## A note on the mean residual life function of a coherent system with exchangeable or nonidentical components.(English)Zbl 1216.62158

Summary: This article investigates some properties of the mean residual life function of $$(n-k+1)$$-out-of-$$n$$ systems, when the lifetimes of the system components are independent random variables but not necessarily identically distributed and when the joint distribution of the component life times is exchangeable, extending results of M. Asadi and S. Goliforushani [On the mean residual life function of coherent systems. IEEE Transact. Reliab. 57, No. 4, 574–580 (2008)] for the case of independent and identically distributed components. The extension to a coherent system with exchangeable components is also given.

### MSC:

 62N05 Reliability and life testing 60K10 Applications of renewal theory (reliability, demand theory, etc.)
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### References:

 [1] Asadi, M.; Goliforushani, S., On the Mean residual life function of coherent systems, IEEE transactions on reliability, 57, 4, 574-580, (2008) · Zbl 1433.62291 [2] Barlow, R.E.; Proschan, F., Statistical theory of reliability and life testing, (1975), Holt, Rinehart and Wineston New York · Zbl 0379.62080 [3] David, H.; Nagaraja, H.N., Order statistics, (2003), John Wiley and Sons · Zbl 1053.62060 [4] Gurler, S.; Bairamov, I., Parallel and k-out-of-n:G systems with nonidentical components and their Mean residual life functions, Applied mathematical modelling, 33, 1116-1125, (2009) · Zbl 1168.90399 [5] Khaledi, B.; Shaked, M., Ordering conditional lifetimes of coherent systems, Journal of statistical planning and inference, 137, 4, 1173-1184, (2007) · Zbl 1111.60012 [6] Khanjari, S.M., Mean past and Mean residual life functions of a parallel system with nonidentical components, Communications in statistics: theory and methods, 37, 1134-1145, (2008) · Zbl 1138.62065 [7] Kochar, S.C.; Mukherjee, H.; Samaniego, F.J., The signature of a coherent system and its application to comparisons among systems, Naval research logistics, 46, 507-523, (1999) · Zbl 0948.90067 [8] Kochar, S.C.; Xu, M., On residual lifetimes of k-out-of-n systems with nonidentical components, Probability in engineering and informational sciences, 24, 109-127, (2010) · Zbl 1190.90060 [9] Li, X.; Zhang, Z., Some stochastic comparisons of conditional coherent systems, Journal of applied stochastic models in business and industry, 24, 541-549, (2008) · Zbl 1198.62147 [10] Navarro, J.; Balakrishnan, N.; Samaniego, F.J., Mixture representations of residual lifetimes of used systems, Journal of applied probability, 45, 4, 1097-1112, (2008) · Zbl 1155.60305 [11] 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 [12] Navarro, J.; Ruiz, J.M.; Sandoval, C.J., A note on comparisons among coherent systems with dependent components using signature, Statistics and probability letters, 72, 179-185, (2005) · Zbl 1068.60026 [13] Navarro, J.; Ruiz, J.M.; Sandoval, C.J., Properties of coherent systems with dependent components, Communications in statistics, theory and methods, 36, 175-191, (2007) · Zbl 1121.60015 [14] Navarro, J.; Samaniego, F.J.; Balakrishnan, N.; Bhattacharya, D., On the application and extension of system signatures in engineering reliability, Naval research logistics, 55, 313-327, (2008) · Zbl 1153.90386 [15] Samaniego, F.J., On the closure of the IFR class under formation of coherent systems, IEEE transactions on reliability, 34, 69-72, (1985) · Zbl 0585.62169 [16] Samaniego, F.J.; Balakrishnan, N.; Navarro, J., Dynamic signatures and their use in comparing the reliability of new and used systems, Naval research logistics, 56, 577-591, (2009) · Zbl 1182.90036 [17] Zhang, Z., Ordering conditional general coherent systems with exchangeable components, Journal of statistical planning and inference, 140, 454-460, (2010) · Zbl 1229.62137
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