[en] Pseudo-Boolean function ; Least squares approximation ; Symmetric function ; Cooperative game theory ; System reliability ; System signature ; Cardinality index

[en] We introduce an index for measuring the influence of the $k$th smallest variable on a pseudo-Boolean function. This index is defined from a weighted least squares approximation of the function by linear combinations of order statistic functions. We give explicit expressions for both the index and the approximation and discuss some properties of the index. Finally, we show that this index subsumes the concept of system signature in engineering reliability and that of cardinality index in decision making.

University of Luxembourg Mathematics resaech unit

Internal project F1R-MTH-PUL-09MRDO of the University of Luxembourg