Properties of batch means from stationary ARMA time series

Kang, Keebom; Schmeiser, Bruce W.

doi:10.1016/0167-6377(87)90005-8

Cited by 15 publications

(8 citation statements)

References 12 publications

(5 reference statements)

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“…Furthermore, the simplicity of the UBM chart is an important benefit, since it avoids the need for ARMA modeling. Kang and Schmeiser (1987) showed how averaging within subgroups dilutes autocorrelation in ARMA processes.…”

Section: Dr Willemain Is An Associate Professor In the Department Ofmentioning

confidence: 99%

“…They recommend that the batch size be selected so as to reduce the lag one autocorrelation of the batch means to approximately 0.10. Table 3 uses the results of Kang and Schmeiser (1987) to estimate the required batch size for AR(l) models depending on the autocorrelation cp. It also shows the corresponding values of UUBM and UWBM the unweighted and weighted batch means, respectively.…”

Section: The U Nweighted Batch Means Chartmentioning

confidence: 99%

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Model-Based and Model-Free Control of Autocorrelated Processes

Runger

Willemain

1995

Journal of Quality Technology

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Advances in automated sampling technology have made autocorrelated data commonplace. Positive autocorrelation degrades control charts designed by classical methods. If a correct time-series model of the autocorrelated process is available, many have advocated the use of control charts on the residuals from the model. Using the average run length criterion in an AR(l) model, we show that plotting averages of batches of the raw data can be an effective alternative to plotting residuals. We consider both weighted averages and the simple, model-free approach of arithmetic averages. We compare these statistics to residuals in both Shewhart and cumulative sum (CUSUM) control charts.

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Section: Dr Willemain Is An Associate Professor In the Department Ofmentioning

confidence: 99%

Section: The U Nweighted Batch Means Chartmentioning

confidence: 99%

Model-Based and Model-Free Control of Autocorrelated Processes

Runger

Willemain

1995

Journal of Quality Technology

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“…Kang and Schmeiser [9] showed how averaging within subgroups shrink the autocorrelation of the observations. There are empirical procedures for determining an appropriate batch size, suggested by Law and Carson [10] and Fishman [11,12].…”

Section: Introductionmentioning

confidence: 99%

“…In Table 1, the minimum required batch sizes for AR(1) models, depending on the autocorrelation coefficient φ, estimated by Kang and Schmeiser [9], are presented.…”

Section: Introductionmentioning

confidence: 99%

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Identifying the mean step change of UBM chart

Saghaei

Mosanna

Najafi³

2011

Int J Adv Manuf Technol

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The traditional control charts are developed based on the assumption that the successive observations are independent and identically distributed. In some processes, the independence assumption is violated when there is autocorrelation between observations. To solve this problem, two methods, classified as model-based and model-free, could be applied. When a control chart alarms an assignable cause, it is essential to detect the process change point in order to remove the root cause. In the presence of autocorrelated data, different methods for change-point identification have been applied only for model-based methods. Hence, this is considered as the research gap and an attempt is made to fill this gap by applying maximum likelihood function in unweighted batch mean control chart, one of the most applied model-free methods. In this article, an estimator is presented to determine the change point for the first-order autoregressive process, AR(1). When a real change occurs, the performance of proposed estimator is evaluated through simulation.

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On coverage probability, independence and normality in batch means algorithms

Adam

Klein

1989

European Journal of Operational Research

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Properties of batch means from stationary ARMA time series

Cited by 15 publications

References 12 publications

Model-Based and Model-Free Control of Autocorrelated Processes

Model-Based and Model-Free Control of Autocorrelated Processes

Identifying the mean step change of UBM chart

On coverage probability, independence and normality in batch means algorithms

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