Estimated Guaranteed Life for a System Model with Redundancy of Heterogeneous Elements

Authors: Pavlov I.V., Razgulyaev S.V. Published: 06.12.2019
Published in issue: #6(87)/2019  
DOI: 10.18698/1812-3368-2019-6-4-17

Category: Mathematics | Chapter: Computational Mathematics  
Keywords: guaranteed life, model, system, redundancy, reliability, gamma-percentile resource, asymptotic expressions

The paper focuses on the problem of confidence estimation of reliability indicators for a system model with loaded redundancy of elements of various sub-systems. The lower confidence limits are constructed for the system reliability function, as well as for the indicator associated with it, the indicator having a given guaranteed level of the system uptime, i.e., its gamma-percentile life. Within the research, we obtained approximate asymptotic --- for the case of high reliability --- expressions for confidence estimates of these basic indicators of system reliability. Rather simple approximate analytical calculation formulas based on these asymptotic expressions are given for the lower confidence boundary of the system reliability function and a similar confidence boundary for the guaranteed system life


[1] Gnedenko B.V., Belyaev Yu.K., Solovyev A.D. Matematicheskie metody v teorii nadezhnosti [Mathematical methods in reliability theory]. Moscow, Librokom Publ., 2013.

[2] Gnedenko B.V., ed. Voprosy matematicheskoy teorii nadezhnosti [Problems of reliability theory]. Moscow, Radio i svyaz Publ., 1983.

[3] Barlow R.E., Proschan F. Statistical theory of reliability and life testing probability models. Holt, Rinehart and Winston, 1975.

[4] Gnedenko B.V., Pavlov I.V., Ushakov I.A. Statistical reliability engineering. John Wiley & Sons, 1999.

[5] Belyaev Yu.K. Confidence intervals for functions of several unknown parameters. Doklady AN SSSR, 1967, vol. 169, no. 4, pp. 755--758 (in Russ.).

[6] Pavlov I.V. Confidence limits for system reliability indices with increasing function of failure intensity. J. Mach. Manuf. Reliab., 2017, vol. 46, iss. 2, pp. 149--153. DOI: https://doi.org/10.3103/S1052618817020133

[7] Pavlov I.V., Razgulyaev S.V. Confidence interval calculations for the system availability index with recoverable components. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2015, no. 4, pp. 15--22 (in Russ.). DOI: 10.18698/1812-3368-2015-4-15-22

[8] Pavlov I.V., Razgulyaev S.V. Confidence estimation of reliability indices of the system with elements duplication and recovery. Matematika i matematicheskoe modelirovanie [Mathematics and Mathematical Modeling], 2017, no. 6, pp. 32--39 (in Russ.). DOI: 10.24108/mathm.0617.0000088

[9] Pavlov I.V., Razgulyaev S.V. Lower confidence limit for mean time between failures in a system featuring repairable components. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2018, no. 5, pp. 37--44 (in Russ.). DOI: 10.18698/1812-3368-2018-5-37-44

[10] Sidnyaev N.I. Mathematical modeling for reliability assessment of complex technical systems. Problemy mashinostroeniya i nadezhnosti mashin, 2003, no. 4, pp. 24--31 (in Russ.).

[11] Sadykhov G.S., Babaev I.A. Computations of the least number of objects necessary for the cyclical reliability testing. J. Mach. Manuf. Reliab., 2016, vol. 45, iss. 3, pp. 239--246. DOI: https://doi.org/10.3103/S1052618816030134

[12] Zuo M.J., Zhigang T. Performance evaluation of generalized multi-state k-out-of-n systems. IEEE Trans. Rel., 2006, vol. 55, iss. 2, pp. 319--327. DOI: https://doi.org/10.1109/TR.2006.874916

[13] Asadi M., Bayramoglu I. The mean residual life function of a k-out-of-n structure at the system level. IEEE Trans. Rel., 2006, vol. 55, iss. 2, pp. 314--318. DOI: https://doi.org/10.1109/TR.2006.874934

[14] Pavlov I.V., Razgulyaev S.V. Reliability asymptotic estimates of a system with redundant heterogeneous elements. Inzhenernyy zhurnal: nauka i innovatsii [Engineering Journal: Science and Innovation], 2015, no. 2 (in Russ.). DOI: https://doi.org/10.18698/2308-6033-2015-2-1365

[15] Pavlov I.V. Estimating reliability of redundant system from the results of testing its elements. Autom. Remote Control, 2017, vol. 78, iss. 3, pp. 507--514. DOI: https://doi.org/10.1134/S0005117917030109

[16] Goryainov V.B., Pavlov I.V., Tsvetkova G.M., et al. Matematicheskaya statistika [Mathematical statistics]. Moscow, BMSTU Publ., 2008.

[17] Zangwill W.I. Nonlinear programming: a unified approach. Prentice-Hall, 1969.