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Pulsed Current Micro Plasma Arc welding (PCMPAW) process is an important joining process widely used in sheet metal fabrication industries. The paper focuses on developing mathematical models to predict grain size and ultimate tensile strength of pulsed current micro plasma arc welded Inconel 625 nickel alloy using Response Surface Method (RSM). The experiments were carried out based on Central Composite Design (CCD) with 31 combinations of experiments. The adequacy of the models is checked by Analysis of Variance (ANOVA) technique. Hooke and Jeeves method is used to minimize grain size and maximize the ultimate tensile strength.