Monitoring variability of autocorrelated processes using standardized time series variance estimators
Abstract
We consider the problem of monitoring variability of autocorrelated processes. This paper combines variance estimation techniques from the simulation literature with a statistical process control chart from statistical process control (SPC) literature. The proposed SPC method does not require any assumptions on the distribution of the underlying process and uses a variance estimate from each batch as a basic observation. The control limits of the chart are determined analytically. The proposed chart is tested using stationary processes with both normal and non-normal marginals.
References
[1]
Alexopoulos, C., D. Goldsman, and R. F. Serfozo. 2005. Stationary processes: statistical estimation. In The Encyclopedia of Statistical Sciences, ed. N. L. Johnson, and C. B. Read, 2nd edition. New York: John Wiley & Sons.
[2]
Billingsley, P. 1968. Convergence of probability measures. New York: John Wiley & Sons.
[3]
Chiu, C. C., M.-K. Chen, and K.-M. Lee. 2001. Shifts recognition in correlated process data using a neural network. International Journal of Systems Science 32:137--143.
[4]
Cook, D. F., and C. C. Chiu. 1998. Using radial basis function neural networks to recognize shifts in correlated manufacturing process parameters. IIE Transactions 30:227--234.
[5]
Cook, D. F., C. W. Zobel, and Q. J. Nottingham. 2001. Utilization of neural networks for the recognition of variance shifts in correlated manufacturing process parameters. International Journal of Production Research 39:3881--3887.
[6]
Goldsman, D., K. Kang, and A. F. Seila. 1999. Craméer-von Mises variance estimators for simulations. Operations Research 47:299--309.
[7]
Johnson, R. A., and M. Bagshaw. 1974. The effect of serial correlation on the performance of CUSUM tests. Technometrics 16:103--112.
[8]
Kim, S.-H. 2006. Distribution-free SPC methods for monitoring variability of autocorrelated processes. Technical Report, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia.
[9]
Kim, S.-H., C. Alexopoulos, D. Goldsman, and K.-L. Tsui. 2006a. A model-free CuSum procedure for autocorrelated processes. Technical Report, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia.
[10]
Kim, S.-H., C. Alexopoulos, K.-L. Tsui, and J. R. Wilson. 2006b. A distribution-free tabular CUSUM chart for autocorrelated data. IIE Transactions, forthcoming.
[11]
Lada, E. K., and J. R. Wilson. 2005. A wavelet-based spectral procedure for steady-state simulation analysis. To appear in European Journal of Operational Research.
[12]
Lu, C.-W., and M. R. Reynolds, Jr. 1999. Control charts for monitoring the mean and variance of autocorrelated processes. Journal of Quality Technology 31:25--274.
[13]
Reynolds, M. R., Jr. and C.-W. Lu. 1997. Control charts for monitoring processes with autocorrelated Data. Nonlinear Analysis, Theory, Methods, and Applications 30:4059--4067.
[14]
Runger, G. C. and T. R. Willemain. 1995. Model-based and model-free control of autocorrelated processes. Journal of Quality Technology 27:283--292.
[15]
Shapiro, S. S., and M. B. Wilk. 1965. An analysis of variance test for normality (complete samples). Biometrika 52:591--611.
[16]
Schmeiser, B. W., and W. T. Song. 1989. Inversetransformation algorithms for some common stochastic processes. In Proceedings of the 1989 Winter Simulation conference, ed. E. A. MacNair, K. J. Musselman, and P. Heidelberger, 490--496.
[17]
Schruben, L. W. 1983. Confidence interval estimation using standardized time series. Operations Research 31:1090--1108.
[18]
von Neumann, J. 1941. Distribution of the ratio of the mean square successive difference to the variance. The Annals of Mathematical Statistics 12:367--395.
[19]
Yashchin, E. 1993. Performance of CUSUM control schemes for serially correlated observations. Technometrics 35:37--52.
- Monitoring variability of autocorrelated processes using standardized time series variance estimators
Recommendations
Properties of Standardized Time Series Weighted Area Variance Estimators
We wish to estimate the variance of the sample mean from a continuous-time stationary stochastic process. This article expands on the results of a technical note Goldsman and Schruben 1990 by using the theory of standardized time series to investigate ...
Standardized time series methods: variance estimation using replicated batch means
WSC '01: Proceedings of the 33nd conference on Winter simulationWe present a new method for obtaining confidence intervals in steady-state simulation. In our replicated batch means method, we do a small number of independent replications to estimate the steady-state mean of the underlying stochastic process. In ...
Standardized Time Series LP-Norm Variance Estimators for Simulations
This paper studies a class of estimators for the variance parameter of a stationary stochastic process. The estimators are based on Lp norms of standardized time series, and they generalize previously studied estimators due to Schruben. We show that the ...
Comments
Information & Contributors
Information
Published In
December 2006
2429 pages
ISBN:1424405017
- Editors:
- L. Felipe Perrone,
- Barry G. Lawson,
- Jason Liu,
- Frederick P. Wieland,
- General Chair:
- David Nicol,
- Program Chair:
- Richard Fujimoto
Sponsors
- IIE: Institute of Industrial Engineers
- ASA: American Statistical Association
- IEICE ESS: Institute of Electronics, Information and Communication Engineers, Engineering Sciences Society
- IEEE-CS\DATC: The IEEE Computer Society
- SIGSIM: ACM Special Interest Group on Simulation and Modeling
- NIST: National Institute of Standards and Technology
- (SCS): The Society for Modeling and Simulation International
- INFORMS-CS: Institute for Operations Research and the Management Sciences-College on Simulation
Publisher
Winter Simulation Conference
Publication History
Published: 03 December 2006
Check for updates
Qualifiers
- Article
Conference
WSC06
Sponsor:
- IIE
- ASA
- IEICE ESS
- IEEE-CS\DATC
- SIGSIM
- NIST
- (SCS)
- INFORMS-CS
Acceptance Rates
WSC '06 Paper Acceptance Rate 177 of 252 submissions, 70%;
Overall Acceptance Rate 3,413 of 5,075 submissions, 67%
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 175Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 07 Mar 2025
Other Metrics
Citations
View Options
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in