Reliability-based multi-objective optimization of post-weld quenching parameters using Monte Carlo uncertainty propagation

Heat-treatment optimization conventionally returns a single deterministic setting, the point maximizing a desirability function, without reference to the experimental scatter around it. For a fabricator, the operative question is different: not which quenching condition is best on average, but what proportion of treated components will satisfy the specification. This paper reframes post-weld quenchant selection as a reliability problem and shows that the information required is already present, and discarded, in any published analysis of variance. Response models for six mechanical properties of shielded metal arc welded AISI/SAE 1020 steel, together with the residual mean squares of the corresponding analyzes of variance, are treated as a calibrated stochastic generator in which the residual mean squares supply a measured estimate of process scatter. A Monte Carlo ensemble is propagated through this generator to construct Pareto fronts by the non-dominated sorting genetic algorithm II and to map the probability of meeting a joint multi-response specification across the design space. Under a specification requiring yield strength at least 40 N/mm2, ductility at least 18% and reduction in area at most 52%, unforced air cooling attains unit conformance probability above 58.6 degrees while water and oil attain zero across the entire 55–60 degree groove range – although deterministic optimization ranks water quenching a close second at a desirability of 0.700, only 11% below air. Scalar aggregation measures average goodness, whereas a specification is a hard constraint on each response. The conclusion is robust to the three principal sources of doubt. The residual standard deviations, estimated on five to seven degrees of freedom, carry 95% confidence intervals spanning factors of 3.1–3.9, yet the ordering is unchanged at their upper bounds; no admissible correlation structure can alter it; and each response admits a wide band of specification limits over which the ordering holds.