A distribution-free control chart for joint monitoring of location and scale in finite horizon productions

We propose a distribution-free Shewhart-type control chart for jointly monitoring location and scale in a finite horizon production, commonly presented in manufacturing environments characterized by high flexibility, production variety, and a limited number of scheduled inspections. The Lepage-type statistic used in this research combines the Wilcoxon rank sums and Mood statistics with control limits obtained through Monte Carlo simulation to achieve a guaranteed in-control performance considering the practitioner-to-practitioner variation across their reference samples. We performed an extensive Monte-Carlo simulation to evaluate the performance of the proposed chart over several scenarios. The in-control results show the benefits of using the guaranteed limits compared with the unconditional version of the proposed control chart. In most scenarios, the out-of-control experimentation presents a better performance of the proposed control chart than the chart using the classical Lepage statistic with the Ansary–Bradley statistic instead of the Mood statistic. We present a real example to show practitioners the implementation of the proposed control chart.