Gráficos de controle para variáveis ambientais duplamente limitadas e autocorrelacionadas

Abstract

In the environmental field, especially in hydrology, several activities require monitoring tools to assist in the process of decision making. Control chart is a statistical process control (SPC) tool that can be used for this purpose. However, one of the assumptions made for its use is the independence between different observations. In some processes, this assumption could not be verified, as in hydrological time series, which reduces the applicability of the usual control charts. A solution for this can be given by monitoring the residuals of a fitted time series model, such as, the Kumaraswamy autoregressive moving averages (KARMA) model, which was recently proposed for modeling double bounded environmental time series. In this context, this work proposes control charts for double bounded and autocorrelated data based on the KARMA model. The results were numerically evaluated using Monte Carlo simulations, by analyzing the average run length (ARL) of the series under control (ARL0) and out of control (ARL1). The performance of the proposed control charts were compared with other methodologies in the literature, under different scenarios. The KARMA control charts outperforms the competitors in several scenarios, presenting the smallest distortions for ARL0 and the best power detection rates under out of control conditions. In a second part of this work, a robust methodology using weighted maximum likelihood estimators is proposed aiming to minimize the effect of outliers, which are typically present in historical hydrological series, in the performance of control charts. The estimators were evaluated with Monte Carlo simulations in terms of specific robustness measures and by comparing the performance of the control charts initially proposed versus the robust approach. It was identified that the robust control charts present better performance in the presence of outliers. Finally, the developed techniques are employed in real monitoring data of hydrological systems and the results are discussed. These control charts proved to be a useful tool for managing water storage, such as the Cantareira System and the reservoir of the Furnas hydroelectric power plant. In 2014, a crisis in the water supply of these systems was reported and the proposed charts were able to identify it. In this way, it is confirmed the potential of the proposed control charts to monitor water reservoir levels.