Decomposition of<i>T</i>2 for Multivariate Control Chart Interpretation

Mason, Robert L.; Tracy, Nola D.; Young, John C.

doi:10.1080/00224065.1995.11979573

Cited by 316 publications

(156 citation statements)

References 17 publications

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“…Mason et al [14] proposed that the distribution governing the components of the MYT decomposition for the situation where there are no signals is F distribution. For the case of p variables, these are given by…”

Section: Properties Of the Myt Decompositionmentioning

confidence: 99%

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Multivariate Statistical Process of Hotelling’s T2 Control Charts Procedures With Industrial Application

Hamed¹

2017

Jour. Stat. Adv. Theory and Appl.

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A control chart is a tool that monitors quality characteristics of a process to ensure that process control is being maintained when monitoring multiple characteristics that are correlated, it is imperative to use multivariate control chart. Hotelling's 2 T quality control chart is used to determine whether or not the process mean vector for two or more variables is in-control. It is allowing us to simultaneously monitor whether two or more related variables are in control, and it is shown that multivariate quality control chart do not indicate which variables cause the out-of control signal so that the interpretation of the out-ofcontrol signal. Also, in this paper develops the multivariate quality control charts of the out of-control signal, this will be maintained by making and industrial application on the fertilizers factory. It is important to know that this M. S. HAMED 2 factory has a special department for quality control, in order to maintain International Standardization Organization (ISO).

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Section: Properties Of the Myt Decompositionmentioning

confidence: 99%

“…The probability of a type II error. The ARL for detecting the shift is given by: Mason et al [14] presented decomposition procedure. They considered that, the…”

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confidence: 99%

Multivariate Statistical Process of Hotelling’s T2 Control Charts Procedures With Industrial Application

Hamed¹

2017

Jour. Stat. Adv. Theory and Appl.

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“…Kalagonda and Kulkarni (2003) propose constructing a model for the in-control process and using dummy variables to determine the nature of the change. Mason et al (1995) decompose T2 into independent components, each reflecting an individual variable Xj. Kourti and MacGregor (1996) show that the T2 reduction works well when the dimension is not too high.…”

Section: Suggested Approaches For Multivariate Surveillancementioning

confidence: 99%

Effect of Dependency in Systems for Multivariate Surveillance

Andersson

2009

Communications in Statistics - Simulation and Computation

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In many situations we need a system for detecting changes early. Examples are early detection of disease outbreaks, of patients at risk and of financial instability. In influenza outbreaks, for example, we want to detect an increase in the number of cases. Important indicators might be the number of cases of influenza-like illness and pharmacy sales (e.g. aspirin). By continually monitoring these indicators, we can early detect a change in the process of interest. The methodology of statistical surveillance is used. Often, the conclusions about the process(es) of interest is improved if the surveillance is based on several indicators. Here three systems for multivariate surveillance are compared. One system, called LRpar, is based on parallel likelihood ratio methods, since the likelihood ratio has been shown to have several optimality properties. In LRpar, the marginal density of each indicator is monitored and an alarm is called as soon as one of the likelihood ratios exceeds its alarm limit. The LRpar is compared to an optimal alarm system, called LRjoint, which is derived from the full likelihood ratio for the joint density. The performances of LRpar and LRjoint are compared to a system where the Hotellings T2 is monitored. The evaluation is made using the delay of a motivated alarm, as a function of the times of the changes. The effect of dependency is investigated: both dependency between the monitored processes and correlation between the time points when the changes occur. When the first change occurs immediately, the three methods work rather similarly, for independent processes and zero correlation between the change times. But when all processes change later, the T2 has much longer delay than LRjoint and LRpar. This holds both when the processes are independent and when they have a positive covariance. When we assume a positive correlation between the change times, the LRjoint yields a shorter delay than LRpar when the changes actually do occur simultaneously, whereas the opposite is true when the changes do actually occur at different time point.

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“…He divided the complete set of variables into two subsets to determine which of the subsets is responsible for the out-of-control signal, but discriminating and knowing the subset suspected to be directly related to the cause of out-ofcontrol is subjective and depends on the practitioner. [13,14] proposed the decomposition of T 2 statistic and showed that the interpretation of a signal from a T 2 statistic is greatly aided if the corresponding value is partitioned into independent parts. [5] It must be stated that limited research work was reported on the combined recognizer approach for pattern recognition as most of the existing ANN model for pattern recognition are mainly generalized-based where only a single classifier was applied in the diagnosis of abnormal pattern.…”

Section: Introductionmentioning

confidence: 99%

Pattern Recognition of Process Mean Shift using Combined ANN Recognizer

Adeoti¹,

Afolabi²

2012

IJCA

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Artificial Neural Network (ANN) based model has been proposed for diagnosis of process mean shift. These are mainly generalized-based where only a single classifier was applied in the diagnosis of abnormal pattern. In this paper, we analyze the performance of a combined recognizer consisting of small-sized artificial neural networks on varying number of nodes in the hidden layer trained with Levenberg Marquardt and Quasi-Newton Algorithm. The results of our study illustrate the effectiveness of the combined recognizer and showed that combined recognizer performed better when number of hidden nodes is small, say, less than 15 in terms of recognition accuracies and mean square error as compared to the single recognizer. .

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Decomposition ofT2 for Multivariate Control Chart Interpretation

Cited by 316 publications

References 17 publications

Multivariate Statistical Process of Hotelling’s T2 Control Charts Procedures With Industrial Application

Multivariate Statistical Process of Hotelling’s T2 Control Charts Procedures With Industrial Application

Effect of Dependency in Systems for Multivariate Surveillance

Pattern Recognition of Process Mean Shift using Combined ANN Recognizer

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