A General Construction Method for Five-Level Second-Order Rotatable Designs

Response surface methodology is widely used for developing, improving, and optimizing processes in various fields. In this article, we present a method for constructing second-order rotatable designs in order to explore and optimize response surfaces based on an infinite class of supplementary difference sets. The produced designs achieve both properties of rotatability and estimation efficiency. Also, they possess good predictive properties.     

On d- and e- minimax optimal designs for estimating the axial slopes of a second-order response surface over hypercubic regions

Design of experiments for estimating the slopes of a response surface is considered. Design criteria analogous to the traditional ones but based upon the variance-covariance matrix of the estimated slopes along factor axes are proposed. Optimal designs under the proposed criteria are derived for second-order polynomial regression over hypercubic regions. Best de¬signs within some commonly used classes of designs are also obtained and their efficiencies are investigated.     

On the Choice of a Prior for Bayesian D-Optimal Designs for the Logistic Regression Model with a Single Predictor

The Bayesian design approach accounts for uncertainty of the parameter values on which optimal design depends, but Bayesian designs themselves depend on the choice of a prior distribution for the parameter values. This article investigates Bayesian D-optimal designs for two-parameter logistic models, using numerical search. We show three things: (1) a prior with large variance leads to a design that remains highly efficient under other priors, (2) uniform and normal priors lead to equally efficient designs, and (3) designs with four or five equidistant equally weighted design points are highly efficient relative to the Bayesian D-optimal designs.     

Sure independence screening for analyzing supersaturated designs

ABSTRACT

Supersaturated designs (SSDs) constitute a large class of fractional factorial designs which can be used for screening out the important factors from a large set of potentially active ones. A major advantage of these designs is that they reduce the experimental cost dramatically, but their crucial disadvantage is the confounding involved in the statistical analysis. Identification of active effects in SSDs has been the subject of much recent study. In this article we present a two-stage procedure for analyzing two-level SSDs assuming a main-effect only model, without including any interaction terms. This method combines sure independence screening (SIS) with different penalty functions; such as Smoothly Clipped Absolute Deviation (SCAD), Lasso and MC penalty achieving both the down-selection and the estimation of the significant effects, simultaneously. Insights on using the proposed methodology are provided through various simulation scenarios and several comparisons with existing approaches, such as stepwise in combination with SCAD and Dantzig Selector (DS) are presented as well. Results of the numerical study and real data analysis reveal that the proposed procedure can be considered as an advantageous tool due to its extremely good performance for identifying active factors.     

Estimating the asymptotic relative efficiency of weighted rankings

Five tests for the hypothesis of no treatment effects in complete blocks designs are compared with respect to asymptotic relative efficiency: the ordinary two-way analysis of variance, the analysis of variance of ranks (Friedman, 1937), the method of ranking after alignment (Hodges and Lehmann, 1962), and a method of weighted rankings proposed by Quade (1972, 1979). This comparison required devising a procedure for estimating the asymptotic relative efficiencies of test statistics with asymp-totic chi-squared distributions.     

Partially efficiency-balanced designs-II

efficiency balanced (£R) and partially efficiency balanced (PEB) designs were studied hy Calinski (1971) and Puri and Higam (1971, 1977a). In tais paper we have studied the dual desinas of two classes of PEB designs. It is shown that the dual of any symmetrical PCS design with HN'=N'H is again a PEB design. Also the dual of a PEB(S) with μ₁ = 0 μ₂ = 0and is shown to the again a PEB(S). The relations between PEB designs and linked and partially linked blocks have heen established. As a conseguence, the analysis of linked Mock and partially linkei block designs can he sinrlififid. Sore useful classes of supplencntcd block designs having simple analysis have also been discussed.     

Using Ordinary Least Squares Software to Compute Combined Intra-Interblock Estimates of Treatment Contrasts

Consideration is given to the computational aspects of the analysis of data from a comparative study, involving two or more treatments, in which the experimental units are arranged in b blocks. It may seem desirable, in making inferences about treatment contrasts, to carry out a combined intra-interblock analysis. Practitioners are sometimes reluctant to employ this analysis because of the computational requirements, which they regard as severe, and because they may not have ready access to directly applicable computer software. It is shown that by augmenting the actual data with b pseudo-observations, all of the computations can be accomplished efficiently, using only ordinary least squares software.     

施工组织设计方法的改进

自从改革开放以来,中国发生了翻天覆地的变化。随着施工企业管理体制的进一步完善,原有的传统施工组织设计编制方法已不能完全适应现代的要求。本文主要结合工程实际对施工组织设计提出了几点看法,及相应的改进方法。     

D-Optimal Axial Designs for Quadratic and Cubic Additive Mixture Models

The paper discusses D-optimal axial designs for the additive quadratic and cubic mixture models σ_1≤i≤q(β_ix_i + β_iix²_i) and σ_1≤i≤q(β_ix_i + β_iix²_i + β_iiix³_i), where x_i≥ 0, x₁ + . . . + x_q = 1. For the quadratic model, a saturated symmetric axial design is used, in which support points are of the form (x₁, . . . , x_q) = [1 ? (q?1)δ_i, δ_i, . . . , δ_i], where i = 1, 2 and 0 ≤δ₂ <_{δ1 ≤} 1/(q ?1). It is proved that when 3 ≤q≤ 6, the above design is D-optimal if δ₂ = 0 and δ₁ = 1/(q?1), and when q≥ 7 it is D-optimal if δ₂ = 0 and δ₁ = [5q?1 ? (9q²?10q + 1)^1/2]/(4q²). Similar results exist for the cubic model, with support points of the form (x₁, . . . , x_q) = [1 ? (q?1)δ_i, δ_i, . . . , δ_i], where i = 1, 2, 3 and 0 = δ₃ <_δ2 < δ_{1 ≤}1/(q?1). The saturated D-optimal axial design and D-optimal design for the quadratic model are compared in terms of their efficiency and uniformity.     

Optimal and efficient crossover designs for comparing test treatments to a control treatment under various models

We study the optimality, efficiency, and robustness of crossover designs for comparing several test treatments to a control treatment. Since A-optimality is a natural criterion in this context, we establish lower bounds for the trace of the inverse of the information matrix for the test treatments versus control comparisons under various models. These bounds are then used to obtain lower bounds for efficiencies of a design under these models. Two algorithms, both guided by these efficiencies and results from optimal design theory, are proposed for obtaining efficient designs under the various models.