Process safety is a critical component in various process industries. Statistical process monitoring techniques were initially developed to maximize efficiency and productivity, but over the past few decades with catastrophic industrial disasters, process safety has become a top priority. Sensors play a crucial role in recording process measurements, and according to the number of monitored variables, process monitoring techniques can be classified into univariate or multivariate techniques. Most univariate process monitoring techniques rely on three fundamental assumptions: that process residuals contain a moderate level of noise, are independent, and are normally distributed. Practically, however, due to a variety of reasons such as modeling errors and malfunctioning sensors, these assumptions are violated, which can lead to catastrophic incidents. Fortunately, multiscale wavelet-based representation of data inherently possesses characteristics that are able to deal with these violations of assumptions. Therefore, in this work, multiscale representation is utilized to enhance the performance of the Shewhart chart (which is a well-known univariate fault detection method) to help improve its performance. The performance of the developed multiscale Shewhart chart was assessed and compared to the conventional chart through two examples, one using synthetic data, and the other using simulated distillation column data. The results of both examples clearly show that the developed multiscale Shewhart chart provides lower missed detection and false alarm rates, as well as lower ARL1 values (i.e., quicker detection) for most cases where the fundamental assumptions of the Shewhart chart are violated. Additionally, the relative simplicity of the proposed algorithm encourages its implementation in practice to help improve process safety.