University of Newcastle upon Tyne

School of Mathematics and Statistics

Statistics Seminars 2004-2005

29 October 2004, M414, 2:00pm or 3:00pm

Dr Kostas Triantafyllopoulos

Abstract

In this paper for oral presentation we discuss novel aspects of feedback adjustment for process improvement. The exponentially weighted moving average (EWMA) model has been applied to a process controlling the thickness of nitride layers in the manufacture of microelectronic devices, involving the standard use of the notions of EWMA control chart, EWMA full adjustment and EWMA deadband adjustment charts for process monitoring and process improvement, as described in Box and Luceno (1997). We suggest that a dynamic step forward to process improvement is gained by considering basic state space models, which are known as local level models. Such models are documented in West and Harrison (1997) and are illustrated in Godolphin (2001) for process control in a seasonal context. Local level models have been applied with success to network security and software engineering, see Triantafyllopoulos and Pikoulas (2002). Since the EWMA predictor is a limiting form of the forecast of th! e local level model, we are able to propose replacing the EWMA by local level models and thus develop relevant feedback adjustment schemes. This proposed forecasting scheme is found to have a better performance than the usually applied EWMA especially when a small number of data is available. A benefit of the proposed model is that the entire forecast distribution is obtained easily, thus providing further insights into process control with state space models. A detailed development of the proposed state space adjustment scheme is given to the nitride layers process and a number of conclusions and recommendations are made.

Box, G.E.P. and Luceno, A. (1997) Statistical Control by Monitoring and Feedback Adjustment. Wiley, New York.

Godolphin, E.J. (2001) Observable trend projecting state space models. J. Appl. Stat., 28, 379-389.

Triantafyllopoulos, K. and Pikoulas, J. (2002) Multivariate Bayesian regression applied to the problem of network security. J. Forecast., 21, 579-594.

West, M. and Harrison, P.J. (1997) Bayesian Forecasting and Dynamic Models, 2nd edition. Springer-Verlag, New York.

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