A novel reliability evaluation procedure of lead-free solders used in electronic packaging (EP) subjected to thermomechanical loading is proposed. A solder ball is represented by finite elements (FEs). Major sources of nonlinearities are incorporated as realistically as practicable. Uncertainties in all design variables are quantified using available information. The thermomechanical loading is represented by five design parameters and uncertainties associated with them are incorporated. Since the performance or limit state function (LSF) of such complicated problem is implicit in nature, it is approximately generated explicitly in the failure region with the help of a completely improved response surface method (RSM)-based approach and the universal Kriging method (KM). The response surface (RS) is generated by conducting as few deterministic nonlinear finite element analyses as possible by integrating several advanced factorial mathematical concepts producing compounding beneficial effect. The accuracy, efficiency, and application potential of the procedure are established with the help of Monte Carlo simulation (MCS) and the results from laboratory investigation reported in the literature. The study conclusively verified the proposed method. Similar studies can be conducted to fill the knowledge gap for cases where the available analytical and experimental studies are limited or extend the information to cases where reliability information is unavailable. The study showcased how reliability information can be extracted with the help of multiple deterministic analyses. The authors believe that they proposed an alternative to the classical MCS technique.

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