The exponentiated exponentially weighted moving average control chart

Memory-type control charts are widely used for monitoring small to moderate shifts in the process parameter(s). In the present article, we present an exponentiated exponentially weighted moving average (Exp-EWMA) control chart that weights the past observations of a process using an exponentiated function. We evaluated the run-length characteristics of the Exp-EWMA chart via Monte Carlo simulations. A comparison study versus the CUSUM, EWMA and extended EWMA (EEWMA) charts under similar in-control (IC) run-length properties demonstrates that the Exp-EWMA chart is more effective for detecting small and, under certain circumstances, moderate shifts for both the zero-state and steady-state cases. Moreover, the Exp-EWMA chart has better zero-state out-of-control (OOC) performance than an EWMA chart with smoothing parameter equal to the limit to the infinity of the exponentiated function, while the two charts perform similarly for the steady-state case. Finally, it is shown that the Exp-EWMA chart is more IC robust than its competitors under several non-normal distributions. Two examples are provided to explain the implementation of the proposed chart.