Study on Order-of-Addition Experiments

添加顺序实验研究

• 批准号: 1810925
• 负责人: Dennis Lin
• 金额: $ 15万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-08-01 至 2022-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1810925&HistoricalAwards=false
• 关键词: Study; Order; Addition; Experiments

In many experiments, a number of reactants are added into the system sequentially rather than simultaneously. The formation, e.g., the amount/size/purity of the reaction products often depend on the order-of-addition (OofA) of different reactants. The OofA experiment can be traced back to Fisher (1937), where a lady was able to distinguish (by tasting) from whether the tea or the milk was first added to the cup. This is probably the first popular OofA experiment. In general, there are m required components and one hopes to determine the optimal sequence for adding these m components one after another. Knowing the optimal addition order of components related in production is crucial. Note that there are m! possible orders to be compared-for the tea-tasting example, there are m!=2!=2 possible orders. However, it is often unaffordable to test all the m! treatments, and the design problem arises (for example, when m = 10, m! is about 3.6 millions). Although it is somewhat primitive in Statistics, the OofA effect is frequently mentioned in many areas during the past decades. This includes bio-chemistry (Shinohara and Ogawa 1998), food science (Jourdain et al. 2009), nutritional science (Karim et al. 2000), and pharmaceutical science (Rajaonarivony et al. 1993), just to name a few. As the order-of-addition effect occurs in all kinds of real experiments as well as computer experiments, successful outcomes of this project can be directly used in many different areas, such as chemistry and biology. Furthermore, the proposed problems provide a golden opportunity for fundamental academic studies in other subjects.In this project, the PI plans to establish the fundamental theory of evaluating OofA designs. The PI also plans to construct classes of OofA designs, under different requirements of design efficiency and experimental budget. From the mathematical point of view, the OofA design is to select a subset of the symmetric group formed by all the m! permutations, and some research topics in group theories or combinatorics may arise thereby. For example, if a pairwise-order (PWO) model is assumed, there are m(m-1)/2 parameters to be estimated, and thus only m(m-1)/2+1 runs are needed (instead of m! runs). More advanced models are proposed and will be investigated as well. A fruitful application of computer science is anticipated, because the computational complexity for finding efficient OofA designs tremendously increases as m becomes large. The proposed approach on OofA experiment, although known in many fields, is a novel and new study in Statistics - it is very different in fundamental work for most prior research in this area, with high potential practical values. Many case studies and applications provide an early indication of the potential success of the proposed study.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

在许多实验中，许多反应物被顺序地而不是同时地添加到系统中。例如，反应产物的量/尺寸/纯度通常取决于不同反应物的加入顺序（OofA）。OofA实验可以追溯到Fisher（1937），在那里一位女士能够区分（通过品尝）是茶还是牛奶首先加入杯子。这可能是第一个流行的OofA实验。一般来说，有m个所需的组件，人们希望确定一个接一个地添加这m个组件的最佳顺序。了解生产中相关组分的最佳添加顺序至关重要。 请注意，有m！要比较的可能顺序-对于品茶的例子，有m！=二！= 2可能的命令 然而，它往往是负担不起的测试所有的m！处理，并且出现设计问题（例如，当m = 10时，m！约360万）。 虽然它在统计学中有些原始，但在过去的几十年中，OofA效应在许多领域经常被提及。 这包括生物化学（Shinohara和Ogawa，1998）、食品科学（Shakidain等人，2009）、营养科学（Karim等人，2000）和制药科学（Rajaonarivony等人，1993），仅举几例。由于加序效应存在于各种真实的实验以及计算机实验中，因此本项目的成功成果可以直接应用于化学和生物学等许多不同的领域。此外，提出的问题提供了一个黄金机会，在其他学科的基础学术研究。在这个项目中，PI计划建立评估OofA设计的基础理论。PI还计划根据设计效率和实验预算的不同要求构建OofA设计类。 从数学的角度来看，OofA设计是选择由所有m！排列，并在群论或组合学的一些研究课题可能会出现。 例如，如果假设成对顺序（PWO）模型，则存在m（m-1）/2个待估计的参数，并且因此仅需要m（m-1）/2+1次运行（而不是m！运行）。 更先进的模型被提出并将被研究。 计算机科学的一个富有成效的应用是预期的，因为找到有效的OofA设计的计算复杂性大大增加，因为m变得很大。提出的OofA实验方法，虽然在许多领域都是已知的，但在统计学中是一种新颖的新研究-它与该领域大多数先前研究的基础工作非常不同，具有很高的潜在实用价值。 许多案例研究和应用提供了一个早期迹象的潜在成功的拟议研究。这个奖项反映了NSF的法定使命，并已被认为是值得支持的评估使用基金会的知识价值和更广泛的影响审查标准。