<p>Normal probability distribution is central to most statistical methods and their applications. In many real scenarios, the normality of the underlying phenomenon is not obvious. However, a deeper investigation can lead to normality through some useful links among various models. The current study aims to present one such approach to the Gaussian model by connecting it with the cumulative distribution function of the rectangular distribution. Some characteristics of the rectangular distribution, such as the quantiles, are used to achieve the said objective. Further, the derived distributional results have been used to design a mechanism to monitor the real-time dependent electron gun and file server processes. The performance of the proposed monitoring methodology is evaluated in terms of probability of signal, average run length, extra quadratic loss and cumulative extra quadratic loss. The expressions for probability to signal are derived mathematically and are supported by some tabular results. The results advocate the usefulness of the proposed methodology for effectively monitoring real-life processes.</p>