Generalized reliability bounds for coherent structures

In this article we introduce generalizations of several well-known reliability bounds. These bounds are based on arbitrary partitions of the family of minimal path or cut sets of the system and can be used for approximating the reliability of any coherent structure with i.i.d. components. An illustration is also given of how the general results can be applied for a specific reliability structure (two-dimensional consecutive-k1 × k2-out-of-n1 × n2 system) along with extensive numerical calculations revealing that, in most cases, the generalized bounds perform better than other available bounds in the literature for this system.