On the Flexible Neo-Normal MSAR MSN-Burr Control Chart in Air Quality Monitoring

Air quality significantly influences human health and the environment, necessitating a robust monitoring to detect abnormalities. This paper aims to develop a new model to accurately capture air quality data's structural changes and asymmetrical patterns. We introduce the neo-normal Markov Switching Autoregressive (MSAR) Modified Skew Normal Burr (MSN-Burr) model, called neo-normal MSAR MSN-Burr. This model extends the MSAR normal framework, handling symmetrical and asymmetrical patterns in air quality data. The MSN-Burr distribution is employed for accurate estimation of skewed and symmetric data. The model efficiency is demonstrated through simulation studies generating symmetric data with normal, double exponential, and Student-t distributions, followed by application to real air quality data using Stan language. The proposed model successfully adapts to asymmetric structural changes, as evidenced by creating the Highest Posterior Distribution (HPD) for upper and lower limits. The model identifies two regimes representing normal and abnormal air quality conditions, with modes of 8 and 19 mu g/m3, respectively. The MSAR-MSN-Burr model exhibits a 32.27% RMSE improvement in simulations and a 16.4% RMSE improvement in real air quality data over the normal-MSAR model. The proposed neo-normal MSAR MSN-Burr model is significantly enhancing the accuracy of air quality monitoring, providing a more efficient tool for detecting air quality abnormalities.