Statistical design of double EWMA controller

Sheng‐Tsaing Tseng · Rouh‐Jane Chou · Shui‐Pin Lee

34 citations0/0 files storedApplied Stochastic Models in Business and Industry

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Advanced Statistical Process Monitoring Control Systems and Identification Fault Detection and Control Systems

Abstract

Abstract The double exponentially weighted moving average (dEWMA) feedback controller is a popular run‐by‐run (RbR) control scheme for adjusting certain semi‐conductor manufacturing process with a linear drift. Del Castillo (IIE Trans. 1999; 31:1157) introduced an interesting state–space representation of the process output of this control scheme, and then the long‐term stability conditions of this closed‐loop system can be derived. The results; however, are very restricted to the case when the process disturbance follows a white noise series or an IMA(1, q) series. For a general process disturbance such as an ARIMA(p, d, q) model, it is not easy to obtain a state–space representation of the process output of this controller. Hence, some statistical properties (such as stability conditions and process yield) of this controller cannot be addressed by using the state–space theory. To overcome this difficulty, this paper first proposed an analytical expression for the process output of this dEWMA controller. Then the stability conditions and the optimal discount factors of this control scheme (based on the criterion of minimizing the average process fallout rate) can be obtained successfully. Finally, we also address some concluding remarks at the end of this paper. Copyright © 2002 John Wiley & Sons, Ltd.

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References

1971Time Series Analysis Forecasting and Control 1997Statistical control by monitoring and feedback adjustment 1995Run by run process control: combining SPC and feedback control 1998Statistical Control by Monitoring and Feedback Adjustment 1993Stability and Sensitivity of an EWMA Controller 1999Long run and transient analysis of a double EWMA feedback controller 2002A study on a multivariate EWMA controller

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2009The optimal drift-compensatory and fault tolerant approach for mixed-product run-to-run control 2006Variable EWMA run-to-run controller for drifted processes 2010An EWMA Algorithm With a Cycled Resetting (CR) Discount Factor for Drift and Fault of High-Mix Run-to-Run Control 2006Statistical process adjustment: a brief retrospective, current status, and some opportunities for further work 2005Sample-Size Determination for Achieving Asymptotic Stability of a Double EWMA Control Scheme 2011Avaliação da distribuição de sementes por uma semeadora de anel interno rotativo utilizando média móvel exponencial

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