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Matrix Method for Determining Structural Reliability of the System and Significance of Its Elements in Terms of Reliability

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Open Journal of Applied Sciences 2015年第11期5卷 669-677页

作者： Victor kravets vladimir kravets Olexiy Burov Department of Automobiles and Transportation Facilities Automobile Sector National Mining University Dnipropetrovsk Ukraine Department of Labor Security Dnipropetrovsk National University of Railway Transport Named after Academician V. Lazaryan Dnipropetrovsk Ukraine Baskin School of Engineering University of California-Santa Cruz Santa Cruz USA

Matrix method is being proposed for qualitative evaluation of the reliability of technical systems on a finite set of structural elements. We are introducing the criteria for qualitative assessment of the reliability in the form of structural reliability of the system as the probability of the troubleproof state of this system and the significancy of the individual elements in ensuring the structural reliability of the system as a general aggregate of conditional probabilities, which compose two (2 × 2) matrices of significancy for each element. We are using chain diagrams for solving the combinatronic problems and matrices for algorithmization of calculating procedures.

关键词： Structural Reliability Matrices of Significance Matrix of States Chain Diagram

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Analytical Solution of Kolmogorov Equations for Four-Condition Homogenous, Symmetric and Ergodic System

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Open Journal of Applied Sciences 2014年第10期4卷 497-500页

作者： Victor V. kravets Konstantin M. Bass vladimir V. kravets Larisa A. Tokar Department of Automobiles and Automobile Sector National Mining University Dnepropetrovsk Ukraine Foreign Languages Department National Mining University Dnepropetrovsk Ukraine

Technical system consisting of two independent subsystems (e.g. hybrid car) is considered. Graduated state graph being homogenous ergodic system of symmetric structure is constructed for the system. Differential Kolmogorov equations, describing homogenous Markovian processes with discrete states and continuous time, are listed in symmetric matrix form. Properties of symmetry of matrix of subsystem failure and recovery flow intensity are analyzed. Dependences of characteristic equation coefficients on intensity of failure and recovery flows are obtained. It is demonstrated that the coefficients of characteristic equation meet the demands of functional dependence matching proposed visible analytical solution of complete algebraic equation of fourth order. Depending upon intensity of failure and recovery flows, four roots of characteristic equation are analytically found out. Analytical formulae for state probability of interactive technical system depending upon the roots of characteristic equation are determined using structurally ordered symmetric determinants, involving proper column of set initial data as well as subsystem failure and recovery flow intensity are proposed.

关键词： State Graph Markovian Process Kolmogorov Equations Intensity Matrix Characteristic Equations State Probabilities

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