Robustness of the EWMA Control Chart to Non-Normality

Abstract

Rational subgroups of size n = 1 are frequently encountered in process monitoring and control. The Shewhart control chart for individuals is often used in these situations. It is well-known that the in-control average run length (ARL) of this chart is 370.4 under the assumption that the observations are selected at random from a normal population. When the assumption of normality is violated, the ARL of the individuals control chart is adversely affected. We show that an exponentially weighted moving average (EWMA) control chart can be designed so that it is robust to the normality assumption, that is, so that the in-control ARL is reasonably close to the normal-theory value for both skewed and heavy-tailed symmetric non-normal distributions. The EWMA chart also performs quite well in detecting shifts in the process mean.