Statistical Process Control Using Modified Robust Hotelling's T² Control Charts - Haddad, Firas Saleem Fares (2013)
Hotelling’s T² chart is a popular tool for monitoring statistical process control. However, this chart is sensitive to outliers. To alleviate the problem, three approaches to the robust Hotelling’s T² chart namely trimming, Winsorizing and median based were proposed. These approaches used robust location and scale estimators to substitute for the usual mean and covariance matrix, respectively. For each approach, three robust scale estimators: MADn, Sn and Tn were introduced, and these estimators functioned accordingly to the approach. The first approach, denoted as T²t, applied the concept of trimming via Mahalanobis distance. The robust scale estimator was used to replace the covariance matrix in Mahalanobis distance. The trimmed mean and trimmed covariance matrix were the location and scale estimators for the T²t chart. The second approach,, T²w, employed each scale estimator as the Winsorized criterion. This approach applied Winsorized modified one step M-estimator and its corresponding Winsorized covariance as the location and the scale matrix for T²w chart, respectively. Meanwhile, in the third approach, T²н, the robust scale estimator took the role of the scale matrix with Hodges-Lehman as the location estimator. This approach worked with the original data without any trimming or Winsorizing. Altogether, nine robust control charts were proposed. The performance of each robust control chart was assessed based on false alarm rates and probability of detection. To investigate on the strengths and weaknesses of the proposed charts, various conditions were created by manipulating four variables, namely number of quality characteristics, proportion of outliers, degree of mean shifts, and nature of quality characteristics (independent and dependent). In general, the proposed charts performed well in terms of false alarm rates. With respect to probability of detection, all the proposed charts outperformed the traditional Hotelling's T² charts. The overall findings showed that, the proposed robust Hotelling's T² control charts are viable alternatives to the disputed traditional charts.