Zero-One Law for the Non-Availability of Multistate Repairable Systems

Abstract

In a monotone system whose failure depends on a large number of independent components, the non-availability should increase abruptly over a relatively short interval of time. Our first step is a reliability interpretation of a result of Friedgut and Kalai.1 Then we prove a zero-one law which is more adapted in a reliability context. In the last section some multistate extensions of classical models are considered as examples.