Uniform Shell Designs
01 Nov 1970-Journal of The Royal Statistical Society Series C-applied Statistics (John Wiley & Sons, Ltd)-Vol. 19, Iss: 3, pp 231-239
TL;DR: In this paper, a set of points lying on concentric spherical shells are generated which have an equally spaced distribution of points and have uniform space-filling properties and are tabulated up to ten factors.
Abstract: Designs are generated which have an equally spaced distribution of points lying on concentric spherical shells. They have uniform space‐filling properties and are tabulated up to ten factors. The designs are shown to be more uniform than familiar experimental designs on the basis of two measures of uniformity. Their use is illustrated by an example with four factors.
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01 Jan 2011
TL;DR: A survey of the various stages in the development of response surface methodology RSM is given in this article, which includes a review of basic experimental designs for fitting linear response surface models, in addition to a description of methods for the determination of optimum operating conditions.
Abstract: The purpose of this article is to provide a survey of the various stages in the development of response surface methodology RSM. The coverage of these stages is organized in three parts that describe the evolution of RSM since its introduction in the early 1950s. Part I covers the period, 1951-1975, during which the so-called classical RSM was developed. This includes a review of basic experimental designs for fitting linear response surface models, in addition to a description of methods for the determination of optimum operating conditions. Part II, which covers the period, 1976-1999, discusses more recent modeling techniques in RSM, in addition to a coverage of Taguchi's robust parameter design and its response surface alternative approach. Part III provides a coverage of further extensions and research directions in modern RSM. This includes discussions concerning response surface models with random effects, generalized linear models, and graphical techniques for comparing response surface designs. Copyright © 2010 John Wiley & Sons, Inc.
1,075 citations
TL;DR: A survey of the various stages in the development of response surface methodology RSM is provided, organized in three parts that describe the evolution of RSM since its introduction in the early 1950s.
Abstract: The purpose of this article is to provide a survey of the various stages in the development of response surface methodology RSM. The coverage of these stages is organized in three parts that describe the evolution of RSM since its introduction in the early 1950s. Part I covers the period, 1951-1975, during which the so-called classical RSM was developed. This includes a review of basic experimental designs for fitting linear response surface models, in addition to a description of methods for the determination of optimum operating conditions. Part II, which covers the period, 1976-1999, discusses more recent modeling techniques in RSM, in addition to a coverage of Taguchi's robust parameter design and its response surface alternative approach. Part III provides a coverage of further extensions and research directions in modern RSM. This includes discussions concerning response surface models with random effects, generalized linear models, and graphical techniques for comparing response surface designs. Copyright © 2010 John Wiley & Sons, Inc.
1,064 citations
Cites background from "Uniform Shell Designs"
...(19) subject to x being on the surface of a hypersphere of radius r and centered at the origin, namely,...
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TL;DR: The surface response methodologies: central composite design, Doehlert matrix and Box-Behnken design are discussed and applications of these techniques for optimization of sample preparation steps and determination of experimental conditions for chromatographic separations are presented.
535 citations
TL;DR: Most frequently used experimental designs are described, concerning their limitations and typical applications, and ways to determine the accuracy and the significance of model fitting for both methodologies described herein are presented.
458 citations
TL;DR: The article covers the niceties of several important experimental designs, mathematical models, and optimum search techniques using numeric and graphical methods, with special emphasis on computer-based approaches, artificial neural networks, and judicious selection of designs and models.
Abstract: Design of an impeccable drug delivery product normally encompasses multiple objectives. For decades, this task has been attempted through trial and error, supplemented with the previous experience, knowledge, and wisdom of the formulator. Optimization of a pharmaceutical formulation or process using this traditional approach involves changing one variable at a time. Using this methodology, the solution of a specific problematic formulation characteristic can certainly be achieved, but attainment of the true optimal composition is never guaranteed. And for improvement in one characteristic, one has to trade off for degeneration in another. This customary approach of developing a drug product or process has been proved to be not only uneconomical in terms of time, money, and effort, but also unfavorable to fix errors, unpredictable, and at times even unsuccessful. On the other hand, the modern formulation optimization approaches, employing systematic Design of Experiments (DoE), are extensively practiced in the development of diverse kinds of drug delivery devices to improve such irregularities. Such systematic approaches are far more advantageous, because they require fewer experiments to achieve an optimum formulation, make problem tracing and rectification quite easier, reveal drug/polymer interactions, simulate the product performance, and comprehend the process to assist in better formulation development and subsequent scale-up. Optimization techniques using DoE represent effective and cost-effective analytical tools to yield the "best solution" to a particular "problem." Through quantification of drug delivery systems, these approaches provide a depth of understanding as well as an ability to explore and defend ranges for formulation factors, where experimentation is completed before optimization is attempted. The key elements of a DoE optimization methodology encompass planning the study objectives, screening of influential variables, experimental designs, postulation of mathematical models for various chosen response characteristics, fitting experimental data into these model(s), mapping and generating graphic outcomes, and design validation using model-based response surface methodology. The broad topic of DoE optimization methodology is covered in two parts. Part I of the review attempts to provide thought-through and thorough information on diverse DoE aspects organized in a seven-step sequence. Besides dealing with basic DoE terminology for the novice, the article covers the niceties of several important experimental designs, mathematical models, and optimum search techniques using numeric and graphical methods, with special emphasis on computer-based approaches, artificial neural networks, and judicious selection of designs and models.
322 citations
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TL;DR: In this paper, a class of incomplete three level factorial designs useful for estimating the coefficients in a second degree graduating polynomial are described and the designs either meet, or approximately meet, the criterion of rotatability and for the most part can be orthogonally blocked.
Abstract: A class of incomplete three level factorial designs useful for estimating the coefficients in a second degree graduating polynomial are described. The designs either meet, or approximately meet, the criterion of rotatability and for the most part can be orthogonally blocked. A fully worked example is included.
3,194 citations
TL;DR: A computer oriented method which assists in the construction of response surface type experimental plans takes into account constraints met in practice that standard procedures do not consider explicitly.
Abstract: A computer oriented method which assists in the construction of response surface type experimental plans is described. It takes into account constraints met in practice that standard procedures do not consider explicitly. The method is a sequential one and each step covers the experimental region uniformly. Applications to well-known situations are given to demonstrate the reasonableness of the procedure. Application to a ‘messy” design situation is given to demonstrate its novelty.
2,667 citations
388 citations