This study proposes a control chart based on functional data to detect anomalies and estimate the normal output of industrial processes and services such as those related to the energy efficiency domain. Companies providing statistical consultancy services in the fields of energy efficiency; heating, ventilation and air conditioning (HVAC); installation and control; and big data for buildings, have been striving to solve the problem of automatic anomaly detection in buildings controlled by sensors. Given the functional nature of the critical to quality (CTQ) variables, this study proposed a new functional data analysis (FDA) control chart method based on the concept of data depth. Specifically, it developed a control methodology, including the Phase I and II control charts. It is based on the calculation of the depth of functional data, the identification of outliers by smooth bootstrap resampling and the customization of nonparametric rank control charts. A comprehensive simulation study, comprising scenarios defined with different degrees of dependence between curves, was conducted to evaluate the control procedure. The proposed statistical process control procedure was also applied to detect energy efficiency anomalies in the stores of a textile company in the Panama City. In this case, energy consumption has been defined as the CTQ variable of the HVAC system. Briefly, the proposed methodology, which combines FDA and multivariate techniques, adapts the concept of the control chart based on a specific case of functional data and thereby presents a novel alternative for controlling facilities in which the data are obtained by continuous monitoring, as is the case with a great deal of process in the framework of Industry 4.0.

A risk assessment model for a smart home Internet of Things (IoT) network is implemented using a Bayesian network. The directed acyclic graph of the Bayesian network is constructed from an attack graph that details the paths through which different attacks can occur in the IoT network. The parameters of the Bayesian network are estimated with the maximum likelihood method applied to a data set obtained from the simulation of attacks, in five simulation scenarios. For the risk assessment, inferences in the Bayesian network and the impact of the attacks are considered, focusing on DoS attacks, MitM attacks and both at the same time to the devices that allow the automation of the smart home and that are generally the ones that individually have lower levels of security.