Analytical Model for Optimal Inspection Frequency with Consideration of Setup Inspections

Inspections are an essential component of the production process in semiconductor fabrication facilities. Inspection frequency influences the process yield as well as the production cost. It is therefore important to identify the optimal frequency by considering both aspects together. Several methods have been proposed in the literature for identifying optimal inspection frequencies. These methods assume that inspections occur only according to a single static rule of a constant predetermined frequency. In reality, inspections may occur due to other reasons, for example after every setup change, and are not necessarily static. In this paper we discuss the effect of setup inspections on the decisions about regular inspections. We show how to modify the basic model for inspection costs and excursion costs in view of setup inspections. We further show how to determine the optimal frequency in this case using our proposed model. We then discuss the potential benefits from using a dynamic inspection rule that makes inspection decisions with consideration of the expected number of batches until the next setup change.