In a screening inspection, all of the items are subject to acceptance inspection. If an item fails to meet the predetermined specification limits, it is rejected. In this research, we consider the economic model for determining the most profitable initial process mean and the length of resetting cycle in a tool-wear process in which there is a linear shift in the process mean. Profit models are constructed which involve selling price, scrap, resetting, production, and inspection costs when the rates of process mean shift are constant and uniformly distributed, respectively. Assuming that the quality characteristic of interest is normally distributed, the optimum initial process mean and the length of resetting cycle are jointly obtained by maximizing the expected profit per unit time. An illustrative example from tube-rolling process is given and numerical studies are performed.