Avaliação do desempenho do gráfico de controle de Shewhart para o processo OIB-INAR(1) e comparação com o desempenho do gráfico de Shewhart do processo Borel INAR(1)

Abstract

In the face of technological advances and the large amount of information generated, count data is becoming increasingly autocorrelated. This creates a growing need for new models and monitoring tools that take into account the specific characteristics of this data. In this paper, we propose a Shewhart control chart for autocorrelated count data that can be modeled by an INAR(1) process with innovations from the inflated Borel distribution of ones (OIB-INAR(1)). This model is well-suited for modeling data with an inflation of ones, as well as underdispesion, equidispersion, or overdispersion. Addicionally, we will compare the performance of this control chart with that of a Borel INAR(1) process, which models series of counts truncated at zero that show underdispersion, equidispersion or overdispersion. The Borel INAR(1) process can be seen as a particular case of the OIB-INAR(1) process. The performance evaluation of the proposed approach is based on the average number of samples required to detect an alarm (NMAF and NMA) in different scenarios. The determination of the upper control limit (UCL) and the evaluation of the performance of the graphs are carried out by means of computational studies using Monte Carlo simulations. To illustrate the applicability of the proposed method, we present an example with real data.