Monitoring Environmental Risk by a Methodology Based on Control Charts
We propose a methodology based on control charts when the contaminant concentration follows a Birnbaum-Saunders distribution, which is implemented in the R software. We investigate the performance of this methodology through Monte Carlo simulations. An example with real-world data is given as an illustration of the proposed methodology.
KeywordsBirnbaum-Saunders distribution Contaminant concentration Maximum likelihood and moment estimation Monte Carlo simulation R software X-bar charts.
The authors wish to thank the Editors of the volume “Risk Assessment Challenges: Theory and Practice” of Springer Proceedings in Mathematics and Statistics, Dr. Christos Kitsos and Dr. Teresa A. Oliveira, and three anonymous referees for their constructive comments on an earlier version of this manuscript which resulted in this improved version. This research was partially supported by FONDECYT 1120879 grant from Chile, and by CAPES, CNPq and FACEPE grants from Brazil. H. Saulo thanks Universidade Federal de Goiás from Brazil for supporting this research.
- 5.Barros, M., Leiva, V., Ospina, R., Tsuyuguchi, A.: Goodness-of-fit tests for the Birnbaum-Saunders distribution with censored reliability data. IEEE Trans. Reliab. 63, 543–554 (2014)Google Scholar
- 20.Leiva, V., Marchant, C., Saulo, H., Aslam, M., Rojas, F.: Capability indices for Birnbaum-Saunders processes applied to electronic and food industries. J. Appl. Stat. 41, 1881–1902 (2014)Google Scholar
- 21.Leiva, V., Saulo, H., Leao, J., Marchant, C.: A family of autoregressive conditional duration models applied to financial data. Comput. Stat. Data Anal. 79, 175–191 (2014)Google Scholar
- 25.Marchant, C., Leiva, V., Cavieres, M.F., Sanhueza, A.: Air contaminant statistical distributions with application to PM10 in Santiago, Chile. Rev. Environ. Contam. Toxicol. 223, 1–31 (2013)Google Scholar
- 27.Montgomery, D.: Introduction to Statical Quality Control. Wiley, New York (2008)Google Scholar
- 35.Woodall, W.H.: The use of control charts in health-care and public-health surveillance. J. Qual. Tech. 38, 89–104 (2006)Google Scholar