A new approach for the economic design of fully adaptive control charts

This paper proposes a unified approach for the development of economically designed Variable‐parameter (Vp) $\overline{X}$ ‐Shewhart, $\overline{X}$ ‐CUSUM and $\overline{X}$ ‐EWMA control chart models, for monitoring the process mean in infinite‐horizon production runs. The use of the models allows at each sampling epoch the determination of the scheme parameters that minimize the quality‐related expected cost of the procedure based on the actual value of the chart statistic. The models are simple and fast as they avoid the inaccuracies and inefficiencies associated with the interim computation of statistical performance measures such as ANSS, ANOS, etc. The effectiveness of the schemes is evaluated by comparing their optimal expected costs against each other and against the costs of Fixed‐parameter (Fp) charts. These comparisons demonstrate the superiority of Vp $\overline{X}$ ‐CUSUM and Vp $\overline{X}$ ‐EWMA charts over Vp $\overline{X}$ ‐Shewhart charts which in turn are economically superior to Fp control charts.