AJOR  Vol.1 No.3 , September 2011
A Coherent System Component Importance under Its Signatures Representation
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.

Cite this paper
nullV. 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

 
 
Top