Dynamic probability control limits for the adaptive multivariate EWMA chart

Effective monitoring of the control charts requires the establishment of appropriate control limits. Various methods have been proposed to determine the fixed control limits (FCLs) based on a specified in-control average run-length value, such as Markov chains, integral equations, and Monte Carlo simulations.With the FCLs, the conditional false alarm rate (CFAR) of a control chart varies over time in an unexpected and undesirable way, where the CFAR refers to the probability of a false alarm at a particular time given no previous false alarm. To address this issue, dynamic probability control limits (DPCLs) can be employed to keep the CFAR constant over time. In this study, we determine the DPCLs using fixed and time-varying sample sizes for the adaptive multivariate EWMA chart when the underlying process is assumed to follow a multivariate normal distribution. The DPCLs are designed to automatically adjust to changes in the probability distribution of the sample size, while maintaining a consistent CFAR. This results in a closely matched run-length performance for an in-control process compared to that of the geometric distribution.