An improved variable sample size and sampling interval S control chart

The standard deviation chart (S chart) is used to monitor process variability. This paper proposes an upper-sided improved variable sample size and sampling interval (VSSI_t) S chart by improving the existing upper-sided variable sample size and sampling interval (VSSI) S chart through the inclusion of an additional sampling interval. The optimal designs of the VSSI_t S chart together with the competing charts under consideration, such as the VSSI S and exponentially weighted moving average (EWMA) S charts, by minimizing the out-of-control average time to signal (ATS₁) and expected average time to signal (EATS₁) criteria, are performed using the MATLAB programs. The performances of the standard S, VSSI S, EWMA S, and VSSI_t S charts are compared, in terms of the ATS₁ and EATS₁ criteria, where the results show that the VSSI_t S chart surpasses the other charts in detecting moderate and large shifts, while the EWMA S is the best performing chart in detecting small shifts. An illustrative example is given to explain the implementation of the VSSI_t S chart.