scholarly journals Robust Multivariate Control Charts to Detect Small Shifts in Mean

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Habshah Midi ◽  
Ashkan Shabbak
Keyword(s):  
Control Charts ◽  
Substantial Improvement ◽  
Data Set ◽  
Multivariate Control Charts ◽  
Mean Vectors ◽  
The Mean ◽  
Simulation Results ◽  
Multivariate Control ◽  
Mean Vector

The classical multivariate CUSUM and EWMA charts are commonly used to detect small shifts in the mean vectors. It is now evident that those charts are easily affected by outliers which may be due to small or moderate changes in the mean vector. In this paper, we propose a robust multivariate CUSUM and Robust multivariate EWMA charts to remedy the problem of small changed in scatter outliers. Both the empirical and simulation results indicate that the proposed robust multivariate CUSUM and EWMA charts offer substantial improvement over other multivariate CUSUM and EWMA charts. This article also discussed the robustness of the proposed charts, when there is a small or moderate sustained shift in the data set.

scholarly journals An Improvement of the HotellingT2Statistic in Monitoring Multivariate Quality Characteristics

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Ashkan Shabbak ◽  
Habshah Midi
Keyword(s):  
Robust Control ◽  
Control Charts ◽  
Control Limit ◽  
Minimum Volume ◽  
Minimum Covariance Determinant ◽  
Absolute Deviation ◽  
Data Set ◽  
Multivariate Control Charts ◽  
Minimum Volume Ellipsoid ◽  
Multivariate Control

The HotellingT2statistic is the most popular statistic used in multivariate control charts to monitor multiple qualities. However, this statistic is easily affected by the existence of more than one outlier in the data set. To rectify this problem, robust control charts, which are based on the minimum volume ellipsoid and the minimum covariance determinant, have been proposed. Most researchers assess the performance of multivariate control charts based on the number of signals without paying much attention to whether those signals are really outliers. With due respect, we propose to evaluate control charts not only based on the number of detected outliers but also with respect to their correct positions. In this paper, an Upper Control Limit based on the median and the median absolute deviation is also proposed. The results of this study signify that the proposed Upper Control Limit improves the detection of correct outliers but that it suffers from a swamping effect when the positions of outliers are not taken into consideration. Finally, a robust control chart based on the diagnostic robust generalised potential procedure is introduced to remedy this drawback.

scholarly journals ON THE HOTELLING’S T, MCUSUM AND MEWMA CONTROL CHARTS' PERFORMANCE WITH DIFFERENT VARISBILITY SOURCES: A SIMULATION STUDY

2015 ◽  
Vol 12 (2) ◽  
pp. 196 ◽  
Author(s):  
D. A. O. Moraes ◽  
F. L. P. Oliveira ◽  
L. H. Duczmal
Keyword(s):  
Simulation Study ◽  
Control Charts ◽  
Average Run Length ◽  
Moving Average ◽  
Control Process ◽  
Average Time To Signal ◽  
Mean Vectors ◽  
Multivariate Control ◽  
The Impact ◽  
Mean Vector

This work is a simulation study to investigate the sensitivity of multivariate control charts for monitoring mean vectors in a bivariate Gaussian process with individual observations. The multivariate cumulative sum (MCUSUM), the multivariate exponentially weighted moving average (MEWMA) and Hotelling’s T charts are selected for analysis due to their common dependency on the noncentrality parameter. The chart performance is evaluated through the average run length (ARL) or the average time to signal. The impact of utilising in-control limits computed from known parameters or Phase I sample estimates is considered for mean vector shifts. Although designed to monitor mean vectors, the sensibility of the control charts is additionally analysed through different variability sources, including the mixing effect of mean vector shifts with increasing variances or positive autocorrelation in the out-of-control process. 

Multivariate Statistical Process Control with Multi-Dots Alarm Rules

2011 ◽  
Vol 120 ◽  
pp. 275-279
Author(s):  
Hai Yu Wang
Keyword(s):  
Statistical Process Control ◽  
Control Charts ◽  
Average Run Length ◽  
Multivariate Statistical Process Control ◽  
Multivariate Statistical ◽  
Statistical Process ◽  
Control Schemes ◽  
The Mean ◽  
Multivariate Control ◽  
Mean Vector

This paper mainly studied to building multivariate control charts of multi-dots alarm rules. For different multi-dots alarm rules, control limit parameters can be given by a kind of method of calculating average run length. Then the performances of those kinds of multivariate control schemes under different alarm rules were compared with Hotelling T2 chart, MCUSUM and MEWMA. We can find from this compare that those charts under different alarm rules have advantage in detecting small changes in the mean vector of a multivariate process. At last, an example is used to illustrate how this method can be used in practice.

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