Missing data estimation for run-to-run EWMA-controlled processes

The problem of metrology delay leading to missing outputs is solved using the disturbance model for a run-to-run EWMA-controlled process which is assumed to have an integrated moving average disturbance of first order. A minimum norm estimation method coupled with Tikhonov regularization is developed and compared with other ad hoc techniques. Simulations are then carried out to investigate disturbance model mismatch, gain mismatch and different sampling rates. A state-space representation of the data is applied to a combination of the forward and backward Kalman filter to obtain the missing values. A modification that uses the minimum norm solution as initial estimates for the Kalman filter is compared with previous methods. We then analyze manufacturing data from an etch process to see how the method performs for different sampling rates. A cumulative study of all datasets involved is also carried out to see which method gives the lowest mean squared error.