“Intelligent and Distribution-Based Software Reliability Growth Models: A Unified Framework with Mathematical Derivations, Graphs, and Comparative Evaluation”

Abstract

In the era of digitally driven systems and pervasive computing, the integrity and dependability of software systems form the backbone of functional and economic ecosystems. This research paper presents a unified and comprehensive study of Software Reliability Growth Models (SRGMs), synthesizing artificial intelligence (AI) - enabled predictive techniques and distribution-based probabilistic modeling approaches. Drawing insights from recent developments, this work investigates both data-driven models such as neural networks, fuzzy logic, and evolutionary algorithms, as well as advanced mathematical models derived from extended probability distributions—particularly the non-homogeneous Poisson process (NHPP) integrated with the Extended Log-Logistic (ELL) distribution. Theoretical formulations are extensively elaborated, along with key reliability metrics such as the Mean Value Function (MVF), Intensity Function, Error Detection Rate (EDR), and Remaining Errors (NRE). Parameter estimation is examined via Maximum Likelihood Estimation (MLE), and comparative performance of models is highlighted through detailed graphs and tables. By integrating the strengths of intelligent systems and classical statistical foundations, this study not only enhances prediction accuracy but also provides interpretability and real-world applicability. This paper concludes with future research pathways and recommendations for optimizing SRGM under uncertainty and limited testing data.