A model is developed for locating quality monitoring stations in a multi-stage production system and determining the parameters of the np-chart (sample size, acceptance number and sampling interval) used at each quality monitoring station. Each production stage can shift to an out-of-control state associated with an assignable cause. Various cost, profit and time elements are included in the derivation of the net profit per unit function. Dynamic programming and direct search techniques are used to maximize this expected net profit per unit function across the production system. Numerical examples and sensitivity analysis of the model are presented.