Comparing the Efficiency of T2 Graphs for Hotelling and Classification by Ranking, Using Different Estimators of Location and Dispersion

Abstract

Quality is defined simultaneously by a set of correlated variables for many products or services. To monitor a multivariate process, the classic control chart T2 (Hotelling (1947)) is often used. This chart is constructed under the assumption of normality of the observations and estimates of usual location and dispersion. It is well known that this chart is very sensitive to the presence of outliers in the historical data set, causing the masking effect and therefore several proposals to construct charts T2 with alternative estimators that have become more powerful and robust charts in the presence of outliers or faster detection of change in the mean vector have been proposed.

The normality of the observations is not always true in practice, then the nonparametric control charts are recommended in this case, one of them is the chart of a ranking method (Liu (1995)). Zertuchi and Cantu (2008), Velasquez and Moreno (2009), comparing the efficiency between the two charts above using conventional estimators under normal and devoid of it. This work, presents a comparative study about the efficiency of the two charts using various estimates of the mean vector and covariance matrix, in the presence of outliers in the construction phase. The efficiency of control charts is determined by the change in the early detection of mean vector. The efficiency of charts in this study is measured calculating the average run length (ARL) under control by statistical simulation through various environments encountered. We present the results obtained with their respective interpretations and conclusions.