On the mean residual life of a \(k\)-out-of-\(n:G\) system with a single cold standby component. (English) Zbl 1253.90089
Summary: The concept of mean residual life is one of the most important characteristics that has been widely used in dynamic reliability analysis. It is a useful tool for investigating ageing properties of technical systems. In this paper, we define and study three different mean residual life functions for \(k\)-out-of-\(n:G\) system with a single cold standby component. In particular, we obtain explicit expressions for the corresponding functions using distributions of order statistics. We also provide some stochastic ordering results associated with the lifetime of a system. We illustrate the results for various lifetime distributions.
MSC:
| 90B25 | Reliability, availability, maintenance, inspection in operations research |
| 62N05 | Reliability and life testing |
| 60E15 | Inequalities; stochastic orderings |
References:
| [1] | Asadi, M.; Bayramoglu, I., The mean residual life function of \(k\)-out-of-\(n\) structure at the system level, IEEE Transactions on Reliability, 55, 314-318 (2006) |
| [2] | Bairamov, I.; Arnold, B., On the residual life lengths of the remaining components in an \(n\)−\(k+1\) out of \(n\) system, Statistics and Probability Letters, 78, 945-952 (2008) · Zbl 1141.62081 |
| [3] | David, H.A., Nagaraja, H.N., 2003. Order Statistics. Wiley Series in Probability and Statistics.; David, H.A., Nagaraja, H.N., 2003. Order Statistics. Wiley Series in Probability and Statistics. · Zbl 1053.62060 |
| [4] | Eryilmaz, S., Dynamic behavior of \(k\)-out-of-\(n\):G systems, Operations Research Letters, 39, 155-159 (2011) · Zbl 1219.93066 |
| [5] | Esary, J. D.; Marshall, A. W., Coherent life functions, SIAM Journal of Applied Mathematics, 18, 810-814 (1970) · Zbl 0198.24804 |
| [6] | Kochar, S., On stochastic orderings between distributions and their sample spacings, Statistics and Probability Letters, 42, 345-352 (1999) · Zbl 0956.62044 |
| [7] | Leung, K. N.F.; Zhang, Y. L.; Lai, K. K., Analysis for a two-dissimilar-component cold standby repairable system with repair priority, Reliability Engineering and System Safety, 96, 1542-1551 (2011) |
| [8] | Mahmoud, M. A.W.; Moshref, M. E., On a two unit cold standby system considering hardware, human error failures and preventive maintanence, Mathematical and Computer Modelling, 51, 736-745 (2010) · Zbl 1190.90061 |
| [9] | Navarro, J.; Hernandez, P. J., Mean residual life functions of finite mixtures, order statistics and coherent systems, Metrika, 67, 277-298 (2008) · Zbl 1357.62304 |
| [10] | Navarro, J.; Rychlik, T., Comparisons and bounds for expected lifetimes of reliability systems, European Journal of Operational Research, 207, 309-317 (2010) · Zbl 1217.62155 |
| [11] | Pandey, D.; Jacob, M.; Yadav, J., Reliability analysis of a powerloom plant with cold standby for its strategic unit, Microelectronics and Reliability, 36, 115-119 (1996) |
| [12] | Papageorgiou, E.; Kokolakis, G., A two unit general parallel system with \((n\)−2) cold standbys – analytic and simulation approach, European Journal of Operational Research, 176, 1016-1032 (2007) · Zbl 1110.90025 |
| [13] | Raqab, M. Z.; Rychlik, T., Bounds for the mean residual life function of a \(k\)-out-of-\(n\) system, Metrika, 74, 361-380 (2011) · Zbl 1226.62100 |
| [14] | Samaniego, F. J., System Signatures and their Applications in Engineering Reliability (2007), Springer: Springer New York · Zbl 1154.62075 |
| [15] | Shaked, M.; Shanthikumar, J. G., Stochastic Orders and their Applications (1994), Springer: Springer New York · Zbl 0806.62009 |
| [16] | Zhang, Y. L.; Wang, G. J., A deteriorating cold standby repairable system with priority in use, European Journal of Operational Research, 183, 278-295 (2007) · Zbl 1127.90334 |
| [17] | Zhang, Z.; Yang, Y., Ordered properties on the residual life and inactivity time of \(k\)-out-of-\(n\) systems under double monitoring, Statistics and Probability Letters, 80, 711-717 (2010) · Zbl 1185.62179 |
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