Untying of clutter-family supports and its role in the monotone-structure reliability theory (Q1347399)

The paper deals with a transformation of supports of a clutter family. It is a natural generalization of the untying transformation of a one-clutter support previously introduced by the same author. It is shown that the new transformation does not decrease the reliability of the corresponding clutter sum. The new bounds for the clutter-sum reliability are given. It is demonstrated that the untying transformation of clutter-family supports and the factor transformation introduced by McDiarmid provide a combinatorial basis for the monotone-structure reliability theory. The paper has a cognitive character and is addressed to researches working in the area of system reliability theory.