Optimal Crossover Designs

This monograph presents a comprehensive and up-to-date account of the developments in optimality aspects of crossover designs. Crossover designs are immensely useful in various areas of human investigation including agriculture, animal nutrition, clinical trials, pharmaceutical studies, biological assays, weather modification experiments, sensory evaluation of food products and learning experiments. Research on the optimality aspects of crossover designs has developed only in the last three decades, and it has now emerged as a potential field for further investigation. This book is the first comprehensive treatise on this subject. It covers optimal crossover designs at length by consolidating vast amounts of material from the literature, and includes many recent and deep results. It is expected that this book will not only provide a one-stop reference for the available results, but also encourage further research in this area of substantial practical relevance.

Many papers deal with the most common model for crossover designs, which typically include period, unit, direct treatment, and carryover effects. However, some authors argue the common model to be too simple in its assumptions and suggest that unit by treatment interaction may be of additional importance. Therefore, the interest of this doctoral thesis is to find optimal crossover designs in an unconstrained model with random assessor effects. The observations are assumed to be influenced by carryover effects and additional interactions between treatments and units. Kushner's method is applied in order to evaluate how interaction and carryover effects operate conjointly in an optimal crossover design. The method by Kushner maximizes the trace of the information matrix of the design on the basis of design-dependent equivalence class functions. There are three equivalence classes of treatment sequences, which are crucial for the generation of an approximated optimal design if the number of periods does not exceed six.

The Design of Active Crossovers is a unique guide to the design of high-quality circuitry for splitting audio frequencies into separate bands and directing them to different loudspeaker drive units specifically designed for handling their own range of frequencies. Traditionally this has been done by using passive crossover units built into the loudspeaker boxes; this is the simplest solution, but it is also a bundle of compromises. The high cost of passive crossover components, and the power losses in them, means that passive crossovers have to use relatively few parts. This limits how well the crossover can do its basic job. Active crossovers, sometimes called electronic crossovers, tackle the problem in a much more sophisticated manner. The division of the audio into bands is performed at low signal levels, before the power amplifiers, where it can be done with much greater precision. Very sophisticated filtering and response-shaping networks can be built at comparatively low cost. Time-delay networks that compensate for phyical misalignments in speaker construction can be implemented easily; the equivalent in a passive crossover is impractical because of the large cost and the heavy signal losses. Active crossover technology is also directly applicable to other band-splitting signal-processing devices such as multi-band compressors. The use of active crossovers is increasing. They are used by almost every sound reinforcement system, by almost every recording studio monitoring set-up, and to a small but growing extent in domestic hifi. There is a growing acceptance in the hifi industry that multi-amplification using active crossovers is the obvious next step (and possibly the last big one) to getting the best possible sound. There is also a large usage of active crossovers in car audio, with the emphasis on routing the bass to enormous low-frequency loudspeakers. One of the very few drawbacks to using the active crossover approach is that it requires more power amplifiers; these have often been built into the loudspeaker, along with the crossover, and this deprives the customer of the chance to choose their own amplifier, leading to resistance to the whole active crossover philosophy. A comprehensive proposal for solving this problem is an important part of this book. The design of active crossovers is closely linked with that of the loudspeakers they drive. A chapter gives a concise but complete account of all the loudspeaker design issues that affect the associated active crossover. This book is packed full of valuable information, with virtually every page revealing nuggets of specialized knowledge never before published. Essential points of theory bearing on practical performance are lucidly and thoroughly explained, with the mathematics kept to an essential minimum. Douglas' background in design for manufacture ensures he keeps a wary eye on the cost of things. Features: Crossover basics and requirements The many different crossover types and how they work Design almost any kind of active filter with minimal mathematics Make crossover filters with very low noise and distortion Make high-performance time-delay filters that give a constant delay over a wide range of frequency Make a wide variety of audio equaliser stages: shelving, peaking and notch characteristics All about active crossover system design for optimal noise and dynamic range There is a large amount of new material that has never been published before. A few examples: using capacitance multipliers in biquad equalisers, opamp output biasing to reduce distortion, the design of NTMTM notch crossovers, the design of special filters for filler-driver crossovers, the use of mixed capacitors to reduce filter distortion, differentially elevated internal levels to reduce noise, and so on. Douglas wears his learning lightly, and this book features the engaging prose style familiar from his other books The Audio Power Amplifier Design Handbook, Self on Audio, and the recent Small Signal Audio Design.

A comprehensive and practical resource for analyses of crossover designs For ethical reasons, it is vital to keep the number of patients in a clinical trial as low as possible. As evidenced by extensive research publications, crossover design can be a useful and powerful tool to reduce the number of patients needed for a parallel group design in studying treatments for non-curable chronic diseases. This book introduces commonly-used and well-established statistical tests and estimators in epidemiology that can easily be applied to hypothesis testing and estimation of the relative treatment effect for various types of data scale in crossover designs. Models with distribution-free random effects are assumed and hence most approaches considered here are semi-parametric. The book provides clinicians and biostatisticians with the exact test procedures and exact interval estimators, which are applicable even when the number of patients in a crossover trial is small. Systematic discussion on sample size determination is also included, which will be a valuable resource for researchers involved in crossover trial design. Key features: Provides exact test procedures and interval estimators, which are especially of use in small-sample cases. Presents most test procedures and interval estimators in closed-forms, enabling readers to calculate them by use of a pocket calculator or commonly-used statistical packages. Each chapter is self-contained, allowing the book to be used a reference resource. Uses real-life examples to illustrate the practical use of test procedures and estimators Provides extensive exercises to help readers appreciate the underlying theory, learn other relevant test procedures and understand how to calculate the required sample size. Crossover Designs: Testing, Estimation and Sample Size will be a useful resource for researchers from biostatistics, as well as pharmaceutical and clinical sciences. It can also be used as a textbook or reference for graduate students studying clinical experiments.

This carefully edited collection synthesizes the state of the art in the theory and applications of designed experiments and their analyses. It provides a detailed overview of the tools required for the optimal design of experiments and their analyses. The handbook covers many recent advances in the field, including designs for nonlinear models and algorithms applicable to a wide variety of design problems. It also explores the extensive use of experimental designs in marketing, the pharmaceutical industry, engineering and other areas.

Optimization is a mathematical tool developed in the early 1960's used to find the most efficient and feasible solutions to an engineering problem. It can be used to find ideal shapes and physical configurations, ideal structural designs, maximum energy efficiency, and many other desired goals of engineering. This book is intended for use in a first course on engineering design and optimization. Material for the text has evolved over a period of several years and is based on classroom presentations for an undergraduate core course on the principles of design. Virtually any problem for which certain parameters need to be determined to satisfy constraints can be formulated as a design optimization problem. The concepts and methods described in the text are quite general and applicable to all such formulations. Inasmuch, the range of application of the optimum design methodology is almost limitless, constrained only by the imagination and ingenuity of the user. The book describes the basic concepts and techniques with only a few simple applications. Once they are clearly understood, they can be applied to many other advanced applications that are discussed in the text. * Allows engineers involved in the design process to adapt optimum design concepts in their work using the material in the text. * Basic concepts of optimality conditions and numerical methods are described with simple examples, making the material high teachable and learnable. * Classroom-tested for many years to attain optimum pedagogical effectiveness.