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On the Conditional Residual Life and Inactivity Time of Coherent Systems

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  30 January 2018

A. Parvardeh  and
N. Balakrishnan
A. Parvardeh*
Affiliation:
University of Isfahan
N. Balakrishnan*
Affiliation:
McMaster University
*
∗ Postal address: Department of Statistics, University of Isfahan, Isfahan, 81744, Iran.
∗∗ Postal address: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L85 4K1, Canada. Email address: [email protected]
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Abstract

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In this paper we derive mixture representations for the reliability functions of the conditional residual life and inactivity time of a coherent system with n independent and identically distributed components. Based on these mixture representations we carry out stochastic comparisons on the conditional residual life, and the inactivity time of two coherent systems with independent and identical components.

Keywords

Residual lifetimesignatureinactivity timehazard rate orderlikelihood ratio orderreversed hazard rate order

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 4 , December 2014 , pp. 990 - 998
Copyright
© Applied Probability Trust 

References

Barlow, R. E. and Proschan, F. (1975). Statistical Theory of Reliability and Life Testing. Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
Goliforushani, S. and Asadi, M. (2011). Stochastic ordering among inactivity times of coherent systems. Sankhya B 73, 241–262.Google Scholar
Goliforushani, S., Asadi, M. and Balakrishnan, N. (2012). On the residual and inactivity times of the components of used coherent systems. J. Appl. Prob. 49, 385–404.CrossRefGoogle Scholar
Khaledi, B.-E. and Shaked, M. (2007). Ordering conditional lifetimes of coherent systems. J. Statist. Planning Infer. 137, 1173–1184.Google Scholar
Kochar, S., Mukerjee, H. and Samaniego, F. J. (1999). The “signature” of a coherent system and its application to comparisons among systems. Naval. Res. Logistics 46, 507–523.Google Scholar
Li, X. and Zhang, Z. (2008). Some stochastic comparisons of conditional coherent systems. Appl. Stoch. Models Business Industry 24, 541–549.Google Scholar
Li, X. and Zhao, P. (2006). Some aging properties of the residual life of k-out-of-n systems. IEEE Trans. Reliab. 55, 535–541.Google Scholar
Li, X. and 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.CrossRefGoogle Scholar
Nama, M. K. and Asadi, M. (2014). Stochastic properties of components in a used coherent system. Methodol. Comput. Appl. Prob. 16, 675–691.Google Scholar
Navarro, J., Balakrishnan, N. and Samaniego, F. J. (2008). Mixture representations of residual lifetimes of used systems. J. Appl. Prob. 45, 1097–1112.Google Scholar
Navarro, J., Ruiz, J. M. and Sandoval, C. J. (2005). A note on comparisons among coherent systems with dependent components using signatures. Statist. Prob. Lett. 72, 179–185.Google Scholar
Navarro, J., Samaniego, F. J. and Balakrishnan, N. (2013). Mixture representations for the Joint distribution of lifetimes of two coherent systems with shared components. Adv. Appl. Prob. 45, 1011–1027.CrossRefGoogle Scholar
Poursaeed, M. H. and Nematollahi, A. R. (2008). On the mean past and the mean residual life under double monitoring. Commun. Statist. Theory Meth. 37, 1119–1133.Google Scholar
Samaniego, F. J. (1985). On the closure of the IFR class under formation of coherent systems. IEEE Trans. Reliab. 34, 69–72.Google Scholar
Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders. Springer, New York.CrossRefGoogle Scholar
Tavangar, M. and 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.Google Scholar
Zhang, Z. (2010a). Mixture representations of inactivity times of conditional coherent systems and their applications. J. Appl. Prob. 47, 876–885.Google Scholar
Zhang, Z. (2010b). Ordering conditional general coherent systems with exchangeable components. J. Statist. Planning Infer. 140, 454–460.Google Scholar
Zhang, Z. and Li, X. (2010). Some new results on stochastic orders and aging properties of coherent systems. IEEE Trans. Reliab. 59, 718–724.CrossRefGoogle Scholar
Zhang, Z. and Meeker, W. Q. (2013). Mixture representations of reliability in coherent systems and preservation results under double monitoring. Commun. Statist. Theory Meth. 42, 385–397.CrossRefGoogle Scholar
Zhang, Z. and Yang, Y. (2010). Ordered properties on the residual life and inactivity time of (n-k+1)-out-of-n systems under double monitoring. Statist. Prob. Lett. 80, 711–717.Google Scholar