In some statistical process control (SPC) applications, it is assumed that a quality characteristic or a vector of quality characteristics of interest follows a univariate or multivariate normal distribution, respectively. However, in certain applications this assumption may fail to hold and could lead to misleading results. In this paper, we study the effect of non-normality when the quality of a process or product is characterized by a linear profile. Skewed and heavy-tailed symmetric non-normal distributions are used to evaluate the non-normality effect numerically. The results reveal that the method proposed by Kimtextitet al. (J. Qual. Technol. 2003; 35:317–328) can be designed to be robust to non-normality for both highly skewed and heavy-tailed distributions. Copyright © 2010 John Wiley & Sons, Ltd.