Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-22T05:59:48.906Z Has data issue: false hasContentIssue false
  • English
  • Français

Two suggestions of how to define a multistate coherent system

Published online by Cambridge University Press:  01 July 2016

B. Natvig
B. Natvig*
Affiliation:
University of Oslo
*
∗Postal address: Institute of Mathematics, University of Oslo, P.O. Box 1053, Blindern, Oslo 3, Norway.
Get access Rights & Permissions [Opens in a new window]

Abstract

One inherent weakness of traditional reliability theory is that the system and the components are always described just as functioning or failed. However, recent papers by Barlow and Wu (1978) and El-Neweihi et al. (1978) have made significant contributions to start building up a theory for a multistate system of multistate components. Here the states represent successive levels of performance ranging from a perfect functioning level down to a complete failure level. In the present paper we will give two suggestions of how to define a multistate coherent system. The first one is more general than the one introduced in the latter paper, the results of which are, however, extendable. (This is also true for a somewhat more general model than ours, treated in independent work by Griffith (1980).) Furthermore, some new definitions and results are given (which trivially extend to the latter model). Our second model is similarly more general than the one introduced in Barlow and Wu (1978), the results of which are again extendable. In fact we believe that most of the theory for the traditional binary coherent system can be extended to our second suggestion of a multistate coherent system.

Keywords

MULTISTATE COHERENT SYSTEMSCOHERENT SYSTEMSRELIABILITYPERFORMANCEREDUNDANCY
Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 2 , June 1982 , pp. 434 - 455
Copyright
Copyright © Applied Probability Trust 1982 

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

Aven, T. (1980) Optimal replacement policies for a multistate system. , Institute of Mathematics, University of Oslo.Google Scholar
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 systems with multi-state components. Math. Operat. Res. 4, 275–281.CrossRefGoogle 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
Block, H. W. and Savits, T. H. (1980) Multidimensional IFRA processes. Ann. Prob. 8, 793–801.Google Scholar
Butler, D. A. (1979) Bounding the reliability of multistate systems. Department of Operations Research and Department of Statistics, Stanford University.Google Scholar
Ei-Neweihi, E., Proschan, F. and Sethuraman, J. (1978) Multistate coherent systems. J. Appl. Prob. 15, 675–688.CrossRefGoogle Scholar
Feller, W. (1968) An Introduction to Probability Theory and its Applications, Vol. I, 3rd. edn. Wiley, New York.Google Scholar
Griffith, W. (1980) Multistate reliability models. J. Appl. Prob. 17, 735–744.Google Scholar
Natvig, B. (1980a) Two suggestions of how to define a multistate coherent system. Technical report, Institute of Mathematics, University of Oslo.Google Scholar
Natvig, B. (1980b) Improved bounds for the availability and unavailability in a fixed time interval for systems of maintained, interdependent components. Adv. Appl. Prob. 12, 200–221.CrossRefGoogle Scholar
Ross, S. (1979) Multivalued state component reliability systems. Ann. Prob. 7, 379–383.Google Scholar
Satyanarayana, A. and Prabhakar, A. (1978) New topological formula and rapid algorithm for reliability analysis of complex networks. IEEE Trans. Reliability 27, 82–100.Google Scholar