On a sequential Markovian decision procedure with incomplete information

Abstract Sequential Markov decision procedures, when only imperfect knowledge of states are available, are discussed for a replacement problem. The situations considered are, 1. (1) states can be known exactly at a cost, 2. (2) states can be known imperfectly, at a cost, by means of observing an associated relevant random variable and 3. (3) states unknown and observation impossible. Optimal procedure are obtained for the various cases. In case (2) the theory of Sequential Analysis is found helpful for obtaining approximations to the optimal procedure.