlines the basics of probability-physical approach to the study and the assessment of the reliability of onboard aerospace equipment. Presents the methods of estimation of reliability parameters of electronic components, as according to reference data and test or operating results in the presence or absence of failures. Developed the methods of calculation of reliability parameters of mechanical elements of aerospace equipment as well as research methods reliability of redundant and non-redundant, non-renewable and renewable systems on the basis of adequate two-parameter distributions of diffusion. Established the theory of planning reliability test with lightweight, durable, including accelerated testing with new methods of processing the testing results and reliability assessment. We propose new methods of evaluation and prediction of the aerospace equipment reliability to measure the determining parameters. Developed methodology of the statistical characteristics evaluation of the degradation process for the study of single samples of aerospace equipment using information about its representative minobject (minibranch, mineralizatsiya). All problems of reliability, which is solved in this book (mathematical modeling, calculation and experimental evaluation of the reliability of systems) result in the identification of the time until failure (or to failure) distribution. It is proved that when assessing the reliability of onboard aerospace equipment, most accurate results diffusion DN-distribution. On the basis of the law of distribution can be carried out the evaluation of all the necessary parameters of aerospace equipment reliability (mathematical expectations developments, gamma-interest developments, the probability of non-failure operating time for the specified time, the residual resource and others). The book provides a large number of examples and problems, proving the effectiveness and efficiency of the proposed methods. Material monograph mostly taught HSE in the various courses of lectures. The monograph is intended for a wide circle of specialists working in the field design, testing and operation of onboard aerospace equipment, as well as students and graduate students of the HSE in the execution of their coursework, independent scientific research, and the preparation of graduation theses and dissertations.
Maintenance of reliability of radio-electronic equipment taking into account thermal modes for various classes of electroradioproducts (ERP) within the limits of system ASONIKA is considered.
Statistical Models and Methods for Reliability and Survival Analysis is a volume of contributions by specialists in statistical theory and their applications that provide up-to-date developments in methods used in survival analysis, statistical goodness of fit, stochastic processes for system reliability among others. Many of them are related to the work of Professor M. Nikulin in statistics for thirty years. The contributors accepted this challenging project to gather various contributions with a wide broad of techniques and results, all of them in the topics of the past S2MRSA conference dedicated to M. Nikulin for his twentieth anniversary as a Professor in the Bordeaux Segalen University. The book is intended for researchers interested in statistical methodology and models useful in survival analysis, system reliability and statistical testing for censored and non censored data.
In this paper the comparative characteristics of the РС ASONIKA-K and PМ of reliability calculations are given.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.
Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.
Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.