Inspection logistics planning for multi-stage production systems with applications to semiconductor fabrication lines

Since the market for semiconductor products has become more lucrative and competitive, research into improving yields for semiconductor fabrication lines has lately received a tremendous amount of attention. One of the most critical tasks in achieving such yield improvements is to plan the in-line inspection sampling efficiently so that any potential yield problems can be detected early and eliminated quickly. We formulate a multi-stage inspection planning model based on configurations in actual semiconductor fabrication lines, specifically taking into account both the capacity constraint and the congestion effects at the inspection station. We propose a new mixed First-Come-First-Serve (FCFS) and Last-Come-First-Serve (LCFS) discipline for serving the inspection samples to expedite the detection of potential yield problems. Employing this mixed FCFS and LCFS discipline, we derive approximate expressions for the queueing delays in yield problem detection time and develop near-optimal algorithms to obtain the inspection logistics planning policies. We also investigate the queueing performance with this mixed type of service discipline under different assumptions and configurations. In addition, we conduct numerical tests and generate managerial insights based on input data from actual semiconductor fabrication lines. To the best of our knowledge, this research is novel in developing, for the first time in the literature, near-optimal results for inspection logistics planning in multi-stage production systems with congestion effects explicitly considered.