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

Abstract

We apply the algebraic reliability method to the analysis of several variants of multi-state k-out-of-n systems. We describe and use the reliability ideals of multi-state consecutive k-out-of-n 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 k-out-of-n systems and show that this provides an efficient algorithms for the computation of their reliability.

Keywords

• multi-state systems
• <i>k</i>-out-of-<i>n</i> systems
• algebraic reliability
• monomial ideals