Joint reliability of linear two-dimensional consecutive k-type systems with shared components

Abstract

In this paper, linear two-dimensional consecutive $k$-type systems with shared components are considered for the first time. This includes the cases of linear connected-$(k,r)$-out-of-$(m,n)$: F systems, linear connected-$(k,r)$-or-$(r,k)$-out-of-$(m,n)$: F systems, linear $l$-connected-$(k,r)$-out-of-$(m,n)$: F systems without/with overlapping, and linear $l$-connected-$(k,r)$-or-$(r,k)$-out-of-$(m,n)$: F systems without/with overlapping. Using Kronecker product, finite Markov chain imbedding approach (FMCIA) is applied in a new way to derive the joint reliability functions of these two-dimensional consecutive $k$-type systems with shared components. Their accuracy and computational efficiency are illustrated with the use of some numerical examples. Finally, some concluding remarks are provided.