A continuum structure function is a nondecreasing mapping from the nonnegative orthant to the nonnegative real numbers which determines the state of a system from the states of its components. It is supposed that the various components can be divided into types such that only components of the same type may be interchanged. Such an interchange, called a cannibalization, is performed to increase system reliability when spare parts or repair facilities are not available. The cannibalization operation induces a new structure function whose properties are examined in detail; in particular, the Block-Savits decomposition is extended to such functions. Optimal cannibalizations are deduced for some special cases.