Economic design of the upper-sided synthetic chart with measurement errors

Considering a quadratic Taguchi loss function for poor quality products, as well as measurement errors in the process characteristic, this paper proposes an economic model for the upper-sided synthetic S2$ S^2 $ chart allowing multiple measurements for each sample item. The steady-state ARL of this chart is computed using a Markov chain method and the optimal number of measurements are obtained through the minimisation of the total cost model. For the proposed economic and economic statistical model, numerical examples are presented to evaluate the effect of measurement errors on the upper-sided synthetic S2$ S^2 $ chart. Finally, the sensitivity analyses of the optimal chart parameters and the cost of the upper-sided synthetic S2$ S^2 $ chart are also investigated using different input parameter values. All the above results are verified through a wide range of the input parameter values. Two illustrative examples are also provided.