In this paper, we address a design problem and a case study of a K-stage back-light-unit(BLU) inspection system, which is composed of K stages, each of which includes an inspection process and a rework process. Assuming the type I, II errors and the inspection-free policy for items classified as good, we determine the smallest integer of K which can achieve a given target defective rate. If K does not exist, holding the current values of the type I, II errors, we search reversely the defective rate of an assembly line and the defective rate of a rework process, to meet the target defective rate. Our formulae and methodology based on a K-stage inspection system could be applied and extended to similar situations with slight modification.