MATHEMATICAL MODELING OF THE INDICATORS OF RELIABILITY OF VENTILATION SYSTEMS WITH REGARD TO THE DEGRADATION OF THE MODULE PARAMETERS

Gorshkov Valentin Ivanovich, Candidate of engineering sciences, associate professor, sub-department of heat-and-gas supply and ventilation, Penza State University of Architecture and Construction (28 Titova street, Penza, Russia) , eoi@pguas.ru
Miroshnichenko Denis Sergeevich, Postgraduate student, Penza State University of Architecture and Construction (28 Titova street, Penza, Russia), eoi@pguas.ru
Svyatkina Anna Aleksandrovna, Postgraduate student, Penza State University of Architecture and Construction (28 Titova street, Penza, Russia) , anja.svjatkina@mail.ru

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Background. Interest in the assessment of reliability of ventilation systems at the stage of development thereof is connected with the prospect of predicting failure absence in these systems during operation. The article considers stochastic branching processes, which serve as abase for a method of calculation of reliability of ventilation systems. The aim of this work is to compare the calculation results obtained by the existing and the proposed procedures, as well as confirmation of the adequacy of the proposed method.
Materials and methods. Comparison of the existing methods with the proposed ones showed that the first do not consider the degradation of the technical parameters of assembly units during the period of operation, which is a major drawback. To prove the adequacy of the developed methods the authors compiled a structure of probabilistic transitions of Markovski stochastic branching process of failure prediction for independent ventilation system.
Results. Comparative analysis of the average time of failure-free operation of the ventilation system following the said techniques showed that the existing method gives overestimated values of the average time of failure-free operation of 13–24 %, whereas the suggested method’s value is 4–5 %.
Conclusions. The proposed method of calculating the reliability characteristics of ventilation systems is more appropriate, making it possible to take into account the degradation of system elements in time and plan the timing of maintenance of its modules.

ventilation system, independent failures, branching processes, differential equations, generating function, expectation, trouble-free operation

1. Polovko A. M., Gurov S. V. Osnovy teorii nadezhnosti [Basic theory of reliability]. Saint Petersburg: BKhV-Peterburg, 2006, 704 p.
2. Sevost'yanov B. A. Vetvyashchiesya protsessy [Branching processes]. Moscow: Nauka, 1971, 307 p.
3. Venttsel' E. S. Teoriya veroyatnostey [Probability theory]. Moscow: Fizmatlit, 1962, 637 p.
4. Korn G., Korn T. Spravochnik po matematike [Mathematics handbook]. Moscow: Nauka, 1974, 701 p.