Deterministic Flow Lines With Applications

Abstract

We demonstrate that flow line models with deterministic service times and an arbitrary arrival process may be exactly decomposed into segments that each exhibit similar behavior. We call the segments channels and demonstrate that this decomposition leads to a recursion for the delay experienced by customers within the system. The consequence, in addition to clearly elucidating the manner in which customers advance, is that the state of a flowline at any time can be completely characterized by a handful of parameters per channel. The recursions and channel decomposition allow us to model a class of state dependent failures that are common in certain cluster tools in semiconductor wafer manufacturing. Using the fact that wafers are typically grouped into batches, we are able to reduce the computation required to simulate the wafer advancement by about 50 times. The models have been tested with data from a clustered photolithography tool in production and provide throughput and process time predictions within 0.5% and 3% of the actual performance, respectively. Note to Practitioners-Flow line models can be used to model assembly lines, tandem manufacturing systems, and robotic work cells such as cluster tools. In semiconductor wafer fabrication, generic cluster tools have become increasingly important and the class of clustered photolithography tools are essential to production. We develop deterministic flow line models allowing for setups that depend on the location of wafers within a tool. A reduction in computational complexity is achieved by noting that wafers are often grouped into wafer lots. Tests of the models against actual production data for clustered photolithography tools have shown that the reduction in computation required to simulate production with setups is on the order of 50 times, while still achieving a throughput and cycle time accuracy of 0.5% and 3%, respectively. Thus, for important classes of tools, the models are good candidates for use in simulation and to determine a tool's intrinsic equipment loss ( that is, the throughput loss caused by setups, tool structure, and tool failures).