M.Sc Student Gilenson-Zalevsky Miri Yield vs. Cycle Time Trade-off Analysis Department of Industrial Engineering and Management Dr. Liron Yedidsion Abstract

Control limits in use in quality monitoring operations are traditionally set by yield requirements. Since deviations from these limits usually trigger production station stoppage, the monitor design has a direct impact on the availability of the station, and thus on the cycle time (CT). We first develop a bi-criteria trade-off formulation between the expected CT and the die yield at a single station based on the impact of the control limits in a system monitored by inspection stations on both performance measures. We then extend our result by formulating the Pareto-Optimal set for an entire flow-shop network rather than just for a single station.

We consider a multi-step flow-shop network of m=1,?,M stations, each of which is immediately followed by an imperfect inspection operation. We assume production stations afflicted by a two-state particle deposition process whose rate can be either low or high. If the inspection indicates high deposition rate, the production is stopped for repair, which guarantees machine recalibration.

We explore the impact of the upper control limit of inspection operation m, (UCLm), on the expected yield and CT of production station m, denoted yieldm and CTm respectively. We model the station evaluation as a Markov Decision Process to obtain the expected run length and the expected contamination rate and to explicitly formulate yieldm and CTm as functions of  UCLm . While the expectation of  yieldm  is calculated using a closed-form equation, CTm  is obtained using a G/G/1 queuing model.

Once yieldm and CTm are well defined, we generate the trade-off curve between these two performance measures, where each point on the curve corresponds to a unique  UCLm  value for given station parameters. Constructing the trade-off curve between yieldm and CTm allows decision makers to select a Pareto-Optimal  UCLm  value that reflects best the importance of each measure. We develop a simple algorithm that ensures the trade-off curve is convex and thus Pareto-Optimal.

To extend our result to a flow-shop network, we present an optimal greedy algorithm that recommends a set of  UCLm  values for each point on the CT to yield Pareto-Optimal curve for the entire line. The CT of the line is approximated using an acceptable G/G/1 queuing network approximation technique. This technique allows us to construct the CT to yield Pareto-Optimal set for the entire network in a polynomial time.