On the mean number of remaining components in three-state kk-out-of-nn system

A three-state k-out-of-nn system with nn independent components is considered, where the vector k of integers is determined by given fixed scalars k1k1 and k2k2 such that k1,k2≤nk1,k2≤n. The mean number of components of each type either in a perfect functioning state or in a partially working state at the time of the system failure and at a time while the system is working are studied. An optimization problem concerned with the most economical value of nn is also formulated.