Analysis of Backward Sequence for Single-Armed Cluster Tools With Processing Time Variations

This article analyzes the backward sequence for single-armed cluster tools with processing time variations. The backward sequence is popularly used to operate a single-armed cluster tool in practice, but its performance has not been analyzed when processing time variations are introduced. To address the problem, we first define a fundamental cycle and derive a formula for cycle time analysis considering processing time variations. We then develop conditions for which the backward sequence is optimal for a certain cycle or all cycles. We also analyze the upper bound of the average cycle time with the backward sequence. Finally, the performance of the backward sequence with processing time variations is investigated experimentally.
Note to Practitioners
—The backward sequence, which is widely used for scheduling single-armed cluster tools, is analyzed with processing time variations in processing modules (PMs). The backward sequence is proven to be optimal in many cases with deterministic processing times. However, in reality, the wafer processing time in a PM is not deterministic and varies within a given time range. With regard to this issue, we analyze the performance of the backward sequence with processing time variations. This study can be very helpful for not only tool engineers but also for researchers who are interested in scheduling automated manufacturing systems.