Reliability growth models are integral to evaluating and improving the reliability of software systems. However, the increasing reliance on sensitive data in reliability modelling raises critical concerns about data privacy and ethical implications. This paper introduces a mathematical framework for integrating data privacy constraints into software reliability growth models, leveraging a public dataset from the NASA Reliability Dataset Repository. By incorporating differential privacy mechanisms, the proposed model ensures robust privacy preservation while maintaining the integrity of reliability metrics. We present the methodology, key mathematical formulations, and an in-depth analysis of trade-offs between privacy and model accuracy. Simulation results demonstrate the effectiveness of the framework, providing actionable insights for ethical and privacy conscious reliability modeling in software systems.