A Sequential Rank-Based Nonparametric Adaptive EWMA Control Chart

Nonparametric control chart is useful when the underlying distribution is unknown, or is not likely to be normal. In this paper, we provide a sequential rank-based nonparametric adaptive EWMA (NAE) control chart for detecting the persistent shift in the location parameter. This NAE chart is a self-starting scheme and thus can be used to monitor processes at the start-up stages rather than waiting for the accumulation of sufficiently large calibration samples. Moreover, we do not require any prior knowledge of the underlying distribution, and to pre-specify any tuning parameter either. A Markov chain model is suggested to calibrate the run-length distribution of NAE, which is shown to has approximate tail probability as a geometric distribution. A simulation study demonstrates that the proposed control chart not only performs robustly for different distributions, but also is efficient in detecting various magnitude of shifts. A real-data example from manufacturing show that it performs quite well in practical applications.