A description is given of the interacting effects which exist between quality control stations associated with the various stages of manufacture of a product, and how these interactions influence the optimal choice of sampling plan for a given station. The applicability of the mathematical theory of dynamic programming to the design of an optimal sequence of such interrelated plans is demonstrated, along with a general description of this theory. In order to illustrate the dynamic programming solution procedure, a digital computer program is discussed which solves a simplified version of the above design problem. Extension of this program to the solution of more general multistage decision problems is also considered.