The adaptive exponential weighted moving average (AEWMA) monitoring technique has recently received increasing attention as a robust alternative requiring no knowledge of the actual shift magnitudes. In this paper, we develop a discrete state nonparametric AEWMA chart based on the Wilcoxon signed‐rank statistics. The major characteristic of this monitoring scheme is that it takes into account the discrete nature in terms of the statistics being used as well as the chart structure design. Moreover, an accurate evaluation of the chart's statistical properties is provided using an appropriate Markov chain approach. Simulation results show that this AEWMA signed‐rank scheme performs robustly across a diverse variety of distributions, and it can also provide an effective performance for detecting both small and large shifts. Finally, a real data example is cited for showing practical implications of our monitoring scheme.

In the past few decades, research on nonparametric process monitoring schemes mainly dealt with the uni‐aspect or bi‐aspect schemes, focusing on monitoring process location or scale separately or jointly. Another critical process characteristic, namely, the process shape, is not explicitly dealt with in‐depth in most existing charting schemes. In classical hypothesis testing, some recent literature clearly showed that the multi‐aspect test statistics, although designed for very restrictive alternatives, often perform as well or better than many statistics for arbitrary distributional shifts. They are often better than Kolmogorov‐Smirnov or Cramér‐von Mises statistics and some empirical likelihood‐based test statistics. The current paper aims to use a tri‐aspect statistic to design a distribution‐free Phase‐II Cumulative Sum (CUSUM) charting scheme for monitoring any arbitrary process changes in the process. The proposal is nonparametric and is equivalent to an unknown standard case. It reflects, in addition, which parameters, among location, scale, or shape, are more responsible for a signal. The construction of the CUSUM scheme from an existing tri‐aspect Shewhart‐type chart is simple, so significant attention is devoted to determining a near‐optimal reference parameter of the chart in keeping an unknown shift type in mind. Comparisons of the optimal performance of various competitors are considered in terms of the median run length (MRL) metric. The proposed charting scheme designed with the tri‐aspect statistic compares highly favorably with many existing SPM schemes. The same is evident from our findings based on the Monte‐Carlo simulation. Finally, the proposed schemes are illustrated with a flow‐width measurement monitoring example.