An economic model is developed for determining optimal locations of screening inspection stations in a multistage production system. The effect of screening inspection on the production rate is explicitly considered, and a fixed cost for maintaining an inspection station is assumed. The product is allowed to have multiple defects, each of which may be inspected at any inspection station after the defect-generating operation. The problem is formulated as a mixed 0-1 linear program which offers the advantage of versatility in handling various system constraints.