A Markov Quality Control Process Subject to Partial Observation

This paper studies the problem of optimally controlling a discrete-time production process with countable state space which is subject to one of three control settings at each time interval: produce, inspect while producing, or repair (revise) the process. The cost of the item produced and the inspection and repair costs are assumed dependent on the state of the production process. It is assumed that the inspector-decisionmaker receives imperfect on-line observations of the production process at both times of production and inspection. Bounds on optimal cost are obtained. For the two-state case, several results associated with observation quality are determined which are sufficient for particularly simple characterizations of an optimal policy. Generalizations of several results due to Ross are also presented.