Response Surface Splitplot Designs: A Literature Review

The fundamental principles of experiment design are factorization, replication, randomization, and local control of error. In many industrial experiments, however, departure from these principles is commonplace. Often in our experiments, complete randomization is not feasible because factor level settings are hard, impractical, or inconvenient to change, or the resources available to execute under homogeneous conditions are limited. These restrictions in randomization result in split-plot experiments. Also, we are often interested in fitting second-order models, which lead to second-order split-plot experiments. Although response surface methodology has experienced a phenomenal growth since its inception, second-order split-plot design has received only modest attention relative to other topics during the same period. Many graduate textbooks either ignore or only provide a relatively basic treatise of this subject. The peer-reviewed literature on second-order split-plot designs, especially with blocking, is scarce, limited in examples, and often provides limited or too general guidelines. This deficit of information leaves practitioners ill-prepared to face the many challenges associated with these types of designs. This article seeks to provide an overview of recent literature on response surface split-plot designs to help practitioners in dealing with these types of designs

Optimal designs for estimating critical effective dose under model uncertainty in a dose response study

Toxicologists have been increasingly using a class of models to describe a continuous response in the last few years. This class consists of nested nonlinear models and is used for estimating various parameters in the models or some meaningful function of the model parameters. Our work here is the first to address design issues for this popular class of models among toxicologists. Specifically we construct a variety of optimal designs under model uncertainty and study their properties for estimating the critical effective dose (CED), which is model dependent. Two types of optimal designs are proposed: one type maximizes the minimum of efficiencies for estimating the CED regardless which member in the class of models is the appropriate model, and (ii) dual-objectives optimal design that simultaneously selects the most appropriate model and provide the best estimates for CED at the same time. We compare relative efficiencies of these optimal designs and other commonly used designs for estimating CED. To facilitate use of these designs, we have constructed a website that practitioners can generate tailor-made designs for their settings. --compound optimal design,critical effect size,local optimal design,maximin optimal design,model discrimination,robust design

Optimal designs for estimating critical effective dose under model uncertainty in a dose response study

Toxicologists have been increasingly using a class of models to describe a continuous response in the last few years. This class consists of nested nonlinear models and is used for estimating various parameters in the models or some meaningful function of the model parameters. Our work here is the first to address design issues for this popular class of models among toxicologists. Specifically we construct a variety of optimal designs under model uncertainty and study their properties for estimating the critical effective dose (CED), which is model dependent. Two types of optimal designs are proposed: one type maximizes the minimum of efficiencies for estimating the CED regardless which member in the class of models is the appropriate model, and (ii) dual-objectives optimal design that simultaneously selects the most appropriate model and provide the best estimates for CED at the same time. We compare relative efficiencies of these optimal designs and other commonly used designs for estimating CED. To facilitate use of these designs, we have constructed a website that practitioners can generate tailor-made designs for their settings. --compound optimal design,critical effect size,local optimal design,maximin optimal design,model discrimination,robust design

State-of-the-Art and Comparative Review of Adaptive Sampling Methods for Kriging

Metamodels aim to approximate characteristics of functions or systems from the knowledge extracted on only a finite number of samples. In recent years kriging has emerged as a widely applied metamodeling technique for resource-intensive computational experiments. However its prediction quality is highly dependent on the size and distribution of the given training points. Hence, in order to build proficient kriging models with as few samples as possible adaptive sampling strategies have gained considerable attention. These techniques aim to find pertinent points in an iterative manner based on information extracted from the current metamodel. A review of adaptive schemes for kriging proposed in the literature is presented in this article. The objective is to provide the reader with an overview of the main principles of adaptive techniques, and insightful details to pertinently employ available tools depending on the application at hand. In this context commonly applied strategies are compared with regards to their characteristics and approximation capabilities. In light of these experiments, it is found that the success of a scheme depends on the features of a specific problem and the goal of the analysis. In order to facilitate the entry into adaptive sampling a guide is provided. All experiments described herein are replicable using a provided open source toolbox. © 2020, The Author(s)

Design of Experiments for Screening

The aim of this paper is to review methods of designing screening experiments, ranging from designs originally developed for physical experiments to those especially tailored to experiments on numerical models. The strengths and weaknesses of the various designs for screening variables in numerical models are discussed. First, classes of factorial designs for experiments to estimate main effects and interactions through a linear statistical model are described, specifically regular and nonregular fractional factorial designs, supersaturated designs and systematic fractional replicate designs. Generic issues of aliasing, bias and cancellation of factorial effects are discussed. Second, group screening experiments are considered including factorial group screening and sequential bifurcation. Third, random sampling plans are discussed including Latin hypercube sampling and sampling plans to estimate elementary effects. Fourth, a variety of modelling methods commonly employed with screening designs are briefly described. Finally, a novel study demonstrates six screening methods on two frequently-used exemplars, and their performances are compared

Self learning strategies for experimental design and response surface optimization

Most preset RSM designs offer ease of implementation and good performance over a wide range of process and design optimization applications. These designs often lack the ability to adapt the design based on the characteristics of application and experimental space so as to reduce the number of experiments necessary. Hence, they are not cost effective for applications where the cost of experimentation is high or when the experimentation resources are limited. In this dissertation, we present a number of self-learning strategies for optimization of different types of response surfaces for industrial experiments with noise, high experimentation cost, and requiring high design optimization performance. The proposed approach is a sequential adaptive experimentation approach which combines concepts from nonlinear optimization, non-parametric regression, statistical analysis, and response surface optimization. The proposed strategies uses the information gained from the previous experiments to design the subsequent experiment by simultaneously reducing the region of interest and identifying factor combinations for new experiments. Its major advantage is the experimentation efficiency such that, for a given response target, it identifies the input factor combination (or containing region) in less number of experiments than the classical designs. Through extensive simulated experiments and real-world case studies, we show that the proposed ASRSM method clearly outperforms the classical CCD and BBD methods, works superior to optimal A- D- and V- optimal designs on average and compares favorably with global optimizations methods including Gaussian Process and RBF

Development of Protocols for Metabolomics in Biomedical Research using Chemometrics

Metabolomics is a rapidly growing research field. It aims for quantification of all the metabolites in a biological sample such as plasma, saliva, cerebrospinal fluid or cells. Because the metabolite levels in a biological sample are the end result of the regulatory processes in cells, metabolomics is a very powerful approach for characterisation of phenotypes. Metabolomics has been used to find disease biomarkers, investigate influences of heavy metals on the metabolism and to elucidate gene function. However, analysis of the complete metabolome puts high demands on the methods used. For instance, the methods should be unbiased to accurately depict the in vivo status in the cell. Furthermore, the methods must have very high resolution and sensitivity to allow detection of all metabolites. To approach these high goals, the protocols used in metabolomics need to be thoroughly optimised. The amount of information contained in the metabolome is immense. Consequently, the data set collected from a metabolomics study is very large. To extract the relevant information from such large sets of data, efficient methods are needed both to plan experiments and to convert the data to useful information. For this task, chemometrics is an ideal approach as it allows efficient experimental planning and multivariate data analysis. The experimental planning is sometimes referred to as statistical experimental design or design of experiments. It aims to systematically and simultaneously vary experimental factors in a structured manner. Hence, fewer experiments are generally needed to efficiently map how the system is affected by prevailing factors. The multivariate data analysis employs powerful projection and regression methods to find patterns in data, create system models and classify data. Hence, chemometrics provides a framework for efficient experimental design and an efficient approach for information retrieval. In this thesis two thorough developments of metabolomics protocols and three metabolomics investigations, relevant to metabolic regulation in diabetes patients and insulin-producing cells, are presented. The design of experiments approach and multivariate data analysis were applied. The developed protocols were optimised and validated for the analysis of human blood plasma and adherent cell cultures, respectively, and included optimisation from the sample preparation to the analysis with gas chromatography/mass spectrometry. The first of the metabolomics studies aimed to find biomarkers reflecting metabolic regulation during an oral glucose tolerance test in humans to aid in the diagnosis of diabetes. The second study was performed on clonal β-cells and aimed to find metabolic regulation coupled to the amplifying pathway of insulin secretion. The last study aimed to identify metabolic dysregulation in clonal β-cells growing under lipotoxic and glucotoxic conditions, respectively. In all studies, metabolomics extended and deepened the understanding of metabolic regulation in cells and patients. As such, metabolomics will help to find explanations for metabolic diseases such as diabete