In numerous practical domains such as reliability and performance engineering, finance, healthcare, and supply chain management, a common and formidable challenge revolves around the accurate modeling of intricate time-based data and event durations. The inherent complexities inherent to real-world systems often render the effective application of conventional statistical distributions a formidable task. Phase-type (PH) distributions emerge as a remarkably adaptable class of distributions ideally suited for modeling scenarios like failure times or response times, thanks to their Markovian representation. These distributions find utility in both analytical and simulation-driven approaches for system evaluation , and they are frequently employed to approximate empirical datasets. This paper introduces an approach that leverages user-friendly tools, graphical adjustment features, and integration with existing tools to streamline the process of fitting PH distributions to empirical data. Simplifying this procedure empowers domain experts to more accurately model complex systems, resulting in enhanced decision-making, more efficient resource allocation, improved reliability assessments, and optimized system performance across an extensive spectrum of practical domains where the analysis of time-based data remains pivotal. Furthermore, this study presents a method for the automated determination of parameters within a fitted Hyper-Erlang distribution. This method utilizes the Bayesian Information Criterion (BIC) within a Bayesian optimization framework integrated into an Expectation-Maximization (EM) algorithm. Consequently , it enables the derivation of the probability density function (pdf) for a given dataset through a combination of Hyper-Erlang distributions. Subsequently, this pdf serves as a critical tool for the assessment of system performance.