Hilbert Functions in Design for Reliability
The algebraic approach to the analysis of system reliability associates an algebraic object, a monomial ideal, to a coherent system (CS), and studies the reliability of the system using the Hilbert series of the monomial ideal. New capabilities of the algebraic methodology in system design are shown, in specific connected to enumeration of operating states. The algebraic method ought to be a helpful tool in reliability, each for performing totally different computations on system features, and to review the structure of systems.
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