# Modeling the influence of short-term mode of component for non reserved system on its reliability

2019;
: 66-72
1
Lviv Polytechnic National University
2
Lviv Polytechnic National University

Aim. To develop an approach for adequately formalizing and calculating reliability using a dynamic fault tree for a two-component system as an example, taking into account the short-term mode of operation of one of the system component. Method. A k-terminal dynamic fault tree is used to formalize reliability. In this tree, the structure and behavior of the system are separated. On the basis of the tree the diagram of states and transitions of the system is developed. The calculations are performed using a Markov model and on the basis Monte-Carlo simulation. Results. In the example of a two-element system that is connected in series, a k-terminal dynamic failure tree is developed. Such tree adequately describes the failure condition of the system, as well as the state of the cycle of short-term mode of operation of one of the system component. A dynamic link is specified in the tree that binds the short-term mode parameters to the specified structural component. A graph of a system containing 6 states and 6 transitions is formed and a table describing the state and transition parameters is presented. In the diagram, the inoperable states are grouped into sets of system failure causes. The probabilistic characteristics of the mathematical model are calculated in two ways. If the parameters of the short-term mode are probabilistic, then the Markov model is used. Monte Carlo simulation was used for the case of deterministic parameters of short-term mode. It is shown that the failure density function has clearly described peaks at moments of increased wear for the determined duration of the short-term mode phases. Scientific novelty. Improved approach based on the use of k-terminal dynamic failure trees to model the reliability of systems with series-connected components that function in short-term modes. Practical significance. The proposed approach can be used to evaluate the reliability when designing systems with nodes that operate in short-term modes. The results obtained are a mathematical basis for the analysis of short-term modes of operation in systems with complex structures.

1  Z. Zhou and Q. Zhang, "Model Event/Fault Trees With Dynamic Uncertain Causality Graph for Better Probabilistic Safety Assessment," in IEEE Transactions on Reliability, vol. 66, no. 1, pp. 178-188, March 2017.
https://doi.org/10.1109/TR.2017.2647845
2 M. Volk, S. Junges and J. Katoen, "Fast Dynamic Fault Tree Analysis by Model Checking Techniques," in IEEE Transactions on Industrial Informatics, vol. 14, no. 1, pp. 370-379, Jan. 2018.
https://doi.org/10.1109/TII.2017.2710316
3 M. Ammar, G. Bany Hamad, O. Ait Mohamed and Y. Savaria, "Towards an Accurate Probabilistic Modeling and Statistical Analysis of Temporal Faults via Temporal Dynamic Fault-Trees (TDFTs)," in IEEE Access, vol. 7, pp. 29264-29276, 2019.
https://doi.org/10.1109/ACCESS.2019.2902796
4 Z. Zeng and E. Zio, "Dynamic Risk Assessment Based on Statistical Failure Data and Condition-Monitoring Degradation Data," in IEEE Transactions on Reliability, vol. 67, no. 2, pp. 609-622, June 2018.
https://doi.org/10.1109/TR.2017.2778804
5 B. Liu and L. Cai, "Monte Carlo Reliability Model for Single-Event Transient on Combinational Circuits," in IEEE Transactions on Nuclear Science, vol. 64, no. 12, pp. 2933-2937, Dec. 2017. doi: 10.1109/TNS.2017.2772267.
https://doi.org/10.1109/TNS.2017.2772267