Abstract
In the past decade, different robust estimators have been proposed by several researchers to improve the ability to detect non-random patterns such as trend, process mean shift, and outliers in multivariate control charts. However, the use of the sample mean vector and the mean square successive difference matrix in the T2 control chart is sensitive in detecting process mean shift or trend but less sensitive in detecting outliers. On the other hand, the minimum volume ellipsoid (MVE) estimators in the T2 control chart are sensitive in detecting multiple outliers but less sensitive in detecting trend or process mean shift. Therefore, new robust estimators using both merits of the mean square successive difference matrix and the MVE estimators are developed to modify Hotelling's T2 control chart. To compare the detection performance among various control charts, a simulation approach for establishing control limits and calculating signal probabilities is provided as well. Our simulation results show that a multivariate control chart using the new robust estimators can achieve a well-balanced sensitivity in detecting the above-mentioned non-random patterns. Finally, three numerical examples further demonstrate the usefulness of our new robust estimators.
| Original language | English |
|---|---|
| Pages (from-to) | 289-300 |
| Number of pages | 12 |
| Journal | Journal of Statistical Computation and Simulation |
| Volume | 81 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2011 Mar 1 |
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All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Modelling and Simulation
- Statistics, Probability and Uncertainty
- Applied Mathematics
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New robust estimators for detecting non-random patterns in multivariate control charts : A simulation approach. / Pan, Jeh-Nan; Chen, Sheau Chiann.
In: Journal of Statistical Computation and Simulation, Vol. 81, No. 3, 01.03.2011, p. 289-300.Research output: Contribution to journal › Article
TY - JOUR
T1 - New robust estimators for detecting non-random patterns in multivariate control charts
T2 - A simulation approach
AU - Pan, Jeh-Nan
AU - Chen, Sheau Chiann
PY - 2011/3/1
Y1 - 2011/3/1
N2 - In the past decade, different robust estimators have been proposed by several researchers to improve the ability to detect non-random patterns such as trend, process mean shift, and outliers in multivariate control charts. However, the use of the sample mean vector and the mean square successive difference matrix in the T2 control chart is sensitive in detecting process mean shift or trend but less sensitive in detecting outliers. On the other hand, the minimum volume ellipsoid (MVE) estimators in the T2 control chart are sensitive in detecting multiple outliers but less sensitive in detecting trend or process mean shift. Therefore, new robust estimators using both merits of the mean square successive difference matrix and the MVE estimators are developed to modify Hotelling's T2 control chart. To compare the detection performance among various control charts, a simulation approach for establishing control limits and calculating signal probabilities is provided as well. Our simulation results show that a multivariate control chart using the new robust estimators can achieve a well-balanced sensitivity in detecting the above-mentioned non-random patterns. Finally, three numerical examples further demonstrate the usefulness of our new robust estimators.
AB - In the past decade, different robust estimators have been proposed by several researchers to improve the ability to detect non-random patterns such as trend, process mean shift, and outliers in multivariate control charts. However, the use of the sample mean vector and the mean square successive difference matrix in the T2 control chart is sensitive in detecting process mean shift or trend but less sensitive in detecting outliers. On the other hand, the minimum volume ellipsoid (MVE) estimators in the T2 control chart are sensitive in detecting multiple outliers but less sensitive in detecting trend or process mean shift. Therefore, new robust estimators using both merits of the mean square successive difference matrix and the MVE estimators are developed to modify Hotelling's T2 control chart. To compare the detection performance among various control charts, a simulation approach for establishing control limits and calculating signal probabilities is provided as well. Our simulation results show that a multivariate control chart using the new robust estimators can achieve a well-balanced sensitivity in detecting the above-mentioned non-random patterns. Finally, three numerical examples further demonstrate the usefulness of our new robust estimators.
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UR - http://www.scopus.com/inward/citedby.url?scp=79951821721&partnerID=8YFLogxK
U2 - 10.1080/00949650903311039
DO - 10.1080/00949650903311039
M3 - Article
VL - 81
SP - 289
EP - 300
JO - Journal of Statistical Computation and Simulation
JF - Journal of Statistical Computation and Simulation
SN - 0094-9655
IS - 3
ER -