Economic-Statistical Design of the Synthetic &Xmacr; Chart with Estimated Process Parameters

In this paper, the effects of process parameter estimation on the cost of the synthetic &Xmacr; chart are studied. We study the increase in cost when the optimal chart's parameters corresponding to the known process parameters case are used to estimate the cost when the process parameters are actually just estimated. By studying the increase in cost, practitioners will be able to determine whether the optimal chart's parameters, computed based on known process parameters, can still be used to reliably estimate the cost when the target values of the process mean and variance are estimated. We also look at the minimum number of preliminary subgroups needed for the estimation of process parameters so that the cost for the estimated process parameters case is almost the same as the cost for the known process parameters case. Furthermore, we also look at the cost savings, in the case of process parameter estimation when the optimal chart's parameters are computed based on estimated process parameters, instead of adopting the chart's parameters corresponding to known process parameters. This enables practitioners to determine the cost advantages of selecting the chart's parameters that minimize the cost when process parameters are estimated, instead of adopting the optimal charting parameters corresponding to the case of known process parameters.