Integrated reliability and cost optimization for multi-version software release decisions with imperfect debugging and delayed fault removal

Modern software-intensive engineering systems require release planning strategies that simultaneously balance software reliability, development cost, and time-to-market under uncertain debugging conditions. Existing software reliability growth models (SRGMs) generally assume perfect debugging or instantaneous fault removal, whereas practical software development often involves imperfect fault correction, delayed debugging processes, and multiple sequential software releases. Moreover, most existing studies primarily focus on reliability estimation rather than optimization-oriented release decision support. To address these limitations, this study proposes an integrated optimization framework for multi-version software release planning that jointly considers imperfect debugging, time-delayed fault removal, and reliability–cost trade-offs. The proposed framework is developed based on a non-homogeneous Poisson process (NHPP) and extends conventional SRGMs by explicitly modeling the interactions among fault detection, delayed correction, and debugging efficiency across successive software versions. A joint optimization model is subsequently formulated to determine economically efficient release policies while satisfying predefined reliability requirements. Numerical experiments demonstrate that the proposed approach consistently achieves lower total expected costs and improved release decisions compared with conventional sequential planning methods. Sensitivity analyses further reveal the significant influence of debugging efficiency, delay effects, and fault-removal dynamics on optimal release policies and overall software reliability. From an industrial engineering perspective, the proposed framework provides an effective computational decision-support methodology for software release management by integrating reliability modeling with optimization techniques. The results offer practical managerial insights for balancing software quality, development resources, and release scheduling in complex multi-version software development environments.