New insights into the assessment of k-out-of-n and related systems

k-out-of-n and related systems have received much attention in the recent past years. Hundreds of articles were devoted to various methods to assess them. In this article, we show that there exist very efficient algorithms to compute the reliability of k-out-of-n, l-to-h-out-of-n and consecutive k-out-of-n systems. k-within-r-out-of-n systems are intrinsically much harder. We study the performance of binary decision diagrams (BDDs) on these systems. Then, we propose a new approximation scheme. This algorithm is much more efficient in practice than already proposed methods.