Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-28T15:38:13.911Z Has data issue: false hasContentIssue false
  • English
  • Français

The Joint Signature of Coherent Systems with Shared Components

Part of: Distribution theory - Probability Special processes

Published online by Cambridge University Press:  14 July 2016

Jorge Navarro ,
Francisco J. Samaniego  and
N. Balakrishnan
Jorge Navarro*
Affiliation:
Universidad de Murcia
Francisco J. Samaniego*
Affiliation:
University of California, Davis
N. Balakrishnan*
Affiliation:
McMaster University
*
∗Postal address: Facultad de Matemáticas, Universidad de Murcia, 30100 Murcia, Spain. Email address: jorgenav@um.es
∗∗Postal address: University of California, Davis, 1 Shields Avenue, Davis, CA 96616, USA. Email address: fjsamaniego@ucdavis.edu
∗∗∗Postal address: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada. Email address: bala@mcmaster.ca
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.

System signatures are useful tools in the study and comparison of coherent systems. In this paper, we define and study a similar concept, called the joint signature, for two coherent systems which share some components. Under an independent and identically distributed assumption on component lifetimes, a pseudo-mixture representation based on this joint signature is obtained for the joint distribution of the lifetimes of both systems. Sufficient conditions are given based on the respective joint signatures of two pairs of systems, each with shared components, to ensure various forms of bivariate stochastic orderings between the joint lifetimes of the two pairs of systems.

Keywords

Coherent systemk-out-of-n systemorder statisticssignaturesingular distributionmatrix orderingsbivariate stochastic orderings

MSC classification

Secondary: 60E15: Inequalities; stochastic orderings 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 1 , March 2010 , pp. 235 - 253
Copyright
Copyright © Applied Probability Trust 2010 

Footnotes

Visiting Professor at King Saud University (Saudi Arabia) and National Central University (Taiwan).

References

[1] Barlow, R. E. and Proschan, F. (1981). Statistical Theory of Reliability and Life Testing. To Begin With, Silver Spring, MD.Google Scholar
[2] Jasiński, K., Navarro, J. and Rychlik, T. (2009). Bounds on variances of lifetimes of coherent and mixed systems. J. Appl. Prob. 46, 894–908.Google Scholar
[3] Kochar, S., Mukerjee, H. and Samaniego, F. J. (1999). The ‘signature’ of a coherent system and its application to comparison among systems. Naval Res. Logistics 46, 507–523.3.0.CO;2-D>CrossRefGoogle Scholar
[4] 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
[5] Navarro, J., Ruiz, J. M. and Sandoval, C. J. (2007). Properties of coherent systems with dependent components. Commun. Statist. Theory Meth. 36, 175–191.Google Scholar
[6] 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
[7] Samaniego, F. (1985). On closure of the IFR class under formation of coherent systems. IEEE Trans. Reliab. 34, 69–72.CrossRefGoogle Scholar
[8] Samaniego, F. (2007). System Signatures and Their Applications in Engineering Reliability (Internat. Ser. Operat. Res. Manag. Sci. 110). Springer, New York.Google Scholar
[9] Samaniego, F. J., Balakrishnan, N. and Navarro, J. (2009). Dynamic signatures and their use in comparing the reliability of new and used systems. Naval Res. Logistics 56, 577–591.Google Scholar
[10] Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders. Springer, New York.Google Scholar