• V. S. Yakovyna 1 Lviv Polytechnic National University, Lviv 2 University of Warmia and Mazury in Olsztyn, Poland, Ukraine
  • M. M. Seniv Lviv Polytechnic National University, Lviv, Ukraine
  • I. I. Symets Lviv Polytechnic National University, Lviv, Ukraine
  • N. B. Sambir Lviv Polytechnic National University, Lviv, Ukraine



Software, reliability, RBD, states and transitions graph.


Context. One of the most essential properties of technical systems is their reliability, i.e. the ability of the system to perform intended functions, preserving with time the values of operation indicators within the predefined boundaries. The failure cost for modern complex technical system can be very high, which can result in events of different severity ranging from economic losses to harm to human life and health. Hence, the requirements for their reliability constantly increase. The reliability assessment of complex technical systems can be simplified by the combination of analytical research methods with computational capabilities of modern computers. The most widely used analytical methods are based on the theory of Markov processes which in turn provide the possibility to determine the time dependencies of probabilities of the system to be in defined states (operating, recovering, failure etc.), and thus the values and time dependencies of the reliability indices needed. These methods can be successfully used for the reliability analysis of different kinds of technical systems: both non-recovered and recovered; non-redundant and redundant of different redundancy types, maintenance priorities etc. However, the application of these methods for complex technical systems containing large number of elements meets the high dimensional calculation problem, which makes it impossible to perform these tasks manually. Hence the problem of automation of complex technical system reliability modeling using modern computational systems is very relevant research topic. To solve this problem, one can use specific algorithmic and software techniques described in this paper.

Objective. The goal of this article is to develop the algorithms for automated RBD processing and reliability indices assessment of complex technical systems along with the software suite for automated reliability assessment.

Method. To perform the reliability analysis the RBD approach is used which allows one to represent and visualize each element of the system in the form of a rectangle, joined by the lines in parallel or in series with other elements of the system. To obtain the reliability indices values the mathematical model of technical system reliability behavior using Markovian random process was suggested. The algorithm of RBD processing and automatic determination of operability conditions of a technical system was further considered. To calculate the minimum and maximum number of operational and failure states for the system of n elements and r recoveries the paper introduces a mathematical model based on combinatorial approach. To develop the software suite the objectoriented approach was used.

Results. The algorithms and software suite allows us to easily construct RBD for a technical system, to automatically determine the operability condition with execution time of about 10 sec for 1,000 elements with mixed type of connection, to form automatically a state-and-transition matrix along with the corresponding differential equation system and solve it with total execution time of about 35 sec for 109 states and, thus to obtain the numerical values of reliability indices for the technical system studied. A case study of the reliability assessment for the system consisting of 22 elements using RBD shows that the total time of software execution is 36.712 sec. During executing of this test case the most time (35.168 sec) was spent for execution of the algorithm for construction of a state-and-transition graph consisting of 52,694 states.

Conclusions. The algorithms and methods for automated reliability indices assessment of complex technical systems based on RBD approach, as well as model for estimating the number of total and working system states are presented. The modular structure of the developed software suite makes it flexible and gives an opportunity to add and make modifications of modules fast and without significant program changes.

Author Biographies

V. S. Yakovyna, 1 Lviv Polytechnic National University, Lviv 2 University of Warmia and Mazury in Olsztyn, Poland

1 Dr. Sc., Professor of Artificial Intelligence Department

2 Faculty of Mathematics and Computer Science 

M. M. Seniv, Lviv Polytechnic National University, Lviv

PhD, Associate Professor of Software Department

I. I. Symets, Lviv Polytechnic National University, Lviv

Assistant of Software Department

N. B. Sambir, Lviv Polytechnic National University, Lviv

Assistant of Software Department


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How to Cite

Yakovyna, V. S., Seniv, M. M., Symets, I. I., & Sambir, N. B. (2020). ALGORITHMS AND SOFTWARE SUITE FOR RELIABILITY ASSESSMENT OF COMPLEX TECHNICAL SYSTEMS. Radio Electronics, Computer Science, Control, (4), 163–177.



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