Most industrial processes are composed of multiple subsequent steps. In this article, we provide a statistical approach to design experiments and to define the manufacturing design space of multi-step processes by taking into account the complex system of interactions among steps. We consider each intermediate outcome as an additional input factor in the next step and we plan experiments following a particular sequential structure. To encompass the potential deviations from the target levels of such input factors, designs are selected according to the D-optimality in average criterion and, in order to assess their prediction capabilities, a suitable extension of the fraction of design space technique has been proposed. The manufacturing design space of the process is then defined by combining the interconnected manufacturing design spaces of the process steps and by deriving the linear combination of the process inputs that ensures the required quality standard for the final outcome. Appealing properties of this approach are also shown by the application to a three-steps biochemical process of expression and purification of a recombinant protein in which 10 input factors are included in the design.

中文翻译：

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多步骤工艺的实验设计和制造设计空间

大多数工业过程由多个后续步骤组成。在本文中，我们提供了一种统计方法来设计实验并通过考虑步骤之间相互作用的复杂系统来定义多步骤过程的制造设计空间。我们将每个中间结果视为下一步中的额外输入因素，并按照特定的顺序结构计划实验。为了包含与这些输入因素的目标水平的潜在偏差，根据平均标准中的 D 最优性选择设计，并且为了评估它们的预测能力，已经提出了设计空间分数技术的适当扩展。然后通过组合工艺步骤的互连制造设计空间并通过导出工艺输入的线性组合来定义工艺的制造设计空间，以确保最终结果所需的质量标准。这种方法的吸引人的特性还通过应用于重组蛋白表达和纯化的三步生化过程而显示出来，其中设计中包含 10 个输入因子。