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On the Deterioration of Nonrepairable Multistate Strongly Coherent Systems

Part of: Operations research and management science Survival analysis and censored data

Published online by Cambridge University Press:  30 January 2018

Bent Natvig
Bent Natvig*
Affiliation:
University of Oslo
*
∗ Postal address: Department of Mathematics, University of Oslo, PO Box 1053 Blindern, Oslo, N-0316, Norway, Email address: [email protected]
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Abstract

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In the present paper, results given in Natvig (1990) are generalized to a multistate, strongly coherent, nonrepairable system of independent components by considering the reduction in remaining system time above a certain state due to a jump downwards of a component. This reduction also equals the increase in remaining system time above a certain state due to a minimal repair of the component at its time of jump downwards. The expected value of the sum of such reductions/increases for the different possible jumps downwards of the component is the building block of the Natvig measure of the importance of the component in the multistate case. Hence, the whole distributions of these reductions/increases are arrived at, not only the expectations, throwing more light on the consequences for the system of the deterioration of the components.

Keywords

Dynamic reliabilityNatvig importance of a system componentmultistate strongly coherent systemnonrepairable system

MSC classification

Primary: 62N05: Reliability and life testing 90B25: Reliability, availability, maintenance, inspection
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 1 , March 2014 , pp. 69 - 81
Copyright
© Applied Probability Trust 

References

Barlow, R. E. and Proschan, F. (1975). Importance of system components and fault tree events. Stoch. Process. Appl. 3, 153–173.Google Scholar
Barlow, R. E. and Proschan, F. (1981). Statistical Theory of Reliability and Life Testing. Probability Models. To Begin With, Silver Springs, MD.Google Scholar
Birnbaum, Z. W. (1969). On the importance of different components in a multicomponent system. In Multivariate Analysis, II, Academic Press, New York, pp. 581–592.Google Scholar
Huseby, A. B. and Natvig, B. (2013). Discrete event simulation methods applied to advanced importance measures of repairable components in multistate network flow systems. Reliab. Eng. System Safety 119, 186–198.Google Scholar
Kuo, W. and Zhu, X. (2012). Importance Measures in Reliability, Risk, and Optimization: Principles and Applications. John Wiley, Hoboken, NJ.CrossRefGoogle Scholar
Natvig, B. (1979). A suggestion of a new measure of importance of system components. Stoch. Process. Appl. 9, 319–330.CrossRefGoogle Scholar
Natvig, B. (1982a). On the reduction in remaining system lifetime due to the failure of a specific component. J. Appl. Prob. 19, 642–652. (Correction: J. Appl. Prob. 20, 713.)CrossRefGoogle Scholar
Natvig, B. (1982b). Two suggestions of how to define a multistate coherent system. Adv. Appl. Prob. 14, 434–455.Google Scholar
Natvig, B. (1985). New light on measures of importance of system components. Scand. J. Statist 12, 43–54.Google Scholar
Natvig, B. (1990). On information-based minimal repair and the reduction in remaining system lifetime due to the failure of a specific module. J. Appl. Prob. 27, 365–375.Google Scholar
Natvig, B. (2011a). Measures of component importance in nonrepairable and repairable multistate strongly coherent systems. Methodol. Comput. Appl. Prob. 13, 523–547.CrossRefGoogle Scholar
Natvig, B. (2011b). Multistate Systems Reliability Theory with Applications. John Wiley, Chichester.Google Scholar
Natvig, B. and Gå{semyr, J.} (2009). New results on the Barlow–Proschan and Natvig measures of component importance in nonrepairable and repairable systems. Methodol. Comput. Appl. Prob. 11, 603–620.CrossRefGoogle Scholar
Ramirez-Marquez, J. E. and Coit, D. W. (2007). Multi-state component criticality analysis for reliability improvement in multi-state systems. Reliab. Eng. System Safety 92, 1608–1619.CrossRefGoogle Scholar
Ramirez-Marquez, J. E., et al. (2006). New insights on multi-state component criticality and importance. Reliab. Eng. System Safety 91, 894–904.CrossRefGoogle Scholar
Zio, E., Marella, M. and Podofillini, L. (2007). Importance measures-based prioritization for improving the performance of multi-state systems: application to the railway industry. Reliab. Eng. System Safety 92, 1303–1314.CrossRefGoogle Scholar
Zio, E., Podofillini, L. and Levitin, G. (2004). Estimation of the importance measures of multi-state elements by Monte Carlo simulation. Reliab. Eng. System Safety 86, 191–204.Google Scholar