Abstract

Robust Parameter Design (RPD) is a quality improvement method to mitigate the effect of input noise on system output quality via adjustment of control and signal factors. This article considers RPD with multiple functional outputs and multiple target functions based on a time-consuming nonlinear simulator, which is a challenging problem rarely studied in the literature. The Joseph–Wu formulation of multi-target RPD as an optimization problem is extended to accommodate multiple functional outputs and use of a Gaussian Process (GP) emulator for the outputs. Due to computational demands in emulator fitting and expected loss function estimation posed by this big-data problem, a separable GP model is used. The separable regression and prior covariance functions, and the Cartesian product structure of the data are exploited to derive computationally efficient formulas for the posterior means of expected loss criteria for optimizing signal and control factors, and to develop a fast Monte Carlo procedure for building credible intervals for the criteria. Our approach is applied to an example on RPD of a coronary stent for treating narrowed arteries, which allows the optimal signal and control factor settings to be estimated efficiently. Supplementary materials are available for this article. Go to the publisher’s online edition of IISE Transactions, datasets, additional tables, detailed proofs, etc.

摘要

稳健参数设计 (RPD) 是一种质量改进方法，通过调整控制和信号因素来减轻输入噪声对系统输出质量的影响。本文基于耗时的非线性模拟器考虑具有多个函数输出和多个目标函数的 RPD，这是文献中很少研究的具有挑战性的问题。作为优化问题的多目标 RPD 的 Joseph-Wu 公式得到了扩展，以适应多个功能输出并使用高斯过程 (GP) 仿真器进行输出。由于这个大数据问题带来的模拟器拟合和预期损失函数估计的计算需求，使用了可分离的 GP 模型。可分离回归和先验协方差函数，并且利用数据的笛卡尔积结构来推导出用于优化信号和控制因素的预期损失标准的后验均值的计算有效公式，并开发快速蒙特卡罗程序以构建标准的可信区间。我们的方法应用于治疗狭窄动脉的冠状动脉支架 RPD 的示例，它允许有效地估计最佳信号和控制因子设置。补充材料可用于本文。转到出版商的在线版本 我们的方法应用于治疗狭窄动脉的冠状动脉支架 RPD 的示例，它允许有效地估计最佳信号和控制因子设置。补充材料可用于本文。转到出版商的在线版本 我们的方法应用于治疗狭窄动脉的冠状动脉支架 RPD 的示例，它允许有效地估计最佳信号和控制因子设置。补充材料可用于本文。转到出版商的在线版本IISE 交易、数据集、附加表、详细证明等。