In this paper, we readdress the optimization problem for minimizing the inspection cost in a back-light unit inspection system, which forms a network including a K-stage inspection system, a source inspection shop, and a re-inspection shop. In order to formulate our objective function when the system is in a steady state, assuming that the number of nonconforming items in a lot follows a binomial distribution when a lot is formed for inspection, we make a steady-state network flow analysis between shops, and derive the steady-state amount of flows between nodes and the steady-state fraction defectives by solving a nonlinear balance equation. Finally we provide some fundamental properties and an enumeration method for determining an optimal value of K which minimizes our objective function. In addition, we compare our results numerically with previous ones.