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L-superadditive structure functions

Published online by Cambridge University Press:  01 July 2016

Henry W. Block ,
William S. Griffith  and
Thomas H. Savits
Henry W. Block*
Affiliation:
University of Pittsburgh
William S. Griffith*
Affiliation:
University of Kentucky
Thomas H. Savits*
Affiliation:
University of Pittsburgh
*
∗Postal address: Department of Mathematics and Statistics, University of Pittsburgh, PA 15260, USA.
∗∗Postal address: Department of Statistics, University of Kentucky, Lexington, KY 40506, USA.
∗Postal address: Department of Mathematics and Statistics, University of Pittsburgh, PA 15260, USA.
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Abstract

Structure functions relate the level of operations of a system as a function of the level of the operation of its components. In this paper structure functions are studied which have an intuitive property, called L-superadditive (L-subadditive). Such functions describe whether a system is more series-like or more parallel-like. L-superadditive functions are also known under the names supermodular, quasi-monotone and superadditive and have been studied by many authors. Basic properties of both discrete and continuous (i.e., taking a continuum of values) L-superadditive structure functions are studied. For binary structure functions of binary values, El-Neweihi (1980) showed that L-superadditive structure functions must be series. This continues to hold for binary-valued structure functions even if the component values are continuous (see Proposition 3.1). In the case of non-binary-valued structure functions this is no longer the case. We consider structure functions taking discrete values and obtain results in various cases. A conjecture concerning the general case is made.

Keywords

ISOTONE DIFFERENCESCRITICAL UPPER VECTORCRITICAL CONNECTION VECTOR
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 4 , December 1989 , pp. 919 - 929
Copyright
Copyright © Applied Probability Trust 1989 

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Footnotes

Supported by AFOSR Grant No. AFOSR-84-0113 and ONR Contract N00014-84-K-0084.

Supported in part by AFOSR Grant No. AFOSR-84-0013, and in part by NSF Grant RII-8610671 and the Commonwealth of Kentucky through the Kentucky EPSCoR Program.

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