Yushimito-Del Valle, Wilfredo F.

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Prediction Models for the In-control ARL in Phase II of a T2 Control Chart
(2006) Yushimito-Del Valle, Wilfredo F.; Artiles-León, Noel; College of Engineering; Acuña, Edgar; González-Barreto, David; Department of Industrial Engineering; Rivera-Betancourt, Loida
Through simulation, an analysis of the run-length in Phase II reveals that the commonly used formula for the upper control limit (UCL) of Hotelling’s T2 control chart, proposed by Alt (1976), is not exact. This study also shows that the in-control ARL depends on: (1) the total samples used to estimate parameters of Phase I, (2) the condition number of the estimated correlation matrix and (3) the desired in-control ARL. This research provides regression models, based on the condition number of the estimated correlation matrix, number of samples, number of variables and the desired in- control ARL, for the prediction of the in-control average run length (ARLo) in Phase II of T2 Control Charts. When large samples are not available, the regressions can be used to correct the UCL to achieve values that are more exact. The corrections obtained are more conservative than the ones recently obtained using simulation by Champ et al. (2005).