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

In this paper we give new lower and upper bounds on the failing probability or reliability of consecutive k-out-of-r-from-n:F reliability systems. They belong to the family of Boole–Bonferroni type bounds. Further we propose the application of the Hunter–Worsley bound in the framework of reliability system analysis. 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.