Review of reliability bounds for consecutive-k-out-of-n systems

This paper reviews many lower and upper bounds for consecutive-k-out-of-n systems presented over the last three decades. The reason is a revived interest to accurately estimate the reliability of (very) large consecutive systems, where exact calculations can be challenging. Main examples are novel nano-architectures targeting FinFETs, nano-magnetic and molecular technologies (where accurate estimations of reliability are of high interest), as well as their associated nanoscale communications (where the reliability of transmission needs to be assessed), which map well onto (very) large consecutive systems.