Atmospheric pollution derives mainly from anthropogenic activities that use combustion and may lead to adverse effects in exposed populations. It is generally accepted that air contamination causes cardiovascular and pulmonary morbidity in addition to increased mortality after exposure, but other epidemiological associations have also been described, including cancer as well as reproductive and immunological toxicity. Thus the concentration of chemicals in the air must be controlled. We propose that monitoring of air quality may be achieved by employing data analytics to generate information within the context of data-driven decision making to prevent and/or adequately alert the population about possible critical episodes of air contamination. In this paper, we propose a methodology for monitoring particulate matter pollution in Santiago of Chile which is based on bivariate control charts with heavy-tailed asymmetric distributions. This methodology is useful for monitoring environmental risk when the particulate matter concentrations follow bivariate Birnbaum-Saunders or Birnbaum-Saunders-t-Student distributions. A case study with real particulate matter pollution from Santiago is provided, which shows that the methodology is suitable to alert early episodes of extreme air pollution. The results are in agreement with the critical episodes reported with the current model used by the Chilean health authority.