State Estimation for Integrated Moving Average Processes in High-Mix Semiconductor Manufacturing

High-mix manufacturing in the semiconductor industry has driven the development of several nonthreaded state estimation methods. These methods share information among different manufacturing contexts and avoid data segregation that threaded methods require. However, existing nonthreaded methods consider either white noise disturbance or integrated white noise disturbance. In this work, we derive the state-space representation of the nonthreaded state estimation problem. The derivation considers an integrated moving average (IMA) disturbance, which is more realistic than white noise or integrated white noise disturbance for most semiconductor processes. In addition, the derivation considers the fact that if a context item is not involved in a process run, then its state does not change. Finally, we propose an improved nonthreaded state estimation method based on the Kalman filter. Simulations examples are given to demonstrate the performance of the proposed method, which is also compared with the existing Kalman filter approach, which considers integrated white noise only. A practical modification of the improved Kalman filter is also proposed to significantly simplify the implementation while providing comparable state estimation performance.