Linear One/Two/Three-Dimensional Consecutive k-Type Systems with Cascading Component Failures

Abstract

Cascading failures are encountered commonly in various practical systems. As one of the most well-known models in reliability, consecutive k-type systems, especially two/three-dimensional ones, have not been studied under the assumption of cascading component failures. In this paper, we consider cascading component failures based on generalized urn model for some linear one/two/three-dimensional consecutive k-type systems. These systems include linear consecutive-k-out-of-n: F systems, linear l-consecutive-k-out-of-n: F systems without/with overlapping, and their two/three-dimensional versions. By applying finite Markov chain imbedding approach (FMCIA) via an original manner, reliability functions of these systems are derived together with several illustrative examples.