Optimal design of the synthetic chart for the process mean based on median run length

Control charts are usually designed using average run length as the criterion to be optimized. The shape of the run length distribution changes according to the shift in the mean, from highly skewed for an in-control process to approximately symmetric when the mean shift is large. Since the shape of the run length distribution changes with the mean shift, the Median Run Length (MRL) provides a more meaningful interpretation for in-control and out-of-control performances of the charts, and it is readily understood by practitioners. This article presents an optimal design procedure for a synthetic chart able to monitor the mean based on the MRL under the zero- and steady-state modes. The synthetic chart integrates (X) over bar and conforming run length charts. Pseudocodes and Mathematica programs are presented for the computation of the optimal parameters of the synthetic chart based on a desired in-control MRL (MRL(0)), a given sample size, and a specified mean shift for which a quick detection is needed.