Hybrid approach advocates combining two or more traditional technologies to overcome the limitations of the conventional practice. The devised Hybrid TIG MAG arc welding process with the help of an indigenous fixture overcomes the shortcomings of the conventional arc welding. The success of any hybrid technology depends on synergistic parameter interactions which demand a rigorous process control through parameter optimization. The devised process is controlled by 13 major parameters. Optimization of all the process controlling parameters is a resource consuming activity. This study manifests an analytic framework as a combination of hierarchical and networking decision making algorithms, which seeks input on parameter effects and their ranges arrived at through experimentation and gives a ranked or prioritized list of process controlling parameters as an output. The framework identifies 5 critical parameters responsible for the 62% of the parameter interactions which need to be optimized based on the application or the job at hand. The remaining 8 parameters responsible for the balance 38% of the parameter interactions have been stabilized through experimentation once for all process variations irrespective of the application or the job at hand. The study works on the merger of the process optimization and the process prioritization techniques.