Alternative Hotelling's T² Charts using Winsorized Modified One‐Step M‐estimator

Abstract

Hotelling's T 2 chart is a popular tool for monitoring statistical process control. However, this chart is sensitive in the presence of outliers. To alleviate the problem, this paper proposed alternative Hotelling's T 2 charts for individual observations using robust location and scale matrix instead of the usual mean vector and the covariance matrix, respectively. The usual mean vector in the Hotelling T 2 chart is replaced by the winsorized modified one-step M-estimator (MOM) whereas the usual covariance matrix is replaced by the winsorized covariance matrix. MOM empirically trims the data based on the shape of the data distribution. This study also investigated on the different trimming criteria used in MOM. Two robust scale estimators with highest breakdown point, namely S n and T n were selected to suit the criteria. The upper control limits for the proposed robust charts were calculated based on simulated data. The performance of each control chart is based on the false alarm and the probability of outlier's detection. In general, the performance of an alternative robust Hotelling's T 2 charts is better than the performance of the traditional Hotelling's T 2 chart.

Robust Linear Discriminant Analysis

“…Winsorization follows the process of trimming, but instead of discarding the trimmed values, they are replaced by the remaining highest and lowest values. Winsorized MOM (WMOM) follows the same trimming process as MOM before replacing the trimmed values with the remaining lowest and highest end of the data (Haddad et al, 2013). Unlike MOM, WMOM will retain the original sample size and this approach can reduce the problem of losing information due to trimming.…”

Monitoring Highly Correlated Multivariate Processes Using Hotelling's T2 Statistic: Problems and Possible Solutions

“…This section is covered quite well in the literature with several robust versions of Hotelling's T 2 control charts on offer (e.g., see Liu, Alfaro and Ortega, Cetin and Aktas, Abu‐Shawiesh et al , Haddad et al ), and therefore, these will not be repeated here. In addition, nonparametric methods are worth considering in these cases because establishing the appropriate distribution is made more difficult in the presence of outliers.…”

“…for the example considered in this paper. An alternative to increasing the sample size is to consider the variance–covariance estimation options outlined by Sullivan and Woodall (1996) or other robust procedures of estimating the mean vector and variance–covariance matrix by Stoumbos and Sullivan, Vargas, Alfara and Ortega, and Haddad et al …”

“…Outliers have caused problems with applying the Hotelling's T 2 statistic. Therefore, Hotelling's T 2 control charts have been considered based on robust estimators of location and dispersion when outliers are masked in the data (Vargas and Haddad, et al ).…”

H-statistic with winsorized modified one-step M-estimator for two independent groups design

“…Ahmad Mahir and Al-Khazaleh [23] applied adaptive winsorize in estimating missing values in time series data and found that the method performed consistently better than other classical methods. In a recent study, winsorized MOM by Haddad, Syed Yahaya and Alfaro [24] was used in as the centre measures in Hotelling's T 2 control chart. The chart was found to be robust (in control of Type I error) regardless of the conditions investigated and attained desirable value of statistical power.…”