Multivariate semiparametric control charts for mixed-type data.

A useful tool that has gained popularity in the Quality Control area is the control chart which monitors a process over time, identifies potential changes, understands variations, and eventually improves the quality and performance of the process. This article introduces a new class of multivariate semiparametric control charts for monitoring multivariate mixed-type data, which comprise both continuous and discrete random variables (rvs). Our methodology leverages ideas from clustering and Statistical Process Control to develop control charts for MIxed-type data. We propose four control chart schemes based on modified versions of the KAy-means for MIxed LArge KAMILA data clustering algorithm, where we assume that the two existing clusters represent the reference and the test sample. The charts are semiparametric, the continuous rvs follow a distribution that belongs in the class of elliptical distributions. Categorical scale rvs follow a multinomial distribution. We present the algorithmic procedures and study the characteristics of the new control charts. The performance of the proposed schemes is evaluated on the basis of the False Alarm Rate and in-control Average Run Length. Finally, we demonstrate the effectiveness and applicability of our proposed methods utilizing real-world data.

Generalizations of Runs and Patterns Distributions for Sequences of Binary Trials.

In the present paper we study the distributions of families of patterns which generalize runs and patterns distributions extensively examined in the literature during the last decades. In our analysis we assume that the sequence of outcomes under investigation includes independent, but not necessarily identically distributed trials. An illustration is also provided how our new results could be exploited to enrich a new system, still in research, related to patients' weaning from mechanical ventilation.