Factorial and response surface designs robust to missing observations

Made available in DSpace on 2018-11-26T17:35:05Z (GMT). No. of bitstreams: 0 Previous issue date: 2017-09-01Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Compound optimum design criteria which allow pure error degrees of freedom may produce designs that break down when even a single run is missing, if the number of experimental units is small. The inclusion, in the compound criteria, of a measure of leverage uniformity is proposed in order to produce designs that are more robust to missing observations. By appropriately choosing the weights of each part of the criterion, robust designs are obtained that are also highly efficient in terms of other properties. Applications to various experimental setups show the advantages of the new methods. (C) 2016 Elsevier B.V. All rights reserved.USP UFSCar, Programa Interinst Posgrad Estat, Sao Carlos, SP, BrazilKings Coll London, Dept Math, London, EnglandUniv Estadual Paulista, Dept Bioestat, IB, Botucatu, SP, BrazilUniv Estadual Paulista, Dept Bioestat, IB, Botucatu, SP, BrazilFAPESP: 2014/01818-

Split-Plot Central Composite Designs Robust to a Pair of Missing Observations

This study constructs robust split-plot central composite designs against missing pairs of observations. Split-plot central composite designs (CCD) consist of factorial (f), whole-plot axial (α), subplot axial (β), and center (c) points. A loss function in terms of determinant (D) criterion was formulated based on two different configurations of the factorial and axial parts; losses due to missing pairs of observations of these different categories of points were investigated. Robust split-plot central composite designs against missing pairs of observations were then developed under each of the two configurations. It was observed that the losses, Lff, Lββ, and Lfβ, due respectively, to missing pairs of observations of the factorial, subplot axial, and, factorial and subplot axial points, were higher than the losses due to missing pairs of observations of the whole-plot axial and center points given by Lαα and Lcc respectively. Thus the factorial (f) and the subplot axial (β) points were found to be the most influential points in these designs while the whole-plot axial (α) and the center (c) points were less influential. This work has therefore identified and properly classified the losses due to missing design points in the split-plot CCD portions. In this way, the practitioner can avoid the experimental points having less influence from the full CCD experiments and this could lead to a possible increase in design efficiency.Keywords: Robustness, Split-plot Central Composite Designs, Missing observations, loss functio

Missing Observations in Split-Plot Central Composite Designs: The Loss in Relative A-, G-, and V- Efficiency

The trace (A), maximum average prediction variance (G), and integrated average prediction variance (V) criteria are experimental design evaluation criteria, which are based on precision of estimates of parameters and responses. Central Composite Designs(CCD) conducted within a split-plot structure (split-plot CCDs) consists of factorial (), whole-plot axial (), subplot axial (), and center () points, each of which play different role in model estimation. This work studies relative A-, G- and V-efficiency losses due to missing pairs of observations in split-plot CCDs under different ratios (d) of whole-plot and sub-plot error variances. Three candidate designs of different sizes were considered and for each of the criteria, relative efficiency functions were formulated and used to investigate the efficiency of each of the designs when some observations were missing relative to the full one. Maximum A-efficiency losses of 19.1, 10.6, and 15.7% were observed at = 0.5, due to missing pairs , , and , respectively, indicating a negative effect on the precision of estimates of model parameters of these designs. However, missing observations of the pairs- , , , , and did not exhibit any negative effect on these designs' relative A-efficiency. Maximum G- and Vefficiency losses of 10.1,16.1,0.1% and 0.1, 1.1, 0.2%, were observed, respectively, at = 0.5, when the pairs- , , , were missing, indicating a significant increase in the designs' maximum and average variances of prediction. In all, the efficiency losses become insignificant as d increases. Thus, the study has identified the positive impact of correlated observations on efficiency of experimental designs. Keywords: Missing Observations, Efficiency Loss, Prediction varianc

SAS Macros for Analysis of Unreplicated 2^k and 2^k-p Designs with a Possible Outlier

Many techniques have been proposed for judging the significance of effects in unreplicated 2^k and 2^k-p designs. However, relatively few methods have been proposed for analyzing unreplicated designs with possible outliers. Outliers can be a major impediment to valid interpretation of data from unreplicated designs. This paper presents SAS macros which automate a manual method for detecting an outlier and performing an analysis of data from an unreplicated 2^k or 2^k-p design when an outlier is present. This method was originally suggested by Cuthbert Daniel and is based on the normal or half normal plot of effects. This automated version was shown in simulation studies to perform better than other procedures proposed to do the same thing.

Orthogonal-Array based Design Methodology for Complex, Coupled Space Systems

The process of designing a complex system, formed by many elements and sub-elements interacting between each other, is usually completed at a system level and in the preliminary phases in two major steps: design-space exploration and optimization. In a classical approach, especially in a company environment, the two steps are usually performed together, by experts of the field inferring on major phenomena, making assumptions and doing some trial-and-error runs on the available mathematical models. To support designers and decision makers during the design phases of this kind of complex systems, and to enable early discovery of emergent behaviours arising from interactions between the various elements being designed, the authors implemented a parametric methodology for the design-space exploration and optimization. The parametric technique is based on the utilization of a particular type of matrix design of experiments, the orthogonal arrays. Through successive design iterations with orthogonal arrays, the optimal solution is reached with a reduced effort if compared to more computationally-intense techniques, providing sensitivity and robustness information. The paper describes the design methodology in detail providing an application example that is the design of a human mission to support a lunar base

Análise de desenhos experimentais com outliers

Primary purpose of the article is to develop outlier robust designs. As a matter of fact, negative effect of outliers in any experimental settings is established where the outliers at any specific design point can destroy the features of the design for which it is being developed. It is attempted here in this article to develop a version of robustness for central composite designs which may protect it for outliers by introducing the idea of minimax outlying effect. This involves the calculation of the degree of outlying effect(s) outlier(s) may produce and then minimize the maximum of these outlying effects in an attempt to equalize the influence of all design points. On comparison, these outlier robust designs are proved to be more optimal, on the scales of A, D, and E optimalities, against existing conventional rotatable, orthogonal, and other such designs. The outlier robust designs, developed here, are suitable for settings prone to outliers where conventional designs fail to represent and analyze the processes and systems.El objetivo principal del artículo es desarrollar diseños robustos atípicos. De hecho, el efecto negativo de los valores atípicos en cualquier configuración experimental se establece donde los valores atípicos en cualquier punto de diseño específico pueden destruir las características del diseño para el que se está desarrollando. En este artículo se intenta desarrollar una versión de robustez para los diseños compuestos centrales que pueden protegerlo de los valores atípicos mediante la introducción de la idea del efecto periférico minimax. Esto implica el cálculo del grado de efecto (s) externo (s) que puede producir un valor atípico y luego minimizar el máximo de estos efectos externos en un intento de igualar la influencia de todos los puntos de diseño. En comparación, se demuestra que estos diseños robustos atípicos son más óptimos, en las escalas de las optimidades A, D y E, frente a los diseños convencionales existentes, ortogonales, rotativos y otros similares. Los diseños robustos atípicos, desarrollados aquí, son adecuados para configuraciones propensas a los valores atípicos en los que los diseños convencionales no representan ni analizan los procesos y sistemas.Objetivo principal do artigo é desenvolver projetos robustos outlier. De fato, o efeito negativo de outliers em qualquer ambiente experimental é estabelecido onde os outliers em qualquer ponto de design específico podem destruir os recursos do design para o qual ele está sendo desenvolvido. Neste artigo, tenta-se desenvolver uma versão de robustez para projetos compostos centrais que possam protegê-lo de outliers, introduzindo a ideia de efeito periférico minimax. Isso envolve o cálculo do grau de efeito (s) outlier (s) outlier (s) pode produzir e, em seguida, minimizar o máximo desses efeitos periféricos em uma tentativa de equalizar a influência de todos os pontos do projeto. Em comparação, esses designs robustos discrepantes são comprovadamente mais otimizados, nas escalas de otimalidades A, D e E, contra os designs convencionais rotacionais, ortogonais e outros existentes. Os designs robustos outlier, desenvolvidos aqui, são adequados para configurações propensas a outliers em que projetos convencionais não representam e analisam os processos e sistemas

Trend-resistant and cost-efficient cross-over designs for mixed models.

A mixed model approach is used to construct optimal cross-over designs. In a cross-over experiment the same subject is tested at different points in time. Consider as an example an experiment to investigate the influence of physical attributes of the work environment such as luminance, ambient temperature and relative humidity on human performance of acceptance inspection in quality assurance. In a mixed model context, the subject effects are assumed to be independent and normally distributed. Besides the induction of correlated observations within the same inspector, the mixed model approach also enables one to specify the covariance structure of the inspection data. Here, several covariance structures are considered either depending on the time variable or not. Unfortunately, a serious drawback of the inspection experiment is that the results may be influenced by an unknown time trend because of inspector fatigue due to monotony of the inspection task. In other circumstances, time trend effects can be caused by learning effects of the test subjects in behavioural and life sciences, heating or aging of material in prototype experiments, etc. An algorithm is presented to construct cross-over designs that are optimally balanced for time trend effects. The costs for using the subjects and for altering the factor levels between consecutive observations can also be taken into account. A number of examples illustrate utility of the outlined design methodology.Optimal; Models; Model;