**Nikiforov**

Vladimir O.

D.Sc., Prof.

Vladimir O.

D.Sc., Prof.

DOI: 10.17586/2226-1494-2016-16-3-524-532

DOI: 10.17586/2226-1494-2016-16-3-524-532

# FINITE MARKOV CHAINS IN THE MODEL REPRESENTATION OF THE HUMAN OPERATOR ACTIVITY IN QUASI-FUNCTIONAL ENVIRONMENT

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**Article in**Russian

**For citation:**Serzhantova M.V., Ushakov A.V. Finite Markov chains in the model representation of the human operator activity in quasi-functional environment.

*Scientific and Technical Journal of Information Technologies, Mechanics and Optics*, 2016, vol. 16, no. 3, pp. 524–532. doi: 10.17586/2226-1494-2016-16-3-524-532

**Abstract**

**Subject of Research**. We analyze the problems of finite Markov chains apparatus application for simulating a human operator activity in the quasi-static functional environment. It is shown that the functional environment stochastic nature is generated by a factor of interval character of human operator properties. **Method.** The problem is solved in the class of regular (recurrent) finite Markov chains with three states of the human operator: with a favorable, median and unfavorable combination of the values of mathematical model parameters of the human operator in a quasi-static functional environment. The finite Markov chain is designed taking into account the factors of human operator tiredness and interval character of parameters of the model representation of his properties. The device is based on the usage of mathematical approximation of the standard curve of the human operator activity performance during work shift. The standard curve of the human operator activity performance is based on the extensive research experience of functional activity of the human operator with the help of photos of the day, his action timing and ergonomic generalizations. **Main Results.** The apparatus of regular finite Markov chains gave the possibility to evaluate correctly the human operator activity performance in a quasi-static functional environment with the use of the main information component of these chains as a vector of final probabilities. In addition, we managed to build an algorithmic basis for estimating the stationary time (time study for transit of human operator from arbitrary initial functional state into a state corresponding to a vector of final probabilities) for a used chain after it reaches the final state based on the analysis of the eigenvalues spectrum of the matrix of transition probabilities for a regular (recurrent) finite Markov chain. **Practical Relevance.** Obtained theoretical results are confirmed by illustrative examples, which demonstrate their suitability for possible use in the organization of the quasi-static and functional environment to solve the problems of its perfection. The results can be used for the rational organization of functional environment in which the human operators could optimally realize their potential.

**Keywords:**quasi-static functional environment, human operator, interval parameters, finite Markov chains, vector of final probabilities, time-consuming evaluation

**Acknowledgements.**This work was supported by the Government of the Russian Federation (Grant 074-U01) and the Ministry of Education and Science of the Russian Federation (Project 14. Z50.31.0031)

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