An Empirical-Likelihood-Based Multivariate EWMA Control Scheme

Nonparametric control charts are useful in statistical process control (SPC) when there is a lack of or limited knowledge about the underlying process distribution, especially when the process measurement is multivariate. This article develops a new multivariate SPC methodology for monitoring location parameter based on adapting a well-known nonparametric method, empirical likelihood (EL), to on-line sequential monitoring. The weighted version of EL ratio test is used to formulate the charting statistic by incorporating the exponentially weighted moving average control (EWMA) scheme, which results in a nonparametric counterpart of the classical multivariate EWMA (MEWMA). Some theoretical and numerical studies show that benefiting from using EL, the proposed chart possesses some favorable features. First, it is a data-driven scheme and thus is more robust to various multivariate non-normal data than the MEWMA chart under the in-control (IC) situation. Second, it is transformation-invariant and avoids the estimation of covariance matrix from the historical data by studentizing internally, and hence its IC performance is less deteriorated when the number of reference sample is small. Third, in comparison with the existing approaches, it is more efficient in detecting small and moderate shifts for multivariate non-normal process.