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.

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Thermal stability in nonoxidizing atmosphere of a polyetherimide (PEI) is investigated by thermogravimetry (TG). It is observed that thermal degradation of this product consists of two overlapping processes, which are conveniently separated by fitting the TG curves to mixtures of generalized logistic functions. Thus, each process is represented by a single function. The analysis of the fitting parameter values obtained for the main degradation process in different isothermal and heating ramp conditions allows to obtain insightful kinetic parameters (critical temperature, energy barrier, and reaction-order) which allow to make predictions in both isothermal and nonisothermal contexts. There is a minimum temperature for each process to occur and a ramp-energy barrier related to the process rate. In the ramp context, the values of these two parameters explain that, although one process starts at lower temperature, it proceeds at a very low rate until reaching temperatures at which the other process goes much faster. V C 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015, 132, 42329.

In spite of the many studies performed, there is not yet a kinetic model to predict the thermal degradation of cellulose in isothermal and nonisothermal conditions for the full extent of conversion. A model proposed by the authors was tested on non-oxidising thermogravimetric data. The method consisted of initially fitting several isothermal and non-isothermal curves, then obtaining a critical temperature and an energy barrier from the set of fittings that resulted from different experimental conditions. While the critical temperature, approximately 226 °C, represented the minimum temperature for the degradation process, the degradation rate at a given temperature was related to both the critical temperature and the energy barrier. These results were compared with those observed in other materials. The quality of fittings obtained was superior to any other reported to date, and the results obtained from each single curve were in line with each other. The peak area. Represents the amount of sample involved in each transformation process, in linear heating conditions Fitting parameter, related to the peak shape in linear heating conditions. If =1, then is 4 times the maximum transformation rate per unit of sample mass KeywordsThe time elapsed from the beginning of the experiment to the instant where the maximum mass loss rate is observed, in linear heating experiments Fitting parameter related to the peak asymmetry ( =1 for a symmetric peak) yiso(t) Transformation rate, as a function of time, in isothermal conditionsThe peak area. Represents the amount of sample involved in each transformation process, in isothermal conditions

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