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This paper proposes a new model which generalizes the linear consecutive k-out-of-r-from-n system to the case of multiple failure criteria. In this model, the system consists of n linearly ordered elements, and fails iff in any group of r1,...,rH consecutive elements less than k1,...,kH elements respectively are in a working state. An algorithm for system reliability evaluation is suggested which is based on an extended universal moment generating function. Examples of system reliability evaluation are presented.