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.

中文翻译：

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随机前沿和灰色关联分析在多目标问题鲁棒设计中的应用

已经提出了在开发产品和过程中进行稳健设计的通用程序，称为 RDPP-SF。该方法使用随机前沿模型来包含随机噪声（例如制造单元间的变异和测量误差）和特殊原因的变异（例如环境、客户使用、磨损和劣化噪声）。即便如此，RDPP-SF方法仍无法解决多目标问题的鲁棒设计，其适用性受限于幅度类型的性能特征（即“越大越好”或“越小越好”） ”）。针对这些局限性，本文试图使用 RDPP-SF 方法解决多目标问题的稳健设计。这是通过重新评估 RDPP-SF 方法的程序方案和假设检验的统计显着性 (H0: γ = 0 vs H1: γ > 0) 在 5% 水平上执行的。根据测试的统计显着性（H0：γ = 0 vs H1：γ > 0），外在和/或内在噪声不敏感分数的数组被分配给灰色关联分析矩阵作为性能度量。然后通过对整体灰色关联等级进行排序来获得针对多目标问题的最稳健的设计解决方案。修改后的 RDPP-SF 方法最终使用三个工业多目标案例研究进行了演示。外在和/或内在噪声不敏感分数的数组被分配给灰色关联分析矩阵作为性能度量。然后通过对整体灰色关联等级进行排序来获得针对多目标问题的最稳健的设计解决方案。修改后的 RDPP-SF 方法最终使用三个工业多目标案例研究进行了演示。外在和/或内在噪声不敏感分数的数组被分配给灰色关联分析矩阵作为性能度量。然后通过对整体灰色关联等级进行排序来获得针对多目标问题的最稳健的设计解决方案。修改后的 RDPP-SF 方法最终使用三个工业多目标案例研究进行了演示。