DOE-10 家活性材料供应商

[#1]

你好 ，

我想设计一个实验来研究活性材料浓度和最终颗粒大小之间的关系。我想测试 10 个不同的活性材料供应商，看看活性材料浓度如何影响最终的颗粒大小。

由于材料非常昂贵，我正在寻找一种高效的实验设计，既可以提供有意义的见解，又能最大限度地减少材料使用。

您能建议我该如何设计这个实验吗？

谢谢

[#2 · Accepted solution]

你好@YanivD ，

以下是我的想法：

一般来说，为了更好地理解因素之间的关系，我通常会采用顺序设计的实验方法，在开始时使用 2 级部分因子设计，采用“粗体”（尽可能分开）的级别设置并严格控制实验噪声（使用不同的噪声策略，例如随机化、映射噪声因子、保持它们恒定或更好地将它们用作因子等），以便发现少数重要效应，然后使用它们进行实验。

如果您离目标还很远，为了节省一些运行时间，我会从折叠设计 Res III 开始，以了解每个因素及其相互作用的效应大小，然后一旦您对响应中产生的变化感到满意，您就可以折叠设计以提高分辨率并开始处理混杂因素，筛选出非活性因素和相互作用，然后继续使用推理空间向最优点移动。一开始我不会运行重复，而是根据效应的稀疏性筛选出因子，使用 Daniel 图，以了解统计显着性，一旦您接近目标（要处理的因素少得多），您可以使用 RSM 方法更好地模拟最佳点附近的表面，重复以改进预测等

现在，关于您的案例，您能否提供更多信息，这 10 家供应商是否供应相同的产品，您需要从中选择一个吗？您是否知道工艺因素及其噪声是否会影响每个供应商的性能？

如果选择了区组策略，我仍然会按照上面提到的相同策略，使用过程因子和已经映射的噪声作为因子，运行部分因子设计，而不是对每个供应商进行重复试验，查看每个供应商的平均值变化，并使用统计测试来判断供应商是否存在统计差异，但这完全取决于您每次运行的成本和您已经拥有的信息。

一旦您为第一个区组运行了第一个部分因子设计，您就可能能够分辨出重要的影响，并且它们对于其他区组来说是有意义的，您可以使用这些知识来改进其他区组的实验。

具有因子设计的区块可能听起来不像是具有最少运行次数的策略，但我相信它将帮助您建立有关流程因素及其与供应商材料的相互作用的坚实知识基础。

如果您想进一步讨论该主题，请告诉我，

真挚地，

[#3]

Hi Emmanuel,

Thank you for the great points and questions - we will try

All the best,

Yaniv

[#4]

Hi @YanivD,

Adding to the great response from @gonzaef, it would be best to start simple and iterate for your DoE.

I'm not sure testing 10 different suppliers in the first experimental round is the most economical way to learn from the differences in raw materials. Furthermore, you may also have to consider batch-to-batch variability, as it may challenge the outcomes and conclusions you gathered from your previous experimental phase, so this would increase even more the number of samples tested/required (as you're not sure that one sample from one supplier may be representative and how much variability each supplier has). 

Instead, if your goal is to better understand how changes in raw materials may affect your process/responses, I would try to find informations/data that could help characterize the raw material, in documents like technical datasheet or by analyzing them prior to their introduction and testing.

• Once you have several factors/parameters that could help describe the variability of your raw material, you can use these factors as covariates in your DoE (thanks to the platform "Custom Design"), to make sure that only the batches that cover the most area of your experimental space (the more different) are selected. Since you won't be able to change the levels of these factors (only the suppliers can control in a certain range these specifications/factors), the use of these factors as covariates (with predefined possible levels) seems appropriate. You would then be able to link your responses directly to raw material characteristics, which helps having a broader view on the topic and help understanding and generalization. 
• You can also select them manually by running a Principal Component Analysis on the several characterization factors of the raw material, and then select only the most dissimilar (far apart) batches, so that you can have a better overview on how these characteristics may change your response(s).

For the DoE choice, there may be too little information to help you set up your design. As we don't know how many factors, which type(s), the constraints you have, your experimental budget, and how difficult to change some factors may be, it's hard to help you. The Custom design platform should be very helpful to deal with a large variety of constraints and design types.

If you would like to deep dive in the DOE choice and construction, feel free to provide more context and informations. 

Some references for further reading/learning about covariates and a Discovery Summit paper that may help you thinking about your topic (and switching from categorical level "supplier" to continuous covariate factors) :

What is a covariate in design of experiments? (jmp.com)

Developer Tutorial - Handling Covariates Effectively when Designing Experiments - JMP User Community

Coding with Continuous and Mixture Variables to Explore More of the Input Space ... - JMP User Commu...

I hope this complementary response will help you,

[#5]

Dear Victor,

Thank you so much for your ideas and solutions - as always including the links are valuable and can help.

all the best,

Yaniv