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An Integer Programming Approach to the Construction of Trend-Free Experimental Plans on Split-Plot Designs

机译：一种整数规划方法，用于分割样地设计的无趋势实验计划的构建

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In many experimental designs, the standard procedure involves randomization of the factor-level combination run order. There are cases, however, where it is known that a time or position trend that can seriously compromise the results of the experiment may be present. These trends include wear of tooling and equipment, learning curves, change in temperatures, and so on, and the trends may show up as linear, quadratic, or even higher order trends. All previously published work has dealt with various methods of constructing trend-resistant run order plans on full and fractional factorial designs. These previous efforts have not addressed any additional dimensions in the trends that emerge when using hierarchical designs such as split-plot plans. These designs are common in many manufacturing experiments where complete randomization is not possible or is too expensive to be practical. The objective of this work is to establish the foundations of a method for constructing linear and quadratic trend-resistant plans in two-level split-plot designs that addresses the two-dimensional trends that may occur. The methodology involves development of a hybrid approach using the foldover method in each of the dimensions of interest and embedding these in a nonlinear integer programming model in the search for a feasible solution. Feasibility of this approach is shown for the particular case of a split-plot design (2~5 whole-plot factors and 3~1 x 2~1 split-plot factors) performed on abrasive machining. In this case study, an experimental plan that is robust against all linear trends and most quadratic trends was achieved.
机译：在许多实验设计中，标准程序涉及因子级组合运行顺序的随机化。但是，在某些情况下，可能会出现严重影响实验结果的时间或位置趋势。这些趋势包括工具和设备的磨损，学习曲线，温度变化等，并且这些趋势可能显示为线性，二次甚至更高阶的趋势。先前所有已发表的工作都涉及了在完全和部分因子设计上构建抗趋势运行订单计划的各种方法。这些先前的努力并未解决使用分层设计（例如分割图计划）时出现的趋势中的任何其他方面。这些设计在许多制造实验中很常见，在这些实验中，完全随机化是不可能的，或者过于昂贵而无法实际应用。这项工作的目的是建立一种在两级分割图设计中构造线性和二次趋势趋势计划的方法的基础，该方法解决可能出现的二维趋势。该方法包括在每个感兴趣的维度中使用折叠方法开发混合方法，并将其嵌入非线性整数规划模型中以寻求可行的解决方案。对于在磨削加工中执行的分块图设计（2〜5个整图因子和3〜1 x 2〜1个分图因子）的特殊情况，显示了这种方法的可行性。在本案例研究中，实现了一个针对所有线性趋势和大多数二次趋势的稳健实验计划。

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