The fault detection rate during the operational phase is directly proportional to the testing and debugging efforts during the software development. Extensive testing on software often reveals hidden faults previously undetected. During fault detection, the change points identify significant variations in software reliability, indicating possible faults. These helps test managers and engineers assess testing effectiveness, evaluate the impact of modifications and accurately track testing progress. Imperfect-debugging models can predict software reliability based on how often faults are found, and the discovered fault can be removed later. This work is an enhancement of the Jelinski-Moranda model by incorporating a hazard rate and imperfect-debugging parameters, including fault introduction and removal with a single change point, and it demonstrates that this proposed model outperforms classical models using various metrics with lesser parameters. The experimental findings show that the proposed work gives better reliability prediction with good results based on metrics such as the Akaike Information Criterion, Root Mean Squared Error, Hazard Rate Approach, Relative Error, Median Error, Multiple Determination Coefficient, Predictive Power and Relative Predictive Error.