Optimal Design of <i>S</i>²‐EWMA Control Chart with Estimated Parameters Based on Median Run Length and Expected Median Run Length

ABSTRACT Control chart application is essential in improving overall production yield and enhancing product quality. Basically, known parameters and estimated parameters have different effects on control chart properties. This work aims to study the effects of parameter estimation for the Shewhart S ‐chart and S 2 EWMA control chart in the context of process variance monitoring. The methodologies to optimally design both the charts in terms of median run length (MRL), standard deviation run length (SDRL), expected median run length (EMRL), and the expected standard deviation run length (ESDRL) are proposed. Then, through simulation studies and real word case analyses, the impacts of parameter estimation on control chart properties are assessed. Results show that both the Shewhart S ‐chart and S 2 EWMA control chart react differently with estimated parameters. The estimated Shewhart S ‐chart is less sensitive to changes in terms of subgroup size ( m ) but the sensitivity improves as the sample size ( n ) increases. Instead, the estimated S 2 EWMA control chart shows better chart sensitivity to both m and n . This demonstrates that the control chart is more responsive to changes in m , making it effective when it comes to detecting variations associated with changes in m . Ultimately, acquiring knowledge about parameter estimation on control chart properties helps practitioners to efficiently implement control chart applications in real‐life scenarios.