Hotelling's T2: is a popular charting statistic to use when it is desired to construct a multivariate control chart using individual observations. In practice, the statistic usually is computed using the sample covariance matrix, S, as an estimate of the population covariance matrix, £. This estimator has many desirable properties, but in some situations other covariance matrix estimators may be more applicable. In this paper, we consider several alternative covariance estimators and present power determinations for the corresponding T2: statistics. The T2: charting procedure based on the sample covariance estimator, S, is shown to be most effective in detecting outliers in a Phase I operation.