In this thesis, a cost based process control model is formulated. A dynamic programming approach is used and along with the techniques of Bayesian decision theory, an optimal set of steady state control policies are shown to exist which are dependent upon prior beliefs about the condition of the process. It is the objective of this thesis to compare the results obtained from this approach to those of an X̅ control chart approach. The model proposed by Knappenberger and Grandage [20] is used as a basis for comparison. Numerical examples are used to illustrate each procedure. The results obtained illustrate that by using the operating policies specified by the dynamic approach, a savings of from 29% to 40% in the optimal cost per unit to operate the quality control procedure can be achieved rather than utilizing the policies of the X̅ control chart model. / Master of Science