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.

中文翻译：

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具有处理时间变化的单臂聚类工具的后退序列分析

本文分析具有处理时间变化的单臂集群工具的向后顺序。实际上，后向序列通常用于操作单臂集群工具，但是在引入处理时间变化时尚未分析其性能。为了解决这个问题，我们首先定义一个基本周期，并考虑到处理时间的变化，得出用于周期时间分析的公式。然后，我们开发出对于某个周期或所有周期，向后顺序最佳的条件。我们还分析了平均循环时间与反向序列的上限。最后，通过实验研究了具有处理时间变化的反向序列的性能。执业者注意 —使用了处理模块（PM）中的处理时间变化来分析广泛用于调度单臂集群工具的反向序列。在确定的处理时间下，向后顺序在许多情况下被证明是最佳的。但是，实际上，PM中的晶片处理时间不是确定性的，而是在给定的时间范围内变化的。关于此问题，我们分析了具有处理时间变化的反向序列的性能。这项研究不仅对工具工程师有很大帮助，而且对有兴趣安排自动化制造系统的研究人员也非常有帮助。