Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-24T03:52:56.272Z Has data issue: false hasContentIssue false
  • English
  • Français

Component importance in coherent systems with exchangeable components

Part of: Survival analysis and censored data Special processes

Published online by Cambridge University Press:  30 March 2016

Serkan Eryilmaz
Serkan Eryilmaz*
Affiliation:
Atilim University
*
∗∗ Postal address: Department of Industrial Engineering, Atilim University, Ankara, Turkey. Email address: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper is concerned with the Birnbaum importance measure of a component in a binary coherent system. A representation for the Birnbaum importance of a component is obtained when the system consists of exchangeable dependent components. The results are closely related to the concept of the signature of a coherent system. Some examples are presented to illustrate the results.

Keywords

Component importanceexchangeabilityorder statisticssignature

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 52 , Issue 3 , September 2015 , pp. 851 - 863
Copyright
Copyright © 2015 by the Applied Probability Trust 

References

Andrews, J. D. (2008). Birnbaum and criticality measures of component contribution to the failure of phased missions. Reliab. Eng. System Safety 93 1861-1866.CrossRefGoogle Scholar
Barlow, R. E. and Proschan, F. (1975). Importance of system components and fault tree events. Stoch. Process. Appl. 3 153-173.Google Scholar
Bergman, B. (1985). On some new reliability importance measures. In Safety of Computer Control Systems (Proc. SAFECOMP'85; Como, Italy), pp. 61–64.Google Scholar
Birnbaum, Z. W. (1969). On the importance of different components in a multicomponent system. In Multivariate Analysis, II, Academic Press, New York, pp. 581–592.Google Scholar
Boland, P. J. (2001). Signatures of indirect majority systems. J. Appl. Prob. 38 597-603.Google Scholar
Boland, P. J and El-Neweihi, E. (1995). Measures of component importance in reliability theory. Comput. Operat. Res. 22 455-463.Google Scholar
Butler, D. A. (1977). An importance ranking for system components based upon cuts. Operat. Res. 25 874-879.Google Scholar
Da, G., Zheng, B. and Hu, T. (2012). On computing signatures of coherent systems. J. Multivariate Anal. 103 142-150.Google Scholar
Eryilmaz, S. (2015). Table of results for vectors s +i , s −i for all coherent systems of order n=4. Available at https://www.dropbox.com/s/krc2gw7pmeegnzp/table2.pdf.Google Scholar
Eryilmaz, S. (2010). Review of recent advances in reliability of consecutive k-out-of-n and related systems. J. Risk Reliab. 224 225-237.Google Scholar
Eryilmaz, S. (2013). On residual lifetime of coherent systems after the rth failure. Statist. Papers 54 243-250.Google Scholar
Eryilmaz, S. (2014). On signatures of series and parallel systems consisting of modules with arbitrary structures. Commun. Statist. Simul. Comput. 43 1202-1211.Google Scholar
Eryilmaz, S., Koutras, M. V. and Triantafyllou, I. S. (2011). Signature based analysis of m-consecutive-k-out-of-n: F systems with exchangeable components. Naval Res. Logistics 58 344-354.Google Scholar
Hwang, F. K. (2001). A new index of component importance. Operat. Res. Lett. 28 75-79.Google Scholar
Iyer, S. (1992). The Barlow–Proschan importance and its generalizations with dependent components. Stoch. Process. Appl. 42 353-359.Google Scholar
Kuo, W. and Zhu, X. (2012). Some recent advances on importance measures in reliability. IEEE Trans. Reliab. 61 344-360.Google Scholar
Kuo, W. and Zuo, M. J. (2003). Optimal Reliability Modeling: Principles and Applications. John Wiley, Chichester.Google Scholar
Natvig, B. (1979). A suggestion of a new measure of importance of system components. Stoch. Process. Appl. 9 319-330.Google Scholar
Natvig, B. (1985). New light on measures of importance of system components. Scand. J. Statist. 12 43-54.Google Scholar
Natvig, B. (2011). Measures of component importance in nonrepairable and repairable multistate strongly coherent systems. Method. Comput. Appl. Prob. 13 523-547.Google Scholar
Natvig, B. and Gäsemyr, J. (2009). New results on the Barlow–Proschan and Natvig measures of component importance in nonrepairable and repairable systems. Method. Comput. Appl. Prob. 11 603-620.Google Scholar
Navarro, J. and Rubio, R. (2011). A note on necessary and sufficient conditions for ordering properties of coherent systems with exchangeable components. Naval Res. Logistics 58 478-489.Google Scholar
Navarro, J., Rychlik, T. (2007). Reliability and expectation bounds for coherent systems with exchangeable components. J. Multivariate Anal. 98 102-113.Google Scholar
Navarro, J. and Spizzichino, F. (2010). Comparisons of series and parallel systems with components sharing the same copula. Appl. Stoch. Models Business Industry 26 775-791.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.Google Scholar
Navarro, J., Samaniego, F. J., Balakrishnan, N. and Bhattacharya, D. (2008). On the application and extension of system signatures in engineering reliability. Naval Res. Logistics 55 313-327.Google Scholar
Parvardeh, A., Balakrishnan, N. (2013). Conditional residual lifetimes of coherent systems. Statist. Prob. Lett. 83 2664-2672.Google Scholar
Samaniego, F. J. (2007). System Signatures and Their Applications in Engineering Reliability. Springer, New York.Google Scholar
Triantafyllou, I. S. and Koutras, M. V. (2014). Reliability properties of (n.f,k) systems, IEEE Trans. Reliability 63 357-366.Google Scholar
Xie, M. (1987). On some importance measures of system components. Stoch. Process. Appl. 25 273-280.Google Scholar
Xie, M. and Bergman, B. (1991). On a general measure of component importance. J. Statist. Planning Inference 29 211-220.Google Scholar
Zarezadeh, S., Asadi, M. and Balakrishnan, N. (2014). Dynamic network reliability modeling under nonhomogeneous Poisson processes. Europ. J. Operat. Res. 232 561-571.Google Scholar
Zhu, X. and Kuo, W. (2014). Importance measures in reliability and mathematical programming. Ann. Operat. Res. 212 241-267.Google Scholar