Algebraic Analysis of Variants of Multi-State <i>k</i>-out-of-<i>n</i> Systems

• Main Authors: Patricia Pascual-Ortigosa, Eduardo Sáenz-de-Cabezón
• Format: Article
• Language: English
• Published: MDPI AG 2021-08-01
• Series: Mathematics
• Subjects: multi-state systems; <i>k</i>-out-of-<i>n</i> systems; algebraic reliability; monomial ideals
• Online Access: https://www.mdpi.com/2227-7390/9/17/2042
• ISSN: 2227-7390

We apply the algebraic reliability method to the analysis of several variants of multi-state <i>k</i>-out-of-<i>n</i> systems. We describe and use the reliability ideals of multi-state consecutive <i>k</i>-out-of-<i>n</i> systems with and without sparse, and show the results of computer experiments on these kinds of systems. We also give an algebraic analysis of weighted multi-state <i>k</i>-out-of-<i>n</i> systems and show that this provides an efficient algorithms for the computation of their reliability.