SPC Monitoring and Variance Estimation
According to W. Shewhart, process variation can be classified into assignable cause and common cause variations. Assignable cause variation can be eliminated by statistical process control (SPC) methods through identification and elimination of the root cause of the process shift. Common cause variation is inherent in the process and is generally difficult to reduce by SPC methods. However, if the common cause variation can be modeled by an autocorrelated process and physical variables are available to adjust the output, the common cause variation can be reduced by automatic process control (APC) methods through feedback/feedforward controllers. Integration of SPC and APC methods can result in major improvements in industrial efficiency.
Most SPC monitoring methods and traditional APC process adjustment methods (such as those based on one-step-ahead minimum mean squared error predictors or proportional integral derivative controllers) involve one or both of the following two steps: (i) “whitening” the process by subtracting a predictor and (ii) monitoring the prediction errors with appropriate control limits. This paper reviews common process monitoring and adjustment methods for process control of autocorrelated data, including model-free methods based on batch means, and investigates the general relationships and properties of the underlying models.
KeywordsControl Chart Minimum Mean Square Error Exponentially Weighted Move Average Statistical Process Control Exponentially Weighted Move Average Chart
Unable to display preview. Download preview PDF.
- 1.Adams, B.M., I. T. Tseng. 1998. Robustness of forecast-based monitoring systems. Journal of Quality Technology 30 328–339.Google Scholar
- 2.Alexopoulos, C., G.S. Fishman, A.F. Seila. 1997. Computational experience with the batch means method. In Proceedings of the 1997 Winter Simulation Conference, 194–201. IEEE, Piscataway, NJ.Google Scholar
- 4.Alexopoulos, C., D. Goldsman, G. Tokol, N. Argon. 2001. Overlapping variance estimators for simulations. Technical Report, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA.Google Scholar
- 5.Alexopoulos, C., A.F. Seila. 1998. Output data analysis. In Handbook of Simulation, J. Banks (ed.), 225–272. John Wiley and Sons, New York.Google Scholar
- 8.Alwan, L.C., H.V. Roberts. 1988. Time-series modeling for statistical process control. Journal of Business and Economic Statistics 6 87–95.Google Scholar
- 14.Cryer, J.D., T.P. Ryan. 1990. The estimation of sigma for an X chart: MR/d2 or S/d 4? Journal of Quality Technology 22 187–192.Google Scholar
- 16.Fishman, G.S. 1998. LABATCH.2 for analyzing sample path data. Technical Report UNC/OR. TR-97/04, Department of Operations Research, University of North Carolina, Chapel Hill, NC.Google Scholar
- 18.Foley, R.D., D. Goldsman. 2001. Confidence intervals using orthonormally weighted standardized times series. To appear in ACM Transactions on Modeling and Computer Simulation.Google Scholar
- 28.Meketon, M.S., B.W. Schmeiser. 1984. Overlapping batch means: Something for nothing? In Proceedings of the 1984 Winter Simulation Conference, 227–230. IEEE, Piscataway, NJ.Google Scholar
- 29.Montgomery, D.C. 1996. Introduction to Statistical Quality Control, 3rd edition. John Wiley and Sons, New York.Google Scholar
- 30.Montgomery, D.C., C.M. Mastrangelo. 1991. Some statistical process control methods for autocorrelated data, Journal of Quality Technology 23 179–204.Google Scholar
- 31.Montgomery, D.C., W.H. Woodall (eds.). 1997. A discussion on statisticallybased process monitoring and control. Journal of Quality Technology 29 121–162.Google Scholar
- 32.Pedrosa, A.C., B.W. Schmeiser. 1994. Estimating the variance of the sample mean: Optimal batch size estimation and 1-2-1 overlapping batch means. Technical Report SMS94-3, School of Industrial Engineering, Purdue University, West Lafayette, IN.Google Scholar
- 33.Runger, G.C., T.R.. Willemain. 1995. Model-based and model-free control of autocorrelated processes. Journal of Quality Technology 27 283–292.Google Scholar
- 39.Sherman, M., D. Goldsman. 2001. Large-sample normality of the batch means variance estimator. To appear in Operations Research Letters.Google Scholar
- 40.Shewhart, W.A. 1931. Economic Control of Quality of Manufactured Product. Van Nostrand, New York.Google Scholar
- 49.Woodall, W.H. 1999. Control charting based on attribute data: Bibliography and Review. Journal of Quality Technology 29 172–183.Google Scholar
- 50.Woodall, W.H., D.C. Montgomery. 1999. Research issues and ideas in statistical process control. To appear in Journal of Quality Technology.Google Scholar
- 51.Woodall, W.H., K.-L. Tsui, G.R. Tucker. 1997. A Review of statistical and fuzzy quality control charts based on categorical data. In Frontiers in Statistical Quality Control, 83–89. Physica-Verlag, Heidelberg, Germany.Google Scholar