Abstract
Some coherent systems are such that failure of the system does not mean that all components fail. This paper investigates the stochastic behavior and reliability properties of the residual lifetime of live components in coherent systems under the assumption that the system fails at time t. We also investigate the stochastic properties of inactivity time of failed components in coherent systems where failure of some components does not cause the failure of the complete system.
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References
Asadi M (2006) On the mean past lifetime of the components of a parallel system. J Stat Plann Inference 136:1197–1206
Asadi M, Asadi AR (2012) On the failure probability of an operating coherent system. Submitted for publication
Asadi M, Bayramoglu I (2006) The mean residual life function of a k-out-of-n structure at the system level. IEEE Trans Reliab 55:314–318
Balakrishnan N, Asadi M (2011) Proposed measure of residual life of live components of a coherent system. IEEE Trans Reliab 61:41–49
Barlow RE, Proschan F (1975) Statistical theory of reliability and life testing. Holt, Rinehart, Winston, New York
Goliforushani S, Asadi M (2011) Stochastic ordering among inactivity times of coherent systems. Sankhya B. doi:10.1007/s13571-011-0028-6
Goliforushani S, Asadi M, Balakrishnan N (2012) On the residual and inactivity times of the components of used coherent systems. J Appl Probab 49:385–404
Khaledi BE, Shaked M (2007) Ordering conditional lifetimes of coherent systems. J Stat Plan Inference 137:1173–1184
Kochar S, Mukerjee H, Samaniego FJ (1999) The “signature” of a coherent system and its application to comparison among systems. Nav Res Logist 46:507–523
Li X, Zhang Z (2008) Some stochastic comparisons of conditional coherent systems. Appl Stoch Models Bus Ind 24:541–549
Li X, Zhao P (2008) Stochastic comparison on general inactivity time and general residual life of k-out-of-n systems. Commun Stat Simul Comput 37:1005–1019
Mahmoudi M, and Asadi M (2011) On the conditional signature of coherent systems. IEEE Trans Reliab 60:817–822
Meserve BE (1982) Fundamental concepts of algebra. Dover Publications, New York
Navarro J, Ruiz JM, Sandoval CJ (2005) A note on comparisons among coherent systems with dependent components using signatures. Stat Probab Lett 72:179–185
Navarro J, Belzunce F, Ruiz M (1997) New stochastic orders based on double truncation. Probab Eng Inf Sci 11:395–402
Navarro J, Balakrishnan N, Samaniego FJ (2008a) Mixture representations of residual lifetimes of used systems. J Appl Probab 45:1097–1112
Navarro J, Samaniego FJ, Balakrishnan N, Bhattacharya D (2008b) On the applications and extension of system signatures in engineering reliability. Nav Res Logist 55:313–327
Samaniego FJ (1985) On closure of the IFR class under formation of coherent systems. IEEE Trans Reliab 34:69–72
Samaniego FJ (2007) System signatures and their applications in engineering reliability. Springer, New York
Shaked M, Shanthikumar JG (2007) Stochastic orders. Springer, New York
Tavangar M, Asadi M (2010) A study on the mean past lifetime of the components of (n − k + 1)-out-of-n system at the system level. Metrika 72:59–73
Zhang Z (2010a) Ordering conditional general coherent systems with exchangeable components. J Stat Plan Inference 140:454–460
Zhang Z (2010b) Mixture representations of inactivity times of conditional coherent systems and their applications. J Appl Probab 47:876–885
Zhang Z, Li X (2010) Some new results on stochastic orders and aging properties of coherent systems. IEEE Trans Reliab 59:718–724
Zhang Z, Yang Y (2010) Ordered properties of the residual lifetime and inactivity time of (n − k + 1)-out-of-n systems under double monitoring. Stat Probab Lett 80:711–717
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Nama, M.K., Asadi, M. Stochastic Properties of Components in a Used Coherent System. Methodol Comput Appl Probab 16, 675–691 (2014). https://doi.org/10.1007/s11009-013-9322-2
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DOI: https://doi.org/10.1007/s11009-013-9322-2