Reliability bounds for two dimensional consecutive systems

In this paper we consider consecutive systems due to their potential for novel nano-architectures in general, where schemes able to significantly enhance reliability at low redundancy costs are expected to make a difference. Additionally, nanoscale communications are also expected to rely on structures and methods allowing to achieve better/lower transmission bit error rates. In particular, certain nano-technologies, like, e.g., nano-magnetic ones (but also nano-fluidic, molecular and even FinFETs), could be mapped onto consecutive systems, a well-established redundancy scheme. That is why this paper will start by briefly mentioning previous results for one dimensional linear consecutive-k-out-of-n: F systems with statistically independent components having the same failure probability q (i.i.d. components), before focusing on 2-dimensional consecutive systems. We shall introduce 2-dimensional consecutive systems and mention some variations, before going over a few upper and lower bounds for estimating their reliability. Afterwards, we shall present simulation results for particular 2-dimensional cases. These will show that some of the lower and upper bounds are able to perfectly match the exact reliability of 2-dimensional consecutive systems for the particular cases considered here. Conclusions and future directions of research are ending the paper.