Many manufacturing processes exhibit a decreasing pattern in the process mean during the course of production. The design of a manufacturing process includes a selection of the starting level and a control limit that determines when to reset the process back to the starting level. The costs to be minimized are the long-run average cost of production, adjustment, and loss for defective items. A cost model is developed that uses a more general assumption about the deterioration process than some previous models. Specifically, the deterioration of the process mean in a given time interval is assumed to be a random variable. The model treats the starting level as a policy parameter in the cost model. In addition to the optimal solution, simple approximate solutions are developed and shown to be more cost-effective than a simple linear policy often applied to this problem.