Cusum and Ewma Multi-charts for Detecting a Range of Mean Shifts

The multi-chart consists of several CUSUM or EWMA charts with different reference values that are used simultaneously to detect anticipated process changes. We not only prove that the chart can quickly achieve the asymptotic optimal bound, but also give an integral equation to determine the reference values to arrive at optimality. Simulation results are used to verify the theoretical optimal properties and to show that the CUSUM multi-chart is superior on the whole to single CUSUM, single EWMA, and EWMA multi-charts in terms of run length and robustness, and can compete with GLR control charts in detecting a range of various mean shifts. We investigate the design of both CUSUM and EWMA multi-charts. Some practical guidelines are provided for determining multi-chart parameters, such as the number of constituent charts and the allocation of their reference values.