<p>In today's competitive marketplace, product and service providers must consider many correlated quality characteristics to maintain market share and increase customer satisfaction. Quality practitioners encounter a high-dimensional process when the number of quality characteristics exceeds the sample size. Since the determinant of the sample covariance matrix tends to zero under high-dimensional settings, conventional multivariate charts for monitoring the dispersion of such processes are no longer applicable. On the other hand, most Phase II control charts neglect the effect of parameter estimation error caused in Phase I analysis. However, the process parameters typically have to be estimated from Phase I reference samples because they are rarely known in practice. This paper investigates the impact of parameter estimation error on the average run length (<i>ARL</i>) properties of the ridge penalized likelihood ratio (RPLR) control chart in both in-control and out-of-control conditions. The minimum number of Phase I samples required by the RPLR control charting method to achieve a desired in-control performance is also determined. The results obtained show that (1) the parameter estimation error increases the false alarm rate of the RPLR control charting scheme, (2) the additional variability caused by the estimation error in the Phase I analysis negatively affects the performance of the RPLR control chart method over a range of possible shifts.</p>