A Coherent System Component Importance under Its Signatures Representation

PDF (Size:134KB) PP. 172-179   DOI: 10.4236/ajor.2011.13019

Author(s)

Vanderlei da Costa Bueno

ABSTRACT

In this paper we discuss how to measure the component importance for a system in its signature representation. The definition is given in terms of compensator transform and it can be considered as a new formalization of the ideas presented by Bergman [1] in the context of system signature.

KEYWORDS

System Signature, Dynamic System Signature, Coherent Systems, Component Importance, Point Processes Martingales

Cite this paper

V. Bueno, "A Coherent System Component Importance under Its Signatures Representation," American Journal of Operations Research, Vol. 1 No. 3, 2011, pp. 172-179. doi: 10.4236/ajor.2011.13019.

References

[1] B. Bergman, “On Some New Reliability Importance Measures,” In: W. J. Quirk, Ed., Proceedings of the 4th IFAC Workshop on Safety of Computer Control Systems (IFAC SAFECOMP), Como, 1-3 October 1985, pp. 61- 64.
[2] F. Samaniego, “System Signatures and Their Applications in Engineering Reliability,” International Series in Operation Research and Management Science, Vol. 110, Springer, New York, 2007.
[3] F. Samaniego, “On Closure of the IFR Class under Formation of Coherent Systems,” IEEE Transactions on Reliability, Vol. R-34, No. 1, 1985, pp. 69-72. Hdoi:10.1109/TR.1985.5221935
[4] S. Kochar, H. Mukherjee and F. Samaniego, “The Signature of a Coherent System and Its Application to Comparisons among Systems,” Naval Research Logistic, Vol. 46, No. 5, 1999, pp. 507-523. Hdoi:10.1002/(SICI)1520-6750(199908)46:5<507::AID-NAV4>3.0.CO;2-D
[5] M. Shaked and A. Suarez-Llorens, “On the Comparison of Reliability Experiments Based on the Convolution Order,” Journal of American Statistical Association, Vol. 98, No. 4, 2003, pp. 693-702. Hdoi:10.1198/016214503000000602
[6] Z. W. Birnbaum, “On the Importance of Different Components in a Multicomponent System,” In: P. R. Krishnaiah, Ed., Multivariate Analysis, Academic Press, New York, 1969, pp. 591-592.
[7] R. Barlow and F. Proschan, “Importance of Systems Components and Fault Trees Events,” Stochastic Processes and Their Applications, Vol. 3, No. 2, 1975, pp. 153-173.
[8] B. Natvig, “New Light on Measure of Importance of Systems Components,” Scandinavian Journal of Statistics, Vol. 12, No. 1, 1985, pp. 43-54.
[9] P. J. Boland and E. El-Neweihi, “Measures of Component Importance in Reliability Theory,” Technical Report, Florida State University, Tallahassee, 1990.
[10] V. C. Bueno, “Dynamics Signature of a Coherent System,” Technical report, S?o Paulo University, S?o Paulo, 2010.
[11] T. Aven and U. Jensen, “Stochastic Models in Reliability,” Springer Verlag, New York, 1999. Hdoi:10.1198/016214503000000602
[12] E. Arjas and A. Yashin, “A Note on Random Intensities and Conditional Survival Functions,” Journal of Applied Probability, Vol. 25, No. 3, 1988, pp. 630-635. Hdoi:10.1198/016214503000000602
[13] J. Jacod, “Multivariate Point Processes: Predictable Projection. Radon-Nikodyn Derivatives, Representation of Martingales,” Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 31, 1975, pp. 235-253. Hdoi:10.1007/BF00536010
[14] E. Arjas and I. Norros, “Change of Life Distribution via a Hazard Transformation: An Inequality with Application to Minimal Repair,” Mathematics of Operations Research, Vol. 14, No. 2, 1989, pp. 355-361.
[15] I. Norros, “Notes on Natvig’s Measure of Importance of Systems Components,” Scandinavian Journal of Statistics, Vol. 12, 1986, pp. 43-54.
[16] V. C. Bueno and I. M. Carmo, “Active Redundancy Allocation for a k-out-of-n:F System of Dependent Components,” European Journal of Operational Research, Vol. 176, No. 2, 2007, pp. 1041-1051. Hdoi:10.1016/j.ejor.2005.09.012