Algebraic reliability of multi-state $k$-out-of-$n$ systems

11 Apr 2020 · Pascual-Ortigosa Patricia, Sáenz-de-Cabezón Eduardo, Wynn Henry P. ·

In this paper we review different definitions that multi-state $k$-out-of-$n$ systems have received along the literature and study them in a unified way using the algebra of monomial ideals. We thus obtain formulas and algorithms to compute their reliability and bounds for it.