Problem statement: On a current operating condition of a laser beam welding process in the hard disk drive industry, it has been found that shear strength of the head support and suspension assembly is slightly higher than customers' specification. This situation leads to an inspection with a large sample size and a high frequency. Shear strength is not only one quality characteristic for this assembly, but other critical physical specifications of welding diameter and depth need to be also considered. Approach: A hybridization strategy, based on linear and nonlinear Constrained Response Surface Optimization Methods (CRSOM), has been developed for this process refinement. The hybridization is having a provision to include both explicit constraints of influential process variables as well as implicit constraints of physical specifications. Results: The proposed levels of influential process variables have been successfully implemented in terms of shear strength and satisfied both welding diameter and depth specifications. Conclusion: The advantage of the hybridization compared with individually CRSOM is that all the data from the experiment is collected together to make a final decision. When engineering problems are large and complicated, an effective finite sequence of instructions from the hybridization can be very useful and practical in setting industrial processes such as semiconductor or automotive manufacturing systems. [ABSTRACT FROM AUTHOR]