Hostname: page-component-848d4c4894-hfldf Total loading time: 0 Render date: 2024-05-20T09:40:32.872Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal allocation of components in parallel–series and series–parallel systems

Published online by Cambridge University Press:  14 July 2016

Emad El-Neweihi ,
Frank Proschan  and
Jayaram Sethuraman
Emad El-Neweihi*
Affiliation:
University of Illinois
Frank Proschan*
Affiliation:
Florida State University
Jayaram Sethuraman*
Affiliation:
Florida State University
*
∗Postal address: Department of Mathematics, University of Illinois, Chicago, IL 60680, USA.
∗∗Postal address: Department of Statistics and Statistical Consulting Center, The Florida State University, Tallahassee, FL 32306, USA.
∗∗Postal address: Department of Statistics and Statistical Consulting Center, The Florida State University, Tallahassee, FL 32306, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper shows how majorization and Schur-convex functions can be used to solve the problem of optimal allocation of components to parallel-series and series-parallel systems to maximize the reliability of the system. For parallel-series systems the optimal allocation is completely described and depends only on the ordering of component reliabilities. For series-parallel systems, we describe a partial ordering among allocations that can lead to the optimal allocation. Finally, we describe how these problems can be cast as integer linear programming problems and thus the results obtained in this paper show that when some linear integer programming problems are recast in a different way and the techniques of Schur functions are used, complete solutions can be obtained in some instances and better insight in others.

Keywords

RELIABILITYSCHUR FUNCTIONSINTEGER PROGRAMMING
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 3 , September 1986 , pp. 770 - 777
Copyright
Copyright © Applied Probability Trust 1986 

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.)

Footnotes

†

Research sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Numbers AFOSR 80–0170 and AFOSR 82–K–0007. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon.

‡

Research supported by the U.S. Army Research under Grant DAAG 29–82–K–0168.

References

Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.Google Scholar
Derman, C., Lieberman, G. J. and Ross, S. M. (1974) Assembly of systems having maximum reliability. Naval Res. Logist. Quart. 21, 1–12.CrossRefGoogle Scholar
Balas, E. (1970) Minimax and duality for linear and nonlinear mixed-integer programming. In Integer and Nonlinear Programming, ed. Abadie, J., North Holland, Amsterdam, 385–418.Google Scholar
Hummer, P. L. and Rudeman, S. (1968) Boolean Methods in Operations Research and Related Areas. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Marshall, A. W. and Olkin, I. (1979) Inequalities: Theory of Majorization and Its Applications. Academic Press, New York.Google Scholar