(186b) Improved State Estimation for High-Mix Semiconductor Manufacturing

High-mix manufacturing in semiconductor industry has driven the development of several non-threaded state estimation methods in the past a few years [1-7], which share information among different manufacturing context and avoid data segregation that threaded methods require.  Assuming that the interaction among different contexts is linear, different algorithms such as linear regression [5-7] and the Kalman filter [1,2,6] have been applied to estimate the contributions from different variation sources. Among these methods, process disturbance is either modeled as a white noise disturbance [2,5,6] or as an integrated white noise disturbance [6,7]. However, it has been recognized that an integrated moving average (IMA) model provides much better approximation of the disturbances in industrial processes [8].

In this work, we extend the previously developed general framework [6]  for non-threaded state estimation to cover a more realistic case, where the state disturbance is modeled as an integrated moving average process. Specifically, we first derive the state-space representation of the non-threaded state estimation problem which not only considers the integrated moving average disturbance, but also considers the fact that if a context item is not involved in a process run then its state does not change. Then the Kalman filter is applied to estimate the state. We use simulation examples to evaluate the performance of the proposed non-threaded state estimation method, and compared with an existing Kalman filter approach which considers integrated white noise disturbance. Three case studies are given to examine the performance and robustness of the proposed method, and we confirm that the proposed approach can provide satisfactory state estimation performance no matter the actually state disturbance is an IMA process or not; in addition, we found that the state estimation performance is not sensitive to the tuning parameter, which enables easy tuning for the proposed method. Finally, we found that by explicitly considering the fact that if a context item is not involved in the process run then its state should not evolve, we modified the Kalman filter based on the integrated white noise model. The modified version performs significantly better than the original one.

References

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