The Performance of the Multivariate Adaptive Exponentially Weighted Moving Average Control Chart with Estimated Parameters

The multivariate adaptive exponentially weighted moving average control chart (MAEWMA) can detect shifts of different sizes while diminishing the inertia problem to a large extent. Although it has several advantages compared to various multivariate charts, previous literature has not considered its performance when the parameters are estimated. In this study, the performance of the MAEWMA chart with estimated parameters is studied while considering the practitioner‐to‐practitioner variation. This kind of variation occurs due to using different Phase I samples by different practitioners in estimating the unknown parameters. The simulation results in this paper show that estimating the parameters results in extensively excessive false alarms and as a result a large number of Phase I samples is needed to achieve the desired in‐control performance. Using small number of Phase I samples in estimating the parameters may result in an in‐control ARL distribution that almost completely lies below the desired value. To handle this problem, we strongly recommend the use of a bootstrap‐based algorithm to adjust the control limit of the MAEWMA chart. This algorithm enables practitioners to achieve, with a certain probability, an in‐control ARL that is greater than or equal to the desired value while using the available number of Phase I samples.