AJOR  Vol.1 No.1 , March 2011
Minimal Repair Redundancy for Coherent Systemin its Signatures Representation
In this paper we discuss how to maintain the signature representation of a coherent system through a minimal repair redundancy. In a martingale framework we use compensator transforms to identify how the components minimal repairs affect the order statistics in the signature representation.

Cite this paper
nullV. Bueno, "Minimal Repair Redundancy for Coherent Systemin its Signatures Representation," American Journal of Operations Research, Vol. 1 No. 1, 2011, pp. 8-15. doi: 10.4236/ajor.2011.11002.
[1]   Arjas, E. and Yashin, A. (1988). A note on randonm intensities and conditional survivalfunctions. Journal of Applied probability. 25, 630 - 635.doi:10.2307/3213991

[2]   Aven, T. and Jensen, U. (1999). Stochastic Models ineliability. Springer Verlag, New York. doi:10.1007/b97596

[3]   Barlow and Proschan,F. (1981). Statistical Theory of Reliability and Life Testing: Probability models. Hold, Reinhart and Wiston , Inc. Silver Spring, MD.

[4]   Bremaud ,P. (1981). Point Processes and Queues: Martingale Dynamics.Springer-Verlag, New York.

[5]   Bueno, V.C. (2005). Minimal standby redundancy allocation in a K-out-of-n:F systemof dependent components. European Journal of Operation Research. 165, 786-793.doi:10.1016/j.ejor.2003.01.004

[6]   Bueno, V.C. (2010). Dynamics signature of a coherent system. Submited.S~ao PauloUniversity, S~ao Paulo, Brazil.

[7]   Kochar, S., Mukherjee, H., Samaniego, F.(1999). The signature of a coherent systemand its application to comparisons among systems. Naval Research Logistic. 46, 507 - 523.doi:10.1002/(SICI)1520-6750(199908)46:5<507::AID-NAV4>3.0.CO;2-D

[8]   Navarro, J., Balakrishnan, N. and Samaniego, F.J. (2008). Mixture representation ofresidual lifetimes of used systems. Journal of Applied Probability. 45, 1097 -1112.doi:10.1239/jap/1231340236

[9]   Norros, I. (1986). A compensator representation of multivariate life length distributions, with applications. Scand. J. Statist. 13, 99-112.

[10]   Samaniego, F. (1985). On closure of the IFR class under formation of coherent systems. IEEE Transactions in Reliability. R-34, 69-72.doi:10.1109/TR.1985.5221935

[11]   Samaniego,F.J. (2007). System signatures and their applications in engineering re-liability. International Series in Operation Research and Management Science, Vol 110, Springer, New York.

[12]   Samaniego, F.J., Navarro, J. and Balakrishnan, N. (2009). Dynamic signatures andtheir in comparing the reliability of a new and used systems. Naval Research Logistic. 56, 577-596.doi:10.1002/nav.20370

[13]   Shaked, M., Suarez-Llorens, A. (2003). On the comparison of reliability experimentsbased on the convolution order. Journal of American Statistical Association. 98, 693-702.doi:10.1198/016214503000000602