Имитационное моделирование неоднородного процесса деградации в системе с постепенными и внезапными отказами
Аннотация
В работе рассматривается неоднородный процесс деградации системы с постепенными и внезапными отказами. Для случая, когда времена пребывания на стадиях деградации независимые и распределены экспоненциально с разными параметрами, получены аналитические выражения для вероятности внезапного отказа на цикле регенерации,
среднего времени до отказа на цикле, среднего длины цикла с отказом и без, средней общей длины цикла. Для случая произвольных распределений и высоконадежных систем, когда отказ является редким событием, предложен имитационный алгоритм на основе техники расщепления для ускоренного построения циклов регенерации.
Представлены результаты экспериментов, полученные методом расщепления и стандартным методом Монте-Карло,
для экспоненциальных стадий деградации проведено сравнение со значениеми по формулам.
Ключевые слова
Полный текст:
PDFЛитература
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Lisnuansky A., Levitin G. Multi-state system reliability: assessment, optimization and application. New Jersey, London, Singapore, Hong-Kong: World Scientific 2003. doi: 10.1142/5221
Morozov E., Aminova I. Steady-state simulation of some weak regenerative networks, European Transa
tions on Telecommunications ETT, Vol. 13, No. 4, July/August, 2002, pp. 409-418. doi: 10.1002/ett.4460130412
Rubinstein R. Y., Kroese D. P. Simulation and the Monte Carlo method.
John Wiley & Sons, Inc., Hoboken, New Jersey, 2016. 396 p. doi: 10.1002/9781118631980
Rykov V., Dimitrov B. On multi-state reliability systems. Proc. of Seminar Applied Stochastic Models and Information Processes, 2002, 128-135.
Rubinstein_2014 Rubinstein R. Y., Ridder A., Vaisman R. Fast Sequential Monte Carlo Methods for Counting and Optimization.
John Wiley & Sons, Inc., Hoboken, New Jersey. 2014. 208 p. doi: 10.1002/9781118612323
Vaisman R., Roughan M., Kroese D.P. The multilevel splitting algorithm for graph coloring with application to the Potts model. Philosophical Magazine. 2017. doi:10.1080/14786435.2017.1312023
Vill'en Altamirano J. RESTART Vs Splitting: A Comparative
Study. Proceedings of the 11th Workshop on Rare Event Simulation,
RESIM’16, Eindhoven (The Netherlands), 2017, pp. 1-12. doi: 10.1016/j.peva.2018.02.002
REFERENCES in ENGLISH
Shiryaev A. N. Veroyatnost [Probability]. Moscow: Nauka. 1980.
Bibinger M. Notes on the sum and maximum of independent exponentially distributed random variables with different scale parameters.
arXiv preprint arXiv:1307.3945, 2013.
Botev Z. I., Kroese D. P. Efficient Monte Carlo simulation via the
generalized splitting method //Statistics and Computing. – 2012. – Т. 22. – №. 1. – С. 1-16. doi: 10.1007/s11222-010-9201-4
Borodina A. V. PhD Thesis. Regenerative modification of the splitting method for estimating the overload probability
in queuing systems, Petrozavodsk State University, 2008. (in russian)
Borodina A. V., Efrosinin D. V., Morozov E. V. Application of Splitting to Failure Estimation in Controllable Degradation System. In: Vishnevskiy V., Samouylov K., Kozyrev D. (eds) Distributed Computer and Communication Networks. DCCN 2017. Communications in Computer and Information Science, Springer, Cham, vol 700, pp. 217-230, 2017. ISBN 978-3-319-66836-9, doi: 10.1007/978-3-319-66836-9
han J.C.C., Kroese D.P. Rare-event probability estimation with conditional Monte Carlo. Ann Oper Res (2011) 189: 43. doi:10.1007/s10479-009-0539-y
Efrosinin D. V., Farhadov M. P. Optimal management of the system with the gradual and instantaneous failures.
Dependability. 2009. No. 1 (28). PP. 27-42.(in Russian)
Ferguson T. S. A course in large sample theory. Chapman and Hall/CRC Texts in Statistical Science, 1996.
Garvels M. PhD Thesis.
The splitting method in rare event simulation, The University of Twente,
The Netherlands May, 2000.
Glynn P. W. Some topics in regenerative steady state
simulation. Acta Applic. Math. 34, 1994, 225-236. doi: 10.1007/BF00994267
Glynn P. W., Iglehart D. L. Conditions for the applicability
of the regenerative method. Management Science 39, 1993, 1108-1111. doi: 10.1287/mnsc.39.9.1108
Glynn P. W., Iglehart D. L. A joint central limit
theorem for the sample mean and regenerative variance estimator. Annals of
Operations Research 8, 1987, 41-55. doi: 10.1007/BF02187081
Heegaard P. E. A survey of Speedup simulation
techniques. Workshop tutorial on Rare Event Simulation, Aachen, Germany, 1997.
Heidelberger P. Fast simulation of rare events in queuieng and relaibility
models, Performance Evaluation of Computers and Communications Systems
Springer-Verlag, LN in Computer Sci., v. 729, 1993, 165-202.
Lisnuansky A., Levitin G. Multi-state system reliability: assessment, optimization and application. New Jersey, London, Singapore, Hong-Kong: World Scientific 2003. doi: 10.1142/5221
Morozov E., Aminova I. Steady-state simulation of some weak regenerative networks, European Transa
tions on Telecommunications ETT, Vol. 13, No. 4, July/August, 2002, pp. 409-418. doi: 10.1002/ett.4460130412
Rubinstein R. Y., Kroese D. P. Simulation and the Monte Carlo method.
John Wiley & Sons, Inc., Hoboken, New Jersey, 2016. 396 p. doi: 10.1002/9781118631980
Rykov V., Dimitrov B. On multi-state reliability systems. Proc. of Seminar Applied Stochastic Models and Information Processes, 2002, 128-135.
Rubinstein_2014 Rubinstein R. Y., Ridder A., Vaisman R. Fast Sequential Monte Carlo Methods for Counting and Optimization.
John Wiley & Sons, Inc., Hoboken, New Jersey. 2014. 208 p. doi: 10.1002/9781118612323
Vaisman R., Roughan M., Kroese D.P. The multilevel splitting algorithm for graph coloring with application to the Potts model. Philosophical Magazine. 2017. doi:10.1080/14786435.2017.1312023
Vill'en Altamirano J. RESTART Vs Splitting: A Comparative
Study. Proceedings of the 11th Workshop on Rare Event Simulation,
RESIM’16, Eindhoven (The Netherlands), 2017, pp. 1-12. doi: 10.1016/j.peva.2018.02.002
DOI: http://dx.doi.org/10.17076/mat836
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