The main goal of this article is to show that the lower and upper bounds on the failing probability resp. reliability of consecutive k-out-of-rfrom-n:F reliability systems developed by Sfakianakis, Kounias and Hillaris [M. Sfakianakis, S. Kounias, A. Hillaris, IEEE Trans Reliability 1992;R-41:442–447] can be improved by applying fourth order Boole… (More)