In these last few decades, control charts have received a growing interest because of the important role they play by improving the quality of the products and services in industrial and non-industrial environments. Most of the existing control charts are based on the assumption of certainty and accuracy. However, in real-life applications, such as weather forecasting and stock prices, operators are not always certain about the accuracy of an observed data. To efficiently monitor such processes, this paper proposes a new cumulative sum (CUSUM) [Formula: see text] chart under the assumption of uncertainty using the neutrosophic statistic (NS). The performance of the new chart is investigated in terms of the neutrosophic run length properties using the Monte Carlo simulations approach. The efficiency of the proposed neutrosophic CUSUM (NCUSUM) [Formula: see text] chart is also compared to the one of the classical CUSUM [Formula: see text] chart. It is observed that the NCUSUM [Formula: see text] chart has very interesting properties compared to the classical CUSUM [Formula: see text] chart. The application and implementation of the NCUSUM [Formula: see text] chart are provided using simulated, petroleum and meteorological data.