Parallel and \(k\)-out-of-\(n\): \(G\) systems with nonidentical components and their mean residual life functions. (English) Zbl 1168.90399

Summary: A system with \(n\) independent components which has a \(k\)-out-of-\(n: G\) structure operates if at least \(k\) components operate. Parallel systems are 1-out-of-\(n: G\) systems, that is, the system goes out of service when all of its components fail. This paper investigates the mean residual life function of systems with independent and nonidentically distributed components. Some examples related to some lifetime distribution functions are given. We present a numerical example for evaluating the relationship between the mean residual life of the \(k\)-out-of-\(n: G\) system and that of its components.


90B25 Reliability, availability, maintenance, inspection in operations research
62N05 Reliability and life testing
60K10 Applications of renewal theory (reliability, demand theory, etc.)
Full Text: DOI


[1] Khaledi, B.-E.; Shaked, M., Ordering conditional lifetimes of coherent systems, J. stat. planning infer., 137, 1173-1184, (2007) · Zbl 1111.60012
[2] Navarro, J.; Shaked, M., Hazard rate ordering of order statistics and systems, J. appl. prob., 43, 2, 391-408, (2006) · Zbl 1111.62098
[3] Navarro, J.; Eryilmaz, S., Mean residual lifetimes of consecutive k-out-of-n systems, J. appl. prob., 44, 82-98, (2007) · Zbl 1135.62084
[4] Hu, T.; Jin, W.; Khaledi, B.-E., Ordering conditional distributions of generalized order statistics, Prob. eng. inform. sci., 21, 401-417, (2007) · Zbl 1125.60015
[5] Asadi, M.; Bairamov, I., A note on the Mean residual life function of a parallel system, Commun. stat.: theory methods, 34, 2, 475-484, (2005) · Zbl 1062.62228
[6] Asadi, M.; Bairamov, I., The Mean residual life function of a k-out-of-n structure at the system level, IEEE trans. reliab., 55, 2, 314-318, (2006)
[7] Sarhan, A.M.; Abouammoh, A.M., Reliability of k-out-of-n nonrepairable systems with nonindependent components subjected to common shocks, Microelectron. reliab., 41, 617-621, (2001)
[8] Li, X.; Chen, J., Aging properties of the residual life length of k-out-of-n systems with independent but nonidentical components, Appl. stochastic mod. business ind., 20, 143-153, (2004) · Zbl 1060.62115
[9] MacDonald, I.G., Symmetric functions and Hall polynomials, (1979), Springer Berlin, pp. 12-13 · Zbl 0487.20007
[10] Oruç, H.; Akmaz, H.K., Symmetric functions and the Vandermonde matrix, J. comput. appl. math., 172, 49-64, (2004) · Zbl 1063.15023
[11] Vaughan, R.J.; Venables, W.N., Permanent expressions for order statistics densities, J. royal stat. soc. B, 34, 2, 308-310, (1972) · Zbl 0239.62038
[12] Bapat, R.B.; Beg, M.I., Order statistics for nonidentically distributed variables and permanents, Sankhya: Indian J. stat., 51, Ser. A, 79-93, (1989) · Zbl 0672.62060
[13] David, H.A., Order statistics, (1981), John Wiley and Sons New York, p. 22 · Zbl 0223.62057
[14] Nelson, W., Applied life data analysis, (1982), John Wiley and Sons New York, pp. 166-167
[15] J. Navarro, P.J. Hernandez, Mean residual life functions of finite mixtures, order statistics and coherent systems, Metrika, in press, doi:10.1007/s00184-007-0133-8. · Zbl 1357.62304
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.