A New Adaptive CUSUM Mean Chart

ABSTRACT Adaptive charts provide greater sensitivity than nonadaptive charts when detecting a range of mean shift sizes. The adaptive CUSUM (ACUSUM) chart updates its reference parameter using an adaptive EWMA (AEWMA) statistic. The weighted CUSUM (WCUSUM) chart assigns an EWMA‐based weight to the increment of the CUSUM statistic. In this study, we propose a new adaptive CUSUM chart that utilizes the Shewhart statistic both to update the reference parameter and to construct the weighting function. Since the Shewhart statistic reflects the most recent process information at each sampling point, the proposed chart is expected to enhance the detection of process mean shifts of different magnitudes. Monte Carlo simulations are used to estimate the zero‐state and steady‐state average run‐length (ARL) profiles of the competing control charts. Moreover, the expected weighted run‐length and expected relative ARL are employed to evaluate the overall detection performance across a range of mean shifts. The results show that the proposed chart outperforms the CUSUM, Shewhart‐CUSUM, AEWMA, ACUSUM, and WCUSUM charts. A real data example illustrates the practical implementation of the proposed chart.