ARMAX model based run-to-run fault diagnosis approach for batch manufacturing process with metrology delay

Abstract

In batch manufacturing process, the product quality data are often gained after several runs owing to the existence of the metrology delay. The metrology delay will affect the stability, performance and reliability of the process. In this paper, the batch processes with exponentially weighted moving average/double EWMA (EWMA/DEWMA) controller and metrology delay are represented by data-based autoregressive moving average with exogenous inputs (ARMAX) models instead of the mechanical models. A parameter-resetting recursive extended least square (PRELS) algorithm is proposed to identify the coefficients of this model. Comparing with traditional RELS algorithm, PRELS have faster convergence speed and higher accuracy when the coefficients greatly vary. The relationship of the process parameters and ARMAX model coefficients is derived. On basis of this, a statistical online fault diagnosis scheme is presented to detect and quickly identify a fault. Dynamic principal component analysis is used on the coefficients of ARMAX model which is stationary instead of the non-stationary process data to detect the process fault. Furthermore, the deviation of the faulty parameter is derived using a least-squares estimation, and the influence matrix algorithm is applied to achieve the online fault isolation. The validity and effectiveness of the proposed approach are illustrated through some simulation results in general semiconductor manufacturing processes.

Keywords:

• run-to-run fault diagnosis
• EWMA controller
• DEWMA controller
• ARMAX
• PRELS