Double sampling hotelling T 2 chart with skip sampling strategy for an autocorrelated process

The multivariate double sampling (DS T2) chart was developed to monitor several variables that are either independent or cross-correlated simultaneously. However, many real-life multivariate processes are not only cross-correlated but also autocorrelated. This paper extends the DS T2 chart for monitoring an autocorrelated process by incorporating the first-order vector autoregressive model into the chart. The performance of the DS T2 chart for an autocorrelated process is evaluated using the average run length (ARL) and average number of observations to signal (ANOS) metrics. The optimal parameters of the DS T2 chart for an autocorrelated process in minimizing the out-of-control ARL and ANOS metrics are obtained. Based on these metrics, the DS T2 chart for an autocorrelated process outperforms the T2 chart for an autocorrelated process for all shift sizes, autocorrelation and cross-correlation levels considered. The s-skipping sampling strategy is incorporated into the DS T2 chart for an autocorrelated process to reduce the impact of autocorrelation.