Reliability model developing for protective fittings taking into account load-sharing effect




protective fittings, reliability model, fault tree, Markov model, failure cause


The mathematical reliability model of protective fittings for the pressure vessel was developed in the paper. The model is intended for the quantitative analysis of the system failure causes. System reliability was formalized by a dynamic fault tree with the set logical conditions of load sharing. Reliability characteristics were calculated based on the split homogeneous Markov model. The split Markov model implies that the operating time of the protective fitting components is distributed according to the Weibull law. The scientific value of the model lies in the fact that it takes into account the load-sharing effect in the three-way tap, safety valves and overpressure valve on the system failure probability. The result of the simulation is a family of probabilistic curves, obtained for different values of load-sharing ratios. The dependence of the change in the main cause of the system failure on the change in these ratios was shown.

Author Biographies

Сергій Володимирович Щербовських, Lviv Polytechnic National University Str. Bandera 12, Lviv, Ukraine, 79013

Doctor of technical sciences, senior researcher

DB/TRIKAF research group

Тетяна Олександрівна Стефанович, Lviv Polytechnic National University Str. Bandera 12, Lviv, Ukraine, 79013

Candidate of technical science, Associate professor

Design and Maintenance of Machinery Department


Landucci, G., Necci, A., Antonioni, G., Tugnoli, A., Cozzani, V. (2014). Release of hazardous substances in flood events: Damage model for horizontal cylindrical vessels. Reliability Engineering & System Safety, 132, 125–145. doi: 10.1016/j.ress.2014.07.016

Chookah, M., Nuhi, M., Modarres, M. (2011). A probabilistic physics-of-failure model for prognostic health management of structures subject to pitting and corrosion-fatigue. Reliability Engineering & System Safety, 96 (2), 1601–1610. doi: 10.1016/j.ress.2011.07.007

Khakzad, N., Khan, F., Amyotte, P. (2013). Risk-based design of process systems using discrete-time Bayesian networks. Reliability Engineering & System Safety, 109, 5–17. doi: 10.1016/j.ress.2012.07.009

Codetta-Raiteri, D. (2011). Integrating several formalisms in order to increase Fault Trees' modeling power. Reliability Engineering & System Safety, 96 (5), 534–544. doi: 10.1016/j.ress.2010.12.027

Yeelyong, N., Kwangpil, C., Yutaek, S., Daejun, C. (2014). Risk-based determination of design pressure of LNG fuel storage tanks based on dynamic process simulation combined with Monte Carlo method. Reliability Engineering & System Safety, 129, 76–82. doi: 10.1016/j.ress.2014.04.018

Munoz Zuniga, M., Garnier, J., Remy, E., Rocquigny, E. (2011). Adaptive directional stratification for controlled estimation of the probability of a rare event. Reliability Engineering & System Safety, 96 (12), 1691–1712. doi: 10.1016/j.ress.2011.06.016

Zamalieva, D., Yilmaz, A., Aldemir, T. (2013). A probabilistic model for online scenario labeling in dynamic event tree generation. Reliability Engineering & System Safety, 120, 18–26. doi: 10.1016/j.ress.2013.02.028

Zamalieva, D., Yilmaz, A., Aldemir, T. (2013). Online scenario labeling using a hidden Markov model for assessment of nuclear plant state. Reliability Engineering & System Safety, 110, 1–13. doi: 10.1016/j.ress.2012.09.002

Mandziy, B., Lozynsky, O., Shcherbovskykh, S. (2013). Mathematical model for failure cause analysis of electrical systems with load-sharing redundancy of component. Przeglad Elektrotechniczny, 89 (11), 244–247.

Shcherbovskykh, S., Lozynsky, O., Marushchak, Ya. (2011). Failure intensity determination for system with standby doubling. Przeglad Elektrotechniczny, 87 (5), 160–162.

Shcherbovskykh, S. (2012). Matematichni modeli ta metodi dlya viznachennya harakteristik nadiynosti bahatoterminalnih system iz urahuvannyam pererozpodilu navantazhennya: monohrafiya, Lviv, Vidavnitstvo Lvivska Politehnika, 296.



How to Cite

Щербовських, С. В., & Стефанович, Т. О. (2015). Reliability model developing for protective fittings taking into account load-sharing effect. Eastern-European Journal of Enterprise Technologies, 1(3(73), 37–44.



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