Enhanced directionally sensitive and directionally invariant MCUSUM and MEWMA charts for process mean

Abstract

Control charts with an appropriate use of auxiliary information based (AIB) strategies have shown improved run length performances compared with control charts without this feature. In this article, by adopting an AIB estimator, enhanced directionally sensitive and directionally invariant MCUSUM and MEWMA charts for monitoring the mean vector of a process that follows a multivariate normal distribution are proposed. The proposed AIB directionally sensitive and directionally invariant MCUSUM and MEWMA charts surpass their existing basic counterparts, in terms of the average run length (ARL), median run length (MRL) and standard deviation of the run length (SDRL) performances obtained via the Monte Carlo simulation approach. In general, it is found that the directionally sensitive charts outperform their directionally invariant counterparts in detecting shifts in the process mean vector, in terms of the ARL, MRL and SDRL criteria. A real dataset is considered to demonstrate the implementation of the existing and proposed charts.