1,573 research outputs found
A general theory of minimum aberration and its applications
Minimum aberration is an increasingly popular criterion for comparing and
assessing fractional factorial designs, and few would question its importance
and usefulness nowadays. In the past decade or so, a great deal of work has
been done on minimum aberration and its various extensions. This paper develops
a general theory of minimum aberration based on a sound statistical principle.
Our theory provides a unified framework for minimum aberration and further
extends the existing work in the area. More importantly, the theory offers a
systematic method that enables experimenters to derive their own aberration
criteria. Our general theory also brings together two seemingly separate
research areas: one on minimum aberration designs and the other on designs with
requirement sets. To facilitate the design construction, we develop a
complementary design theory for quite a general class of aberration criteria.
As an immediate application, we present some construction results on a weak
version of this class of criteria.Comment: Published at http://dx.doi.org/10.1214/009053604000001228 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Past developments and future opportunities in the design and analysis of crop experiments
A review of papers on the statistical design and analysis of experiments published in the Journal of Agricultural Science, Cambridge, over the last 100 years is presented. The development of significant ideas in the practical design of field experiments is reviewed. Some possible future developments in the design of spatial field trials and computer-aided design of experiments are discussed
Split-plot designs: What, why, and how
The past decade has seen rapid advances in the development of new methods for the design and analysis of split-plot experiments. Unfortunately, the value of these designs for industrial experimentation has not been fully appreciated. In this paper, we review recent developments and provide guidelines for the use of split-plot designs in industrial applications
Designing fractional factorial split-plot experiments with few whole-plot factors
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73673/1/j.1467-9876.2003.05029.x.pd
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 selection of blocked robust parameter designs and their applications
Blocking is a useful technique to control systematic variation in experiments. Robust parameter design is widely used as an effective tool to reduce process variability by appropriate selection of control factors to make the process insensitive to noise. In this paper, we propose and study a method for selecting the optimal blocked robust parameter designs when some of the control-by-noise interactions are included in the model. We then discuss how to search for the best designs according to this method and present some results for designs of 8 and 16 runs.Includes bibliographical references
Optimal Design Generation and Power Evaluation in R: The skpr Package
The R package skpr provides a suite of functions to generate and evaluate experimental designs. Package skpr generates D, I, Alias, A, E, T, and G-optimal designs, and supports custom user-defined optimality criteria, N-level split-plot designs, mixture designs, and design augmentation. Also included are a collection of analytic and Monte Carlo power evaluation functions for normal, non-normal, random effects, and survival models, as well as tools to plot fraction of design space plots and correlation maps. Additionally, skpr includes a flexible framework for the user to perform custom power analyses with external libraries and user-defined functions, as well as a graphical user interface that wraps most of the functionality of the package in a point-and-click web application
Practical inference from industrial split-plot designs.
Many industrial response surface experiments are deliberately not conducted in a completely randomized fashion. This is because some of the factors investigated in the experiment are hard to change. The resulting experimental design then is of the split-plot type and the observations in the experiment are in many cases correlated. A proper analysis of the experimental data therefore is a mixed model analysis involving generalized least squares estimation. Many people, however, analyze the data as if the experiment was completely randomized, and estimate the model using ordinary least squares. The purpose of the present paper is to quantify the differences in conclusions reached from the two methods of analysis and to provide the reader with guidance for analyzing split-plot experiments in practice. The problem of choosing the number of degrees of freedom for significance tests in the mixed model analysis is discussed as well.Containment method; Data; Design; Experimental design; Factors; Fashion; Generalized least squares; Least-squares; Method of Kenward and Roger; Methods; Model; Ordinary least squares; Residual method; Satterthwaite's method; Split-plot experiment; Squares;
Design and analysis of a microplate assay in the presence of multiple restrictions on the randomization
Experiments using multi-step protocols often involve several restrictions on
the randomization. For a specific application to in vitro testing on
microplates, a design was required with both a split-plot and a strip-plot
structure. On top of two-level treatment factors and the factors that define
the randomization restrictions, a multi-level fixed blocking factor not
involving further restrictions on the randomization had to be added. We develop
a step-by-step approach to construct a design for the microplate experiment and
analyze a response. To consolidate the approach, we study various alternative
scenarios for the experiment.Comment: 31 pages, 13 tables, 4 figure
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