We suppose that a production process may be in any one of a countable number of states and that the quality of the item produced is a function of this underlying state. It is also supposed that the state of the process at time t is not known and only becomes known when an item is sampled. We suppose that there are inspection, production, and revision costs and provide a framework for handling problems of this nature. We also treat in detail a 2-state version of this problem, and in this case show that the optimal policy does not necessarily have the three region structure which intuition suggests.