The Statistical Design of Cusum Charts

Woodall, William H.; Adams, Benjamin M.

doi:10.1080/08982119308918998

Cited by 116 publications

(56 citation statements)

References 16 publications

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“…Cumulative deviation is a visualization tool used in process control engineering to identify changes in statistical parameters. [6] Its expectation is a level trend, and a change in the measured parameter is readily observed as a positive or negative slope when plotting the cumulative sum of the deviations from expectation. All three statistics show apparent structure persisting over several hours with slopes beginning near T = 0.…”

Section: Methodsmentioning

confidence: 99%

Anomalous Anticipatory Responses in Networked Random Data

Nelson

Bancel²

2006

AIP Conference Proceedings

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Abstract.We examine an 8-year archive of synchronized, parallel time series of random data from a world spanning network of physical random event generators (REGs). The archive is a publicly accessible matrix of normally distributed 200-bit sums recorded at 1 Hz which extends from August 1998 to the present. The primary question is whether these data show non-random structure associated with major events such as natural or man-made disasters, terrible accidents, or grand celebrations. Secondarily, we examine the time course of apparently correlated responses. Statistical analyses of the data reveal consistent evidence that events which strongly affect people engender small but significant effects. These include suggestions of anticipatory responses in some cases, leading to a series of specialized analyses to assess possible nonrandom structure preceding precisely timed events. A focused examination of data collected around the time of earthquakes with Richter magnitude 6 and greater reveals non-random structure with a number of intriguing, potentially important features. Anomalous effects in the REG data are seen only when the corresponding earthquakes occur in populated areas. No structure is found if they occur in the oceans. We infer that an important contributor to the effect is the relevance of the earthquake to humans. Epoch averaging reveals evidence for changes in the data some hours prior to the main temblor, suggestive of reverse causation.

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Section: Methodsmentioning

confidence: 99%

Anomalous Anticipatory Responses in Networked Random Data

Nelson

Bancel²

2006

AIP Conference Proceedings

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“…We calibrated the charts to detect a 25% shift in Poisson rates and have an in-control average run length (ARL 0 ) of 370 approximately, close to a standard c-chart (see Woodall and Adams (1993)). The resultant Poisson CUSUM charts 22.4, 22) and 17.4, 14).…”

Section: Discussionmentioning

confidence: 96%

Bayesian change point estimation in Poisson-based control charts

2013

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Precise identification of the time when a process has changed enables process engineers to search for a potential special cause more effectively. In this paper, we develop change point estimation methods for a Poisson process in a Bayesian framework. We apply Bayesian hierarchical models to formulate the change point where there exists a step change, a linear trend and a known multiple number of changes in the Poisson rate. The Markov chain Monte Carlo is used to obtain posterior distributions of the change point parameters and corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the well-known c-, Poisson exponentially weighted moving average (EWMA) and Poisson cumulative sum (CUSUM) control charts for different change type scenarios. We also apply the Deviance Information Criterion as a model selection criterion in the Bayesian context, to find the best change point model for a given dataset where there is no prior knowledge about the change type in the process. In comparison with built-in estimators of EWMA and CUSUM charts and ML based estimators, the Bayesian estimator performs reasonably well and remains a strong alternative. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.

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“…His approximation requires a table of constants to apply and is accurate to within 1-3% of the true ARL value. Woodall and Adams [19] recommend the ARL approximation given by Siegmund [16] because of its simplicity.…”

Section: Let Imentioning

confidence: 99%

McUsum Control Chart Procedure: Monitoring the Process Mean With Application

2016

Jour. Stat. Adv. Theory and Appl.

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Multivariate cumulative sum (MCUSUM) control charts are widely used in industry because they are powerful and easy to use. They cumulate recent process data to quickly detect out-of-control situations. MCUSUM procedures will usually give tighter process control than classical quality control charts. A MCUSUM signal does not mean that the process is producting bad product.Rather it means that action should be taken so that the process does not produce bad product. MCUSUM procedures give an early indication of process change, they are consistant with a management philosophy that encourages doing it right the first time (Pignatiello and Kasunic [14]). MCUSUM charts tend to have inertia that later data points carry with them. As a result, when a trend occurs on one direction of the target mean and a resulting shift occurs in the other direction of the target mean, the two types of charts will not pick up M. S. HAMED et al. 106 the shift immediately. Industry fertilizers is important one of the chemical industries in Egypt, so that this work concerns the fertilizers industries quality control, especially urea fertilizer with application on Delta fertilizer and chemical industries which is considered one of the leading companies the field of fertilizer production in Middle east with application of multivariate quality control procedures to achieve best one procedure for multivariate quality control. This application shows that the company should use the multivariate quality control chart to determine whether not the process is in-control because the production have several correlated variables, and the used of separate control charts is misleading because the variables jointly affect the process.

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The Statistical Design of Cusum Charts

Cited by 116 publications

References 16 publications

Anomalous Anticipatory Responses in Networked Random Data

Anomalous Anticipatory Responses in Networked Random Data

Bayesian change point estimation in Poisson-based control charts

McUsum Control Chart Procedure: Monitoring the Process Mean With Application

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