A Sequential Rank-Based Nonparametric Adaptive EWMA Control Chart

Abstract

Nonparametric control chart is useful when the underlying distribution is unknown, or is not likely to be normal. In this article, 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 prespecify any tuning parameter either. A Markov chain model is suggested to calibrate the run-length distribution of NAE, which is shown to have 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 shows that it performs quite well in practical applications.