The growing need for decarbonization and renewable energy integration has highlighted hydrogen's potential as a versatile energy carrier. However, the diverse production methods - green, blue, pink, grey, and emerging forms - exhibit distinct variability, cost structures, and environmental impacts, complicating unified analysis and planning. This article addresses this challenge by introducing a novel unified modeling framework for hydrogen production using a Weibull cumulative distribution function (CDF) approach. By dynamically adjusting the Weibull parameters (scale C and shape k) for each hydrogen type, the model provides a cohesive representation of production variability, stability, and operational characteristics. The results reveal significant differences in the Weibull parameters across hydrogen types: green hydrogen exhibits moderate C (556.1) and low k (3.73), indicating high variability due to renewable energy inputs. Blue and grey hydrogen have stable production profiles with higher k values (26.12 and 17.16, respectively), reflecting reduced sensitivity to fluctuations. Pink hydrogen demonstrates exceptional stability, with k exceeding 106, highlighting the continuous nature of nuclear power as an input source. These quantitative insights emphasize the framework's ability to accurately capture variability and stability across diverse hydrogen production pathways. This framework enables integrated analysis and optimization of hydrogen production, storage, and dispatch while facilitating direct comparisons across hydrogen types in terms of cost, emissions, and grid contributions. By supporting strategic decision-making in economic, environmental, and grid-stability planning, the model advances hydrogen's role in renewable energy integration and sustainable infrastructure development. This unified framework offers a versatile tool for driving innovation in hydrogen deployment and accelerating the global energy transition.