Showing papers on "Optimal design published in 1982"

Branch-and-Bound Search for Experimental Designs Based on D Optimality and Other Criteria

Abstract: This article presents a branch-and-bound algorithm that constructs a catalog of all D-optimal n-point designs for specified design region, linear model, and number of observations, n. While the primary design criterion is D optimality, the algorithm may also be. used to find designs performing well by other secondary criteria, if a small sacrifice in ellkiency as measured by D optimahty is accepted. Finally, some designs are supplied for a quadratic response surface model.

Model Robust, Linear-Optimal Designs

Abstract: Motivated by a pioblem concerning the estimation of uranium content in calibration standards, a new design criterion is developed that generalizes linear optimality to a situation in which, a priori, the exact form of the regression model need not be known. An equivalence theorem is given, some properties of the new designs are delineated, and iterative methods for design construction are presented. Finally, by using methods developed within, optimal designs are computed in a number of situations, including that of the motivating example.

An Optimal Design of Simple Symmetric Laminates Under the First Ply Failure Criterion

Abstract: : Optimal design of various types of symmetric laminates for T300/5208 graphite epoxy composites was investigated under the first ply failure criteria. The symmetric laminates considered include continuous laminate and angle ply laminate. The optimal design angles 0 were obtained and presented in graphic form as functions of the loading conditions (N1, N2, N6). The results presented here are directly useful for designers for making a choice of composites for optimal performance. (Author)

Optimal designs for weighted polynomial regression using canonical moments

Abstract: This chapter discusses some D -optimal designs. These are the designs that minimize the determinant of the covariance matrix of the least squares estimates of the highest s parameters β r +1 ,…, β m , where r + s = m . These designs are obtained using canonical moments. The D-optimal design and the design for estimating the highest coefficient are the extremal cases where r = –1 and r = m – l respectively. The chapter presents an analog of the equivalence theorem for D -optimal designs using canonical moments.

Distribution‐free tests for comparing several treatments with a control

Abstract: In this paper we propose distribution-free treatments versus control tests for the one- and two-way classifications. The null distribution properties are shown to be equivalent to those of well-known statistics for which critical values have been extensively tabled. Asymptotic relative efficiencies with respect to corresponding normal theory competitors are derived and optimal designs for the allocation of experimental units to the treatments and control are obtained.

Some E‐Optimal Designs for the One‐Way and Two‐Way Elimination of Heterogeneity

Abstract: SUMMARY In exploratory experiments aimed at providing as much information as possible on the effects of the treatments being studied and where heterogeneity needs to be eliminated in one or two directions, use of an equally replicated block or row-column design may mean wasting some of the available experimental units. In this paper we prove the E-optimality of several different types of block and row-column designs that have unequally replicated treatments; such unequally replicated designs can maximize the information on treat- ment effects without wasting units. BLOCK designs are used for experiments where it is important to eliminate heterogeneity in one direction. Those considered here have v treatments arranged in b blocks containing k experimental units each. The structure of any such block design is determined by its v x b incidence matrix whose (i, j)th entry gives the number of times treatment i occurs in block j. In many experimental situations, the position that an experimental unit occupies within a block can also affect observed responses. When this happens, row-column designs can often be used to eliminate heterogeneity in two directions. The row-column designs considered here have bk experimental units arranged in a rectangular array of b columns and k rows such that each unit receives only one of the v treatments being studied. We say that a block or row-column design is equally replicated if each treatment is replicated the same number of times and otherwise unequally replicated. This paper gives some optimal block and row-column designs which can be used where equal replication is impossible if all the available experimental material is to be used. Let d denote an arbitrary row-column design such as is described above. Observations Ymnp obtained after applying the mth treatment to the unit occurring in the nth column and pth row are assumed to follow the usual three-way additive model, i.e.

Construction of optimal designs in random coefficient regression models

Abstract: We consider the problem of optimal experimental design in random coefficient regression models with respect to a quadratic loss function. By application of WHITTLE'S general equivalence theorem we obtain the structure of optimal designs. An alogrithm is given which allows, under certain assumptions, the construction of the information matrix of an optimal design. Moreover, we give conditions on the equivalence of optimal designs with respect to optimality criteria which are analogous to usual A-D- and _E/-optimality.

Channel Design to Minimize Lining Material Costs

Abstract: A direct algebraic technique is developed to determine open channel cross-sectional designs which minimize lining material costs when base and side wall unit costs are different. Solution graphs, which indicate both the optimal parameter combination and the costs of deviating from the optimal design, are presented. The graphs or analytical technique are also effective in designing any trapezoidal channels. Use of the technique shows that moderate deviations from optimal designs are not costly.

A Note on Optimal and Asymptotically Optimal Designs for Certain Time Series Models

Abstract: The problem of regression design in the presence of correlated errors is considered. Under the assumption that derivative information is available on the response process, uniqueness results for optimal designs given in Eubank, Smith and Smith (1981) for the BLUE of the regression coefficient are extended to a wider class of processes. In the event that derivatives cannot be sampled, an asymptotic solution is developed and extended to the multiparameter setting.

Optimal Design Based on Approximate Scaling

Abstract: A new optimal design procedure, intended to reduce the number of exact analyses during the solution process, is proposed. High quality explicit approximations of the structural behaviour and a scaling procedure are combined to achieve this goal. Explicit behavior models are introduced for a set of lines (directios of move) in the design space. Some algorithms for selecting these lines are presented. For each checked design along a given line the structural behavior is evaluated. The design is then scaled. This procedure, which involves small computational effort, is repeated the various step sizes until the best constrained design is obtained. A new direction of move is selected and a modified approximate model is introduced. Each selected direction requires only a single exact analysis of the structure. The result is an efficient path to the optimum with a relatively small number of exact analyses. Simple examples illustrate the solution process, the quality and the efficiency of the explicit behavior model, and the potential of the proposed procedure.

Low dose extrapolation under single parameter dose response models

Abstract: Asymptotically optimal experimental designs for animal bio-assays conducted in order to estimate virtually safe levels of exposure to chemical carcinogens are derived under the one-hit model and the probit model with known slope parameter. For these two models, the optimal designs involve assigning all available animals to the dose levels corresponding to the 80% and 50% response rates respectively. In both cases, the optimal designs are highly robust in the sense that the loss in efficiency is minimal if the dose actually employed is at all close to the optimal dose. In addition, the bias, variance and mean square error of the maximum likelihood estimator of the safe level of exposure under these two models are computed and compared with those of the jackknife estimator as well as an alternative estimator with reduced bias proposed by Salama, Koch & Tolley 1978. Twelve different procedures for obtaining approximate lower confidence limits on the safe dose are also compared in terms of their actual covera...

Branch-and-Bound Search for Experimental Designs Based on D Optimality and Other

Abstract: This article presents a branch-and-bound algorithm that constructs a catalog of all D-optimal n-point designs for specified design region, linear model, and number of observations, n. While the primary design criterion is D optimality, the algorithm may also be used to find designs performing well by other secondary criteria, if a small sacrifice in efficiency as measured by D optimality is accepted. Finally, some designs are supplied for a quadratic response surface model.

A comparison of characteristic locus and optimal designs for dynamic ship positioning systems

Abstract: Dynamic ship positioning systems are now required to operate within closer position tolerances and in more adverse weather conditions. There are also stricter requirements on the minimization of energy losses. To optimize performance, recent positioning systems have been designed using Kalman filters and optimal control theory and such a scheme is reviewed briefly. The characteristic locus design method has not previously been used for the design of a stochastic system and it is therefore of interest to see whether or not it may be employed in the above problem. It is shown that not only may this frequency domain design method be used for such systems, but that it has some advantages with regard to the flexibility of the design process. The advantages of using a Kalman filter together with controllers designed by this approach are also demonstrated.

Optimal risk-based hydraulic design of bridges.

Abstract: The hydraulic design of highway bridges entails the evaluation of flood hazard associated with a proposed bridge structure and the determination of socio-environmental effects of the bridge project. A procedure for treating hydrologic uncertainties is incorporated into an optimization framework to develop the optimal risk-based design of the bridge openings and the embankment heights that minimizes the total expected cost. The optimization technique used is called Hooke-Jeeves pattern search. The procedure to determine the optimal bridge design is applied to Leaf River, Mississippi. The effect of using different procedures for hydrogic parameter estimation and the effect of using different hydrologic probability models on the optimal design are examined.

An optimal design approach for tracking problems and its assessment against classical controllers

Abstract: A class of linear regulator problems, referred to as tracking problems, impose the requirements of zero steady state error, elimination of disturbance effects and immunity to system parameter changes. A controller design approach for this problem, using linear optimal control theory, is presented, and its advantages are outlined by comparison with previous modern and classical approaches.

Designs for discriminating between binary dose response models with applications to animal carcinocenicity experiments

Abstract: A procedure is proposed for designing an experiment to have optimal power for rejecting a particular subclass of dose-response models when the true model is from a different subclass. Theoretical results are presented on the number of dose levels required in an optimally-designed experiment and applications to dose-response problems arising in animal carcinogenicity bioassays are discussed

Optimizing Surface Irrigation System Design Parameters: Simplified Analysis

Abstract: THE geometric programming method was described Simple techniques such as monotonicity analysis, constraint activity, and condensation were utilized to reduce the size of the problem Example optimal designs for borders and furrows were solved on a hand calculator following the suggested methodology Results were the same as previously obtained from generalized geometric programming and extensive use of a digital computer Globally optimal solutions for minimum cost and max-imum profit designs were obtained by using this mathematically rigorous but simple optimization pro-cedure

Channel design to minimize lining material costs

Abstract: A direct algebraic technique is developed to determine open chan- nel cross-sectional designs which minimize lining material costs when base and side wall unit costs are different. Solution graphs, which indicate both the optimal parameter combination and the costs of deviating from the optimal design, are presented. The graphs or analytical technique are also effective in designing any trapezoidal channels. Use of the technique shows that mod- erate deviations from optimal designs are not costly.

On the Computation of Optimal Designs for Certain time Series Models with Applications to Optimal Quantile Selection for Location or Scale Parameter Estimation

Abstract: Using the results of Chow (Ph.D. dissertation, Texas A & M Univ., 1978) on the optimal placement of knots in the approximation of functions by piecewise polynomials, we present an algorithm for the computation of optimal designs for certain time series models considered by Eubank, Smith and Smith (Ann. Statist., 9 (1981), pp. 486–493), (Tech. Rep. 150, Southern Methodist Univ., 1981). The ideas underlying this algorithm form a unified approach to the computation of optimal spacings for the sample quantiles used in the asymptotically best linear unbiased estimator of a location or scale parameter.