Optimal design of systems with competing failure modes

Consider the problem of achieving optimal system size, n, and threshold value, k, for {k, n-k+1}-out-of-n and majority systems with competing failure modes. Components are s-independent and identically distributed, and the two system failure modes can have different costs. The authors determine optimal k, given n; optimal n, given k; and optimal k,n. Optimal implies minimum mean system cost for the {k, n-k+1}-out-of-n or majority system. The authors study the behavior of the optimal k as a function of failure probabilities, and of maximizing the reliability of majority systems. Numerical examples illustrate the results