Dynamic-moving-window scheme for virtual-metrology model refreshing

Virtual metrology (VM) is a method to conjecture manufacturing quality of a process tool based on data sensed from the process tool without physical metrology operations. Historical data is used to produce the initial VM models, and then these models are applied to operating in a process drift or shift environment. The accuracy of VM highly depends on the modeling samples adopted during initial-creating and online-refreshing periods. Since large resources are required, design-of-experiments may not be performed. In that case, how could we guarantee the stability of the models and predictions as they move into the unknown environment? Conventionally, static-moving-window (SMW) schemes with a fixed window size are adopted in the online-refreshing period. The purpose of this paper is to propose a dynamic-moving-window (DMW) scheme for VM model refreshing to enhance prediction accuracy. The DMW scheme adds a new sample into the model and applies a clustering technology to do similarity clustering. Next, the number of elements in each cluster is checked. If the largest number of the elements is greater than the predefined threshold, then the oldest sample in the cluster with the largest population is deleted. Both the adaptive-resonance-theory-2 and the newly proposed weighted-Euclidean-distance methods are applied to do similarity clustering.