In this paper, we address an optimization problem and a case study for minimizing the cost of inspections incurred throughout an inspection system, which includes a K-stage inspection system, a source inspection shop, and a re-inspection shop. In order to formulate the inspection cost function, we make a time-based flow analysis between nodes (or shops), and derive the limiting sizes of flows between nodes and limiting defective rates by solving a set of nonlinear balance equations. It turns out that the number of items reworked throughout the inspection system is invariant irrespective of the defective rate of items moved through the K-stage inspection system. Hence we define the inspection cost as the total number of items inspected, and we provide an enumeration method for determining an optimal value of K which minimizes the number of items inspected.