On Subadditive and Superadditive Functions

1965 ◽  
Vol 72 (6) ◽  
pp. 653 ◽  
Author(s):  
S. P. S. Rathore
Keyword(s):  
Superadditive Functions

Component allocation for a distributed system: reliability maximization

1993 ◽  
Vol 30 (2) ◽  
pp. 471-477 ◽  
Author(s):  
Mikhail Revyakov
Keyword(s):  
Distributed System ◽  
Convex Functions ◽  
System Reliability ◽  
Optimal Allocation ◽  
System Structure ◽  
External Influences ◽  
Component Allocation ◽  
Schur Convex ◽  
Superadditive Functions

An optimal allocation of subsystems depending on the system structure and reliability ordering of inherent subsystem components is determined, in the presence of various external influences on the reliability of components in different locations. It is carried out with the help of L-superadditive functions and Schur-convex functions.

scholarly journals A survey of dual-feasible and superadditive functions

2008 ◽  
Vol 179 (1) ◽  
pp. 317-342 ◽  
Author(s):  
François Clautiaux ◽  
Cláudio Alves ◽  
José Valério de Carvalho
Keyword(s):  
Superadditive Functions

Superadditive Functions and a Statistical Application

1989 ◽  
Vol 20 (5) ◽  
pp. 1255-1259 ◽  
Author(s):  
S. Y. Trimble ◽  
Jim Wells ◽  
F. T. Wright
Keyword(s):  
Statistical Application ◽  
Superadditive Functions

Component allocation for a distributed system: reliability maximization

1993 ◽  
Vol 30 (02) ◽  
pp. 471-477
Author(s):  
Mikhail Revyakov
Keyword(s):  
Distributed System ◽  
Convex Functions ◽  
System Reliability ◽  
Optimal Allocation ◽  
System Structure ◽  
External Influences ◽  
Component Allocation ◽  
Schur Convex ◽  
Superadditive Functions

An optimal allocation of subsystems depending on the system structure and reliability ordering of inherent subsystem components is determined, in the presence of various external influences on the reliability of components in different locations. It is carried out with the help of L-superadditive functions and Schur-convex functions.

scholarly journals Minimal superadditive extensions of superadditive functions

1960 ◽  
Vol 10 (4) ◽  
pp. 1155-1162 ◽  
Author(s):  
Andrew Bruckner
Keyword(s):  
Superadditive Functions

L-superadditive structure functions

1989 ◽  
Vol 21 (04) ◽  
pp. 919-929 ◽  
Author(s):  
Henry W. Block ◽  
William S. Griffith ◽  
Thomas H. Savits
Keyword(s):  
Structure Functions ◽  
Basic Properties ◽  
Binary Structure ◽  
Paper Structure ◽  
Discrete Values ◽  
Superadditive Functions

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.

L-superadditive structure functions

1989 ◽  
Vol 21 (4) ◽  
pp. 919-929 ◽  
Author(s):  
Henry W. Block ◽  
William S. Griffith ◽  
Thomas H. Savits
Keyword(s):  
Structure Functions ◽  
Basic Properties ◽  
Binary Structure ◽  
Paper Structure ◽  
Discrete Values ◽  
Superadditive Functions

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.

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