Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-19T15:22:39.575Z Has data issue: false hasContentIssue false

Binary structure functions with dependent components

Published online by Cambridge University Press:  01 July 2016

Nader Ebrahimi*
Affiliation:
Northern Illinois University

Abstract

In this paper we attempt to develop an axiomatic theory of binary structure functions with dependent components. This is an important problem, hitherto largely ignored. The concept of coherent structure in probability is introduced and studied. The relationship to the classical coherent structure is discussed. In the new concept the relevancy is defined through reliability of the system, while in the classical concept it is defined through the structure function.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1990 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
Barlow, R. E. and Wu, A. S. (1978) Coherent system with multistate components. Math. Operat. Res. 4, 275281.CrossRefGoogle Scholar
Birnbaum, Z. W. (1968) On the importance of components in a system. Selected Statistical Papers 2, Mathematical Centre Tracts 27, Amsterdam, 8395.Google Scholar
Dobrusin, R. L. (1963) General formulation of Shannon's main theorem. Amer. Math. Soc. Transl. 33, 323428.Google Scholar
Ebrahimi, N. (1984) Multistate reliability models. Naval Research Logistics 31, 671680.Google Scholar
El-Newehi, E. and Proschan, F. (1984) A survey of multistate system theory. Commun. Statist. A 13, 405432.Google Scholar
El-Newehi, E. Proschan, F. and Sethuraman, J. (1978) Multistate coherent systems. J. Appl. Prob. 15, 675688.Google Scholar
Esary, J. D. and Marshall, A. W. (1970) Coherent life functions. SIAM J. Appl. Math. 18, 810814.Google Scholar
Griffith, W. (1980) Multistate reliability models. J. Appl. Prob. 17, 35744.Google Scholar
Natvig, B. (1979) A suggestion of a new measure of importance of system components. Stoch. Proc. Appl. 9, 319330.Google Scholar
Natvig, B. (1982a) Two suggestions of how to define a multistate coherent system. Adv. Appl. Prob. 14, 434455.Google Scholar
Natvig, B. (1982b) On the redution in remaining lifetime due to failure of a specific component. J. Appl. Prob. 19, 642653.Google Scholar
Ross, S. (1979) Multivalued state component systems. Ann. Prob. 7, 379383.CrossRefGoogle Scholar