On the mean number of remaining components in three-statek-out-of-nsystem

A three-state k -out-of- n system with n independent components is considered, where the vector k of integers is determined by given fixed scalars k 1 and k 2 such that k 1 , k 2 ? 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 n is also formulated.