DOI: https://doi.org/10.15588/1607-3274-2020-4-16

### ALGORITHMS AND SOFTWARE SUITE FOR RELIABILITY ASSESSMENT OF COMPLEX TECHNICAL SYSTEMS

#### Abstract

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.

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PDF#### References

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Seniv M., Yakovyna V., Symets I. Software for visualization of reliability block diagram and automated formulation of operability conditions of technical systems, Perspective Technologies and Methods in MEMS design MEMSTECH’2018 : ХІV International Conference, Lviv-Polyana, 18–22 April 2018 : proceedings. Lviv, IEEE, 2018. pp. 191–195. doi : 10.1109/MEMSTECH.2018.8365731

#### GOST Style Citations

1. Pham H. System software reliability / H. Pham. – London : Springer, 2006. – 440 p. doi : 10.1007/1-84628-295-0

2. Fowler K. Dependability [reliability] / K. Fowler // IEEE Instrumentation & Measurement Magazine. – 2005. – Volume 8, Issue 4. – P. 55–58. DOI: 10.1109/MIM.2005.1518623

3. Mulyak A. Influence of software reliability models on reliability measures of software and hardware systems / A. Mulyak, V. Yakovyna, B. Volochiy // Eastern-European Journal of Enterprise Technologies. – 2015. – Volume 4, Issue 9. – P. 53– 57. DOI : 10.15587/1729-4061.2015.47336

4. Catelani M. A simplified procedure for the analysis of Safety Instrumented Systems in the process industry application / M. Catelani, L. Ciani, V. Luongo // Microelectronics Reliability. – 2011. – Volume 51, Issues 9–11. – P. 1503–1507. DOI : 10.1016/j.microrel.2011.07.044

5. Haxthausen A. E. A Domain-Specific Framework for Automated Construction and Verification of Railway Control Systems / A. E. Haxthausen // Computer Safety, Reliability, and Security : International conference SAFECOMP 2009, Hamburg, 15–18 September 2009 : proceedings. – Berlin : Springer, 2009. – P. 1–3. DOI : 10.1007/978-3-642-04468-7_1

6. Lyu M. R. Software Reliability Engineering: A Roadmap / M. R. Lyu // Future of Software Engineering (FOSE’07), Minneapolis, 23–25 May 2007 : proceedings. – Minneapolis : IEEE, 2007. – Р. 153–170. DOI : 10.1109/FOSE.2007.24

7. Catelani M. Improved RBD analysis for reliability assessment in industrial application / M. Catelani, L. Ciani, M. Venzi // International Instrumentation and Measurement Technology (I2MTC) : 2014 IEEE Conference, Montevideo, 12–15 May 2014 : proceedings. – Montevideo : IEEE, 2014. – P. 670–674. DOI : 10.1109/I2MTC.2014.6860827

8. Pérez-Rosés H. Sixty Years of Network Reliability / H. PérezRosés // Mathematics in Computer Science. – 2018. – Volume 12, Issue 3. – P. 275–293. doi : 10.1007/s11786-018-0345-5

9. Brown J. I. The average reliability of a graph / J. I. Brown, D. Cox, R. Ehrenborg // Discrete Applied Mathematics. – 2014. – Volume 177. – P. 19–33. DOI : 10.1016/j.dam.2014.05.048

10. Sahinoglu M. RBD tools using compression, decompression, hybrid techniques to code, decode, and compute reliability in simple and complex embedded systems / M. Sahinoglu, C. V. Ramamoorthy // IEEE Transactions on Instrumentation and Measurement. – 2005. – Volume 54, Issue 5. – P. 1789–1799. doi: 10.1109/TIM.2005.855103

11. Bennetts R. G. Analysis of Reliability Block Diagrams by Boolean Techniques / R.G. Bennetts // IEEE transactions on reliability. – 1982. – Volume R-31, Issue 2. – P. 159–166. doi : 10.1109/TR.1982.5221283

12. Catelani M. Reliability assessment for complex systems: A new approach based on RBD models / M. Catelani, L. Ciani, M. Venzi // Systems Engineering (ISSE) : 2015 IEEE International Symposium, Rome, 28–30 September 2015 : proceedings. – Rome : IEEE, 2015. – P. 286–290. DOI : 10.1109/SysEng.2015.7302771

13. A Practical Analytical Approach to Increase Confidence in PLD-Based Systems Safety Analysis / [A. V. da Silva Neto, L. F. Vismari, R. A. V. Gimenes et al.] // IEEE Systems Journal. – 2018. – Volume 12, Issue 4. – P. 3473–3484. doi : 10.1109/JSYST.2017.2726178

14. Redundancy allocation for series-parallel warm-standby systems / [O. Tannous, L. Xing, P. Rui et al.] // Industrial Engineering and Engineering Management : 2011 IEEE International Conference, Singapore, 6–9 December 2011 : proceedings. – Singapore : IEEE, 2011. – P. 1261–1265, doi: 10.1109/IEEM.2011.6118118

15. Synthesis of Neurocontroller for Intellectualization Tasks of Process Control Systems / [T. Teslyuk, V. Teslyuk, P. Denysyuk et al.] // The Experience of Designing and Application of CAD Systems (CADSM) : 2019 IEEE 15th International Conference, Polyana, 26 February – 2 March 2019 : proceedings. – Lviv : IEEE, 2019. – P. 1–4. DOI : 10.1109/CADSM.2019.8779295

16. Catelani M. A new proposal for the analysis of safety instrumented systems / M. Catelani, L. Ciani, V. Luongo // Instrumentation and Measurement Technology : 2012 IEEE International Conference, Graz, 13–16 May 2012 : proceedings. – Graz : IEEE, 2012. – P. 1612–1616. DOI : 10.1109/I2MTC.2012.6229556

17. Method of Reliability Block Diagram Visualization and Automated Construction of Technical System Operability Condition / [Yu. Ya. Bobalo, M. M. Seniv, V. S. Yakovyna et al.] // Advances in Intelligent Systems and Computing III. – 2019. – Volume 871. – P. 599–610. DOI : 10.1007/978-3-030-010690_43

18. Technique of automated construction of states and transitions graph for the analysis of technical systems reliability / [Yu. Bobalo, V. Yakovyna, M. Seniv et al.] // Computer Science and Information Technologies CSIT-2018 : XIII International Scientific and Technical Conference, Lviv, 11–14 September 2018 : proceedings. – Lviv : IEEE, 2018. – P. 314–317. DOI : 10.1109/STC-CSIT.2018.8526698

19. Techniques of automated processing of Kolmogorov – Chapman differential equation system for reliability analysis of technical systems / [Yu. Bobalo, V. Yakovyna, M. Seniv et al.] // The Experience of Designing and Application of CAD Systems (CADSM) : 2019 IEEE 15th International Conference, Polyana, 26 February – 2 March 2019 : proceedings. – Lviv : IEEE, 2019. – P. 267–272. DOI : 10.1109/CADSM.2019.8779271

20. Seniv M. Software for visualization of reliability block diagram and automated formulation of operability conditions of technical systems / M. Seniv, V. Yakovyna, I. Symets // Perspective Technologies and Methods in MEMS design MEMSTECH’2018 : ХІV International Conference, LvivPolyana, 18–22 April 2018 : proceedings. – Lviv : IEEE, 2018. – P. 191–195. DOI : 10.1109/MEMSTECH.2018.8365731

Copyright (c) 2020 V. S. Yakovyna, M. M. Seniv, I. I. Symets, N. B. Sambir

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