Razi J. Markov models Processes incidents in Man-Machine Systems

The object of study is the process of "Human-Machine-Environment" (H-M-E) system dynamics with external flow of natural or man-made accidents. The purpose of research is to simulate H-M-E systems and solve the problem of determining the probabilities of its states and cost characteristics to improve the efficiency of the system in emergency situations. Research methods include the theory of Markov chains, Kolmogorov equations and solving algebraic systems for the limiting probabilities of states and numerical optimization. Equipment consists of various tools from mathematical packages, such as Mathematica, MatLab, Statistica, etc. under OS Windows. Theoretical and practical results of the research are mathematical models of the object being restored with consideration of transition probabilities between the states and possible changes of efficiency for the human operator in the H-M-E systems. The resulting probabilities of the states of the system are used in solving optimization problems for recovery cost of the system. Scientific novelty - Markov models were first proposed to simulate different H-M-E systems, namely: 1) model with discrete time that describes process of incidents in a closed stationary H-M-E system; 2) dynamic model for H-M-E systems (simplified, as well as considering the state of a person's health); 3) model for the case of multi-catastrophe in H-M-E systems; 4) an extrapolation of the models (2) on the case of unsteady flow of accidents - all that allowed us to estimate the mean cost of recovery activities and losses from accidents; for the first time application of the "maximum information entropy" method was made to determine the parameters of health and performance of the operator. Modeling techniques in the determination of the transition probabilities between the states of subsystems "Machine" and "Human" were improved in order to study a new class of systems with dynamical multi-step recovery; the method for the average estimates of the intensity of events was improved. The results of the thesis are implemented at the Research-and-production enterprise "Elektroprom" that allowed to make the estimate for the mean value of the cost of system's restoration, and apply the method of "maximum information entropy" to determine the parameters of the contractors' health. Some of the results are implemented in educational process at Kharkiv National University of Radio Electronics for teaching courses as "Simulation", "Catastrophe theory", "Synergetics", and in degree designing as well.