A variable sample size and sampling interval control chart for monitoring the process mean using auxiliary information

A variable sample size and sampling interval (VSSI) control chart using the auxiliary information (VSSI AI) is proposed for efficiently monitoring the process mean. The control chart's statistics, optimal design and implementation are discussed. The average time to signal (ATS) and expected ATS (EATS) criteria are adopted to evaluate the performance of the VSSI AI chart. The ATS and EATS performances of the VSSI AI chart, exponentially weighted moving average (EWMA) chart, EWMA chart with AI (EWMA AI) and the synthetic chart with AI (Syn AI) are compared and explored for common patterns. The proposed VSSI AI chart shows a better performance than the EWMA, EWMA AI and Syn AI charts, in terms of the ATS and EATS criteria. An example is also presented to illustrate the implementation of the VSSI AI chart.