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Notes on Natvig's measure of importance of system components

Published online by Cambridge University Press:  14 July 2016

Ilkka Norros
Ilkka Norros*
Affiliation:
University of Helsinki
*
∗ Postal address: Department of Mathematics, University of Helsinki, Hallituskatu 15, 00100 Helsinki 10, Finland.
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Abstract

Natvig's measure of importance of system components is defined and investigated, using martingale notions and methods. Most results are proved in the case of dependent component life lengths. The sum of the ‘absolute importances' of the components is studied as a quantity expressing the ‘share of failures' in the destruction of the system, contrasted to the ‘share of time’.

Keywords

MARTINGALE METHODS IN RELIABILITY THEORYMINIMAL REPAIR

Information

Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 3 , September 1986 , pp. 736 - 747
Copyright
Copyright © Applied Probability Trust 1986 

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References

Arjas, E. (1981) A stochastic process approach to multivariate reliability systems: notions based on conditional stochastic order. Math. Operat. Res. 6, 263–276.Google Scholar
Arjas, E. (1985) Comment on the paper by B. Bergman. Scand. J. Statist., 12, 30–31.Google Scholar
Barlow, R. E. and Proschan, F. (1975) Importance of system components and fault tree events. Stoch. Proc. Appl. 3, 153–173.Google Scholar
Birnbaum, Z. W. (1969) On the importance of different components in a multicomponent system. In Multivariate Analysis II, ed. Krishnaiah, P. R., Academic Press, New York, 581–592.Google Scholar
Bremaud, P. (1981) Point Processes and Queues: Martingale Dynamics. Springer-Verlag, New York.Google Scholar
Dellacherie, C. (1972) Capacités et Processus stochastiques. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Jacod, J. (1975) Multivariate point processes: predictable projection, Radon-Nikodym derivatives, representation of martingales. Z. Wahrscheinlichkeitsth. 34, 225–244.Google Scholar
Kurtz, T. (1980) Representations of Markov processes as multiparameter time changes. Ann. Prob. 8, 682–715.Google Scholar
Natvig, B. (1979) A suggestion of a new measure of importance of system components. Stoch. Proc. Appl. 9, 319–330.CrossRefGoogle Scholar
Natvig, B. (1982) On the reduction in remaining system lifetime due to the failure of a specific component. J. Appl. Prob. 19, 642–652 (Correction 20, 713).CrossRefGoogle Scholar
Natvig, B. (1985) New light on measures of importance of system components. Scand. J. Statist. 12, 43–54.Google Scholar
Norros, I. (1985) Systems weakened by failures. Stoch. Proc. Appl. 20, 181–196.CrossRefGoogle Scholar
Norros, I. (1986) A compensator representation of multivariate life length distributions, with applications. Scand. J. Statist. To appear.Google Scholar
Shaked, M. and Shanthikumar, J. (1984) The multivariate imperfect repair. Technical Report, University of Arizona.Google Scholar
Shaked, M. and Shanthirumar, J. (1985) The multivariate hazard construction. Technical Report, University of Arizona.CrossRefGoogle Scholar