Skip to main content
Log in

Calculation of the Basic Reliability Parameters for the Model of a System with Dual Redundancy in Different Subsystems

  • RELIABILITY, STRENGTH, AND WEAR RESISTANCE OF MACHINES AND STRUCTURES
  • Published:
Journal of Machinery Manufacture and Reliability Aims and scope Submit manuscript

Abstract

A model of a system with dual (active and standby) redundancy of the components in different subsystems, which significantly enhances its reliability, is considered. The basic formulas have been obtained for the calculation of the reliability function of the system depending on the multiplicity of the active and standby redundancy in the subsystems. The problem of constructing the lower confidence bound for the reliability criterion, which is the probability of the failure-free operation of the system for a preset time, has been considered. Approximate asymptotic expressions, for the case of high reliability, have been obtained for the reliability function of the system and its lower confidence bound.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. Gnedenko, B.V., Belyaev, Yu.K., and Solov’ev, A.D., Matematicheskie metody v teorii nadezhnosti (Mathematical Methods in the Theory of Reliability), Moscow: Kn. Dom Librokom, 2013.

  2. Voprosy matematicheskoi teorii nadezhnosti (Problems of the Mathematical Theory of Reliability), Gnedenko, B.V., Ed., Moscow: Radio i Svyaz’, 1983.

    MATH  Google Scholar 

  3. Barlow, R.E. and Proschan, F., Statistical Theory of Reliability and Life Testing: Probability Models, University of Michigan, 1981.

    MATH  Google Scholar 

  4. Belyaev, Yu.K., Confidence intervals for functions of many unknown parameters, Dokl. Akad. Nauk SSSR, 1967, vol. 196, no. 4, p. 755.

    Google Scholar 

  5. Belyaev, Yu.K., Dulina, T.N., and Chepurin, E.V., Calculation of the lower confidence bound for the probability of failure-free operation of complex systems, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1967, no. 2, p. 52.

  6. Pavlov, I.V. and Razgulyaev, S.V., The lower confidence limit for the mean time of failure of a system with recoverable elements, Vestn. Mosk. Gos. Tekh. Univ. im. N. E. Baumana, Ser.: Estestv. Nauki, 2018, no. 5, p. 37.

  7. Sidnyaev, N.I., Mathematical modeling of estimation of the reliability of objects of complex technical systems, Probl. Mashinostr. Nadezhnosti Mash., 2003, no. 4.

  8. Lixuan Lu and Gregory Lewis, Configuration determination for k-out-of-n partially redundant systems, Reliab. Eng. Syst. Saf., 2008, vol. 93, no. 11, p. 1594.

    Article  Google Scholar 

  9. Zuo, M.J. and Zhigang Tian, Performance evaluation of generalized multi-state k-out-of-n systems, IEEE Trans. Reliab., 2006, vol. 55, no. 2, p. 319.

    Article  Google Scholar 

  10. Asadi, M. and Bayramoglu, I., The mean residual life function of a k-out-of-n structure at the system level, IEEE Trans. Reliab., 2006, vol. 55, no. 2, p. 314.

    Article  Google Scholar 

  11. Mann, N.R., Schafer, R.E., and Singpurwalla, N.D., Methods for Statistical Analysis of Reliability and Life Data, Wiley, 1974.

    MATH  Google Scholar 

  12. Pavlov, I.V. and Razgulyaev, S.V., Reliability assessment for a system with loaded reservation and recovery based on the results of testing its elements, J. Mach. Manuf. Reliab., 2018, vol. 47, pp. 368–372.

    Article  Google Scholar 

  13. Pavlov, I.V. and Razgulyaev, S.V., Asymptotic estimates of the reliability of a system with redundancy by different types of elements, Inzh. Zh.: Nauka Innovatsii, 2015, vol. 2, no. 38. http://engjournal.ru/articles/1365/1365.pdf.

  14. Pavlov, I.V., Estimating reliability of redundant system from the results of testing its elements, Autom. Remote Control, 2017, vol. 78, pp. 507–514.

    Article  MathSciNet  Google Scholar 

  15. Wei-Chang Yeh, A simple algorithm for evaluating the k-out-of-n network reliability, Reliab. Eng. Syst. Saf., 2004, vol. 83, no. 1, p. 93.

    Article  Google Scholar 

  16. Barlow, R.E. and Proschan, F., Mathematical Theory of Reliability, Wiley, 1965.

    MATH  Google Scholar 

  17. Zangwill, W.I., Nonlinear Programming: A Unified Approach, Prentice-Hall, 1969.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to I. V. Pavlov or S. V. Razgulyaev.

Ethics declarations

The authors declare no conflict of interest.

Additional information

Translated by O. Lotova

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pavlov, I.V., Razgulyaev, S.V. Calculation of the Basic Reliability Parameters for the Model of a System with Dual Redundancy in Different Subsystems. J. Mach. Manuf. Reliab. 49, 829–835 (2020). https://doi.org/10.3103/S1052618820100076

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1052618820100076

Keywords:

Navigation