Use of the stochastic frontier and the grey relational analysis in robust design of multi-objective problems

A generic procedure for robust design in developing products and processes, which is referred to as RDPP-SF has been proposed. The method uses the stochastic frontier model to encompass both stochastic noise (e.g. manufacturing unit-to-unit variation, and measurement errors) and special-cause variation (e.g. environment, customer use, wearing, and deterioration noises). Even then, the RDPP-SF method has fallen short of tackling robust design of multi-objective problems, and its applicability is restrained to the performance characteristics of magnitude type (i.e., “the larger is the better” or “the smaller is the better”). Aiming at these limitations, the article seeks to address the robust design of the multi-objective problems using the RDPP-SF method. This is performed by reassessing the procedural scheme of the RDPP-SF method and the statistical significance of the hypothesis test (H₀: γ = 0 vs H₁: γ > 0) at 5% level. Depending on the statistical significance of the test (H₀: γ = 0 vs H₁: γ > 0), the arrays of the extrinsic and/or the intrinsic noise insensitivity scores are assigned to the grey relational analysis matrix as performance measures. The most robust design solution for the multi-objective problem is then obtained by sorting the overall grey relational grades. The amended RDPP-SF method is finally demonstrated using three industrial multi-objective case studies.