A distribution-free Max-EWMA scheme for multi-aspect process monitoring with industrial applications

Abstract

In Statistical Process Monitoring, Distribution-free charting schemes play a vital role in Industry 4.0 for their superior effectiveness compared to parametric methods, especially in cases where the underlying process distribution is not well-defined or poses challenges in estimation. Traditional distribution-free charting schemes focus on surveilling only one process aspect: the location or scale parameter. The past two decades have also witnessed a rapid expansion of research on joint monitoring of the two aspects, location and scale, using combined bi-aspect charting schemes. However, there is a notable scarcity of methods that addressing complex industrial scenarios where multiple parameters (like location, scale, and shape) need simultaneous monitoring with high sensitivity and specificity. Our research is motivated by this challenge, and this paper describes a distribution-free tri-aspect monitoring procedure called the Maximum Exponentially Weighted Moving Average (Max-EWMA) scheme This scheme can effectively monitor shifts in three process characteristics, encompassing aspects related to process location, scale, and shape parameters. We utilize weighted versions of well-known statistical measures such as the Wilcoxon, Ansari-Bradley, and Savage-type statistics to construct the plotting statistics. An essential feature of our proposed Max-EWMA chart is its robustness under various continuous distributions, ensuring reliable performance in in-control situations. Competing schemes are compared via intensive computing techniques based on Monte Carlo using the Median Run Length metric, which evaluates the effectiveness of the proposed scheme. Finally, our proposed schemes are illustrated with two examples. Some concluding remarks and limitations of the study are noted.