Reliability bounds for multistage structures with independent components

In this note, the lower bound and the upper bound on the reliability of a coherent multistage system are considered for independent components. The main tool used to obtain these bounds is the theory of Markov chains on lattices of structure states. Such a reliability structure is described as a family of convex sets. Numerical examples show the relationships between the bounds presented in this paper and the bounds obtained by Fu and Koutras (1995) for bridge structure and for structures derived from a projective plane of rank 2.