Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-26T18:20:18.213Z Has data issue: false hasContentIssue false
  • English
  • Français

Schur Structure Functions

Published online by Cambridge University Press:  27 July 2009

A. M. Abouammah ,
E. El-Neweihi  and
F. Proschan
A. M. Abouammah
Affiliation:
Department of StatisticsKing Saud University Riyadh, 11451, Saudi Arabia
E. El-Neweihi
Affiliation:
Department of StatisticsKing Saud University Riyadh, 11451, Saudi Arabia and Department of Mathematics, Statistics, and Computer ScienceUniversity of Illinois at Chicago Chicago, Illinois 60680
F. Proschan
Affiliation:
Department of StatisticsThe Florida State University Tallahassee, Florida 32306
Get access Rights & Permissions [Opens in a new window]

Abstract

We define two new classes of multistate coherent systems by requiring, among other conditions, that their structure functions be Schur-concave (Schurconvex). The M + 1 performance levels of both the systems and their components are represented by the set [0, 1,…, M]. We present basic structural properties of the new classes. In particular, we study in some detail the number and form of the critical upper (lower) vectors to the various performance levels. We also present some probabilistic aspects of the new classes.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 3 , Issue 4 , October 1989 , pp. 581 - 591
Copyright
Copyright © Cambridge University Press 1989

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

REFERENCES

Barlow, R.E. & Proschan, F. (1981). Statistical theory of reliability and life testing, Silver Spring, Maryland: To Begin With.Google Scholar
Barlow, R.E. & Wu, A.S. (1978). Coherent systems with multistate components. Mathematics of Operations Research 3: 275–281.CrossRefGoogle Scholar
Block, H.W. & Savits, T.H. (1982). A decomposition for multistate monotone systems. Journal of Applied Probability 19: 391–402.CrossRefGoogle Scholar
Block, H.W., Griffith, W.S., & Savits, T.H. (1989). L-Superadditive structure functions. Advances in Applied Probability 21(4).CrossRefGoogle Scholar
El-Neweihi, E., Proschan, F., & Sethuraman, J. (1978). Multistate coherent systems. Journal of Applied Probability 15: 675–688.CrossRefGoogle Scholar
Griffith, W.S. (1980). Multistate reliability models. Journal of Applied Probability 17: 745–774.CrossRefGoogle Scholar
Marshall, A.W. & Olkin, I. (1979). Inequalities: Theory of majorization and its application. New York: Academic Press.Google Scholar
Natvig, B. (1982). Two suggestions of how to define a multistate coherent system. Advances in Applied Probability 14: 434–455.CrossRefGoogle Scholar
Proschan, F. & Sethuraman, J. (1977). Schur functions in statistics, 1: The preservation theorem. Annals of Statistics 5: 256–262.CrossRefGoogle Scholar
Ross, S. (1979), Multivalued state component systems. Annals of Probability 7: 379–383.CrossRefGoogle Scholar