New bounds on the reliability of the consecutive k-out-of-r-from-n:F system

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-r-from-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–Bonferroni bounds. Further we propose the application of the Hunter–Worsley bound in the framework of reliability system analysis, too. Numerical results of the formerly published test examples and harder problems are given. The computer code was written in Fortran and is available on request from the authors.