Reliability Interval Estimation for a System Model with Element Duplication in Different Subsystems

Авторы: Pavlov I.V., Gordeev L.K. Опубликовано: 16.10.2020
Опубликовано в выпуске: #5(92)/2020  
DOI: 10.18698/1812-3368-2020-5-4-13

Раздел: Математика | Рубрика: Вычислительная математика  
Ключевые слова: reliability, system, failure-free operation mean time, confidence boundary, redundancy

The problem was considered of estimating reliability for a complex system model with element duplication of various subsystems and ensuring possibility of additional redundancy in a more flexible dynamic (or 'sliding') mode in each of the subsystems, which significantly increases reliability of the system in general. For the system considered, general model and analytical expressions were obtained in regard to the main reliability indicators, i.e., probability of the system failure-free operation (reliability function) for a given time and mean time of the system failure-free operation. On the basis of these analytical expressions, the lower confidence limit for the system reliability function was found in a situation, where the element reliability parameters were unknown, and only results of testing the system elements for reliability were provided. It was shown that the system resource function was convex in the reliability parameters vector of the system separate elements various types. Based on this, the lower confidence boundary construction for the system reliability function was reduced to the problem of finding the convex function extremum on a confidence set in the system element parameter space. In this case, labor consumption of the corresponding computational procedure increases linearly with an increase in the problem dimension. Numerical examples of calculating the lower confidence boundary for the system reliability function were provided


[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] Lloyd D.K., Lipov M. Reliability: management, methods and mathematics. Prentice-Hall, 1962.

[3] Barlow R., Proschan F. Mathematical theory of reliability. John Wiley & Sons, 1965.

[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. Dokl. Akad. Nauk SSSR, 1966, vol. 169, no. 4, pp. 755--758 (in Russ.).

[6] Pavlov I.V. Eastimating reliability of redundant system from the results of testing its elements. Automat. Remote Control, 2017, vol. 78, no. 3, pp. 507--514. DOI: https://doi.org/10.1134/S0005117917030109

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

[8] 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, no. 3, pp. 239--246. DOI: https://doi.org/10.3103/S1052618816030134

[9] Ramirez-Marqueza J.E., Levitin G. Algorithm for estimating reliability confidence bounds of multi-state systems. Reliab. Eng. Syst. Saf., 2008, vol. 93, iss. 8, pp. 1231--1243. DOI: https://doi.org/10.1016/j.ress.2007.07.003

[10] Hryniewicz O. Confidence bounds for the reliability of a system from subsystem data. RT A, 2010, vol. 1, no. 2, pp. 145--160.

[11] 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 (61), pp. 15--22 (in Russ.). DOI: http://dx.doi.org/10.18698/1812-3368-2015-4-15-22

[12] 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 (80), pp. 37--44 (in Russ.). DOI: http://dx.doi.org/10.18698/1812-3368-2018-5-37-44

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

[14] Lu L., Lewis G. Configuration determination for k-out-of-n partially redundant systems. Reliab. Eng. Syst. Saf., 2008, vol. 93, iss. 11, pp. 1594--1604. DOI: https://doi.org/10.1016/j.ress.2008.02.009

[15] Yeh W.-C. A simple algorithm for evaluating the k-out-of-n network reliability. Reliab. Eng. Syst. Saf., 2004, vol. 83, no. 1, pp. 93--101. DOI: https://doi.org/10.1016/j.ress.2003.09.018

[16] Krishchenko A.P., Zarubin V.S., eds. Matematicheskaya statistika [Mathematical statistics]. Moscow, BMSTU Publ., 2008.

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