A Directional Multivariate Sign EWMA Control Chart For Monitoring Autocorrelated Processes

The importance of statistical process control (SPC) techniques in quality improvement iswell recognized in industry. However, most conventional SPC methods have been developedunder the assumption of independent, identically and normally distributed observations. Withadvancements in measurement and data collection technology, processes can be sampled athigher rates, which often leads to data autocorrelated and skewed. It is well known that the runlength (RL) properties of conventional SPC techniques are strongly affected by dataautocorrelation and skewness. Specifically, false alarm rates (FAR) are so high that true alarmsare often ignored.Much recent research has focused on the development of appropriate SPC techniques forautocorrelated data, but the design of most autocorrelated SPC methods supposes that thedistribution of the quality characteristic has to be normal or approximately normal and fewstudies have considered the impact of non-normality on these methods. In this dissertation, wefirst transform the univariate autocorrelated process variables into multivariate vectors by amoving window, and develop a new multivariate nonparametric control chart for monitoring themean vector. The proposed control chart is based on integrating a directional multivariatespatial-sign test with the exponentially weighted moving average (EWMA) control scheme toon-line sequential monitoring. It is obvious that the process multivariate vector is notmultivariate normal and is unknown skewness if the random white noise in the autoregressivemoving average (ARMA) model of the univariate autocorrelated process is not an independentGaussian process. So we investigate the numerical performance comparison between ourproposed technique and other univariate autocorrelated multivariate control chart methods insuch an environment.Monte Carlo simulation studies show that our proposed chart has robustness in in-control(IC) performance. In other words, its in-control run length distribution can attain or is alwaysclose to the nominal one when using the same control limit designed for a multivariate normaldistribution. We can also see that our method is generally more sensitive to the small andmoderate mean shifts for non-normality and skew underlying distribution than other existingmultivariate chart methods for univariate autocorrelated process.