Mixed-product Run to Run Control Algorithm using Bayesian method

To improve the performance of exponentially-weighted moving average (EWMA) controller and detect the system's faults in the high mixed semiconductor manufacturing processes, the states of tools and products should be estimated firstly. The common algorithm is to construct the context matrix according to the product fabricating thread, and estimate those states using the Moore-Penrose pseudo-inverse. Although the algorithm works well, the computational burden is high. In this paper, a new state estimation algorithm which combines the Bayesian statistical theory and analysis of variance (ANOVA) method is proposed. Firstly, an unknown probability density function is calculated recursively using incoming observations. Then the relative states of tools and products is estimated without calculating the inverse of context matrix. Comparing to the threaded EWMA (t-EWMA) algorithm, the presented method provides better performance, which is confirmed using the simulation studies.