Consider a production process where items are produced continuously. A lower limit is specified for the quality characteristic of interest, and an item is defective if its value of the quality characteristic is smaller than the specification limit. The process mean (target value) may be set higher to reduce the costs incurred by producing defective items. Using a higher process mean, however, results in a higher production cost when production cost is an increasing function of the quality characteristic. An inspection procedure is used to screen outgoing items from the defective ones. In this paper, we consider a situation where inspection is based on a surrogate variable instead of the quality characteristic of interest. A model is developed to jointly determine the most economical process mean and the inspection specification limit.