Confidence bounds for the reliability of a system from subsystem data

The paper is concerned with the construction of lower bounds for the reliability of a system when statistical data comes from independent tests of its elements. The overview of results known from literature and obtained under the assumption that elements in a system are independent is given. It has been demonstrated using a Monte Carlo experiment that in the case when these elements are dependent and when their dependence is described by Clayton and Gumbel copulas these confidence bounds are not satisfactory. New simple bounds have been proposed which in some practical cases have better properties than the classical ones.