A two-stage k-out-of-n system is a l-out-of-m system except that each of the m parts is itself a ki-out-of-ni system. The problem is to assign a set of Σmab36iŸ=1ni probabilities to the Σ’mab36iŸ=1ni components in the system to maximize its reliability. This paper considers the case ki=k for all i. It gives optimal assignments when the first stage is a parallel system or the second stage is a series system. The paper conjectures that the optimal assignment problems for all other two-stage k-out-of-n systems, are NP-complete, but it is able to prove this only when the second stage is a parallel system. It also proposes a heuristic assignment algorithm for the general case.
