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Robust T 2 control chart using median‐based estimators
Author(s) -
Maleki Fatemeh,
Mehri Saeed,
Aghaie Abdollah,
Shahriari Hamid
Publication year - 2020
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2691
Subject(s) - estimator , outlier , mathematics , statistics , covariance matrix , control chart , covariance , x bar chart , sample size determination , control limits , computer science , process (computing) , operating system
One of the most widely used multivariate control charts is the Hotelling T 2 . In order to construct a Hotelling T 2 control chart, the mean vector (μ) and the variance–covariance matrix (Σ) must be first estimated. The classical estimators of μ and Σ are usually used to design Hotelling T 2 control chart. The classical estimators are sensitive to the presence of outliers. One way to deal with outliers is to use robust estimators. In this study, a robust T 2 control chart is proposed. The mean vector is obtained from the sample median. The median absolute deviation and the comedian are used as the estimates of the elements of the variance–covariance matrix. The proposed robust estimators of the mean vector and the variance–covariance matrix are compared with the sample mean vector and the sample variance–covariance matrix, and the M estimator of these parameters, through efficiency and robustness measures. The performances of the proposed robust T 2 control chart and the classical and the M estimators are also compared by means of average run length. Simulation results reveal that the proposed robust T 2 control chart has much better performance than the traditional Hotelling T 2 and similar performance to the M estimator in detecting shifts in process mean vector. Use of other robust estimators to estimate the process parameters is an area for further research.