Joint statistical design of &Xmacr; and s charts with combined double sampling and variable sampling interval

A combination of double sampling and variable sampling interval (DSVSI) charts can increase the efficiency of signaling small shifts. This study proposes joint DSVSI &Xmacr; and s charts and investigates their statistical performance. The proposed approach uses a Markov chain approach to compute the statistical performance, and uses a statistical design model to design DSVSI &Xmacr; and s charts for detecting the mean shift and variance increase. A comparison study shows that the DSVSI &Xmacr; and s charts are better able to signal the shifts of both mean and variance than joint double sampling &Xmacr; and s chart, adaptive &Xmacr; and R charts, EWMA, and CUSUM charts.