Second-order Designs Research Articles

Prediction variance capability of orthogonal uniform composite designs and orthogonal array composite designs in the spherical region

In this paper, the prediction variance capabilities of two new second-order designs orthogonal uniform composite designs and orthogonal array composite designs are examined using the variance dispersion graph and the fraction of design space plot in the spherical region. Also, the D- and G-optimality criteria are evaluated for these two response surface designs. The orthogonal array composite designs were shown to have a better prediction variance in terms of the fraction of design space plot and the variance dispersion graphs over the orthogonal uniform composite designs.

Robustness of orthogonal uniform composite designs against outlier

Outliers are inconsistent values that commonly occur in every experimental setting and damage the designs' properties to be explored. Based on the orthogonal uniform composite designs (OUCDs) proposed by Zhang et al., this article introduces a new class of second-order designs called orthogonal array composite minimax outlying designs by using the minimax outlying criterion that minimizes the maximum outlying effect of all design points. The proposed designs' efficiencies and generalized scaled standard deviations are compared with central composite design, small composite designs, orthogonal array composite designs, orthogonal array composite minimax loss designs, and OUCDs. The proposed designs are more robust to outlier than the existing OUCDs. These new designs are more optimal in terms of D-, E-, G- and T- efficiencies in most cases than the existing composite designs.

Mechanical Properties of PolyJet 3D-Printed Composites Inspired by Space-Filling Peano Curves.

This paper proposes a design of novel composite materials inspired by the Peano curve and manufactured using PolyJet 3D printing technology with Agilus30 (flexible phase) and VeroMagentaV (rigid phase) materials. Mechanical properties were evaluated through tensile and compression tests. The general rule of mixture (ROM) for composites was employed to approximate the tensile properties of the hybrid materials and compare them to the experimental results. The effect of reinforcement alignments and different hierarchies are discussed. The results indicated that the 5% inclusion of the Peano reinforcement in tensile samples contributed to the improvement in the elastic modulus by up to 6 MPa, but provided no obvious enhancement in ultimate tensile strength. Additionally, compressive strengths between 2 MPa and 6 MPa were observed for compression cubes with first-order reinforcement, while lower values around 2 MPa were found for samples with second-order reinforcement. That is to say, the first-order reinforcement has been demonstrated more effectively than the second-order reinforcement, given the same reinforcement volume fraction of 10% in compression cubes. Different second-order designs exhibited slightly different mechanical properties based on the ratio of reinforcement parallel to the loading direction.

Robust second-order rotatable invariably designs for some lifetime distributions

First-order rotatable designs for the lifetime response with distributions such as lognormal, Weibull, gamma, and exponential, assuming autocorrelated errors have been studied. A first-order model in practice is an adequate approximation to the true unknown surface in a small region of the explanatory variables x’s. For an unknown experimental region or a system with any curvature, then the second-order model is always appropriate. It is aimed herein to extend the above ideas in the current paper for second-order models. Second-order lifetime correlated models along with rotatability conditions have been derived in the paper. Invariant (independent of the above considered four distributions) robust (independent of the correlation parameter values) second-order rotatable designs have been derived for the autocorrelated error structure. The derived designs in the paper are robust second-order rotatable for all values of the autocorrelation coefficient, and for all the above considered four lifetime distributions. The present derived designs in the paper satisfy four lifetime distributions with autocorrelated errors, while the usual uncorrelated second-order designs are unable to satisfy the similar conditions. In this sense, the current designs are most appropriate for lifetime improvement experiments.

UTILIZING RESPONSE SURFACE METHODS DESIGNS FOR OPTIMIZATION OF TECHNOLOGICAL PARAMETERS ON THE VIBRATION AMPLITUDE OF CNC ROUTER SPINDLE

For CNC machines, machining accuracy is of ultimate importance since it determines the quality of the products. Among many factors, vibration amplitude and stiffness are the key ones that influence the machining accuracy of a CNC machine. Remarkably, it is essential to conduct study into structural stiffness and the effect of technological parameters on the vibration amplitude of CNC router spindle with various second-order designs in order to improve machining accuracy. The research focuses on the application and comparison of the response-surface methods, the experimental research on the factors affecting the vibration amplitude, and the determination of the optimal working parameters for the CNC router.

Odd- and even-order electronically controlled wave active filter employing differential difference trans-conductance amplifier (DDTA)

ABSTRACT In recent years, several current mode wave active filters have been reported in literature. However, most schemes only have a few higher-order filters that employ a wave-equivalent inductor in a series branch as well as a wave-equivalent capacitor in the shunt branch. As a result, it is very difficult to design wave active filters with all the filter frequency responses using lower – to higher-order filters. Hence, in this research work, we propose to construct a uniform framework for the design of a wave active filter using a complementary metal oxide semiconductor (CMOS) differential difference transconductance amplifier (DDTA) for lower and higher-order filter configurations. A traditional wave-equivalent method is incorporated for the reflected and incident waves of series and shunt inductors and capacitors. The theoretical verification of the proposed wave active filter uses second-order, third-order, fourth-order, fifth-order, and sixth-order filter designs. Technical verification is conducted through Simulation Program with Integrated Circuit Emphasis (SPICE) simulations using the Cadence Virtuoso tool with 0.18 µm CMOS (Taiwan Semiconductor Manufacturing Company, TSMC) parameters for the DDTA. In addition, experimental validation of the proposed wave active filter is performed with the operational transconductance amplifier as CA3080 for the implementation of DDTA.

A note on a Comparison of Starting Points for the Generation of D-optimal Second-order Designs

Agricultural monitoring has become an absolute necessity in the Sahel countries, especially with climate change which constitutes a real threat for this sector. The aim of this work is to develop a methodology for identifying crops and mapping agricultural areas using Sentinel-2 data from the Copernicus program. The purpose of this work consisted in discriminating the crops of millet, maize and peanuts. This is to analyse the scientific and technical obstacles related to this problem. For this, we have made a mathematical analysis of optical satellite images. High temporal and spatial resolution images (10m to 60m) of Sentinel 2 sensors were used in this work. This unique set of data coupled with field data, has permitted to carry out a diagnosis of land cover and cultivated land surfaces, and evaluating the contribution of this type of data for crop forecast

Plasmonic metamaterial-based filtering structures with dynamic tunability.

In this Letter, we report the design, analysis, and characterization of first- and second-order plasmonic metamaterial-based multi-mode filtering structures. Further, electronic adaptivity in filter transfer functions is introduced and characterized. First, the basic operating principle of the engineered multi-mode resonator-based bandpass filter is presented. Then the concept is extended by introducing electronic (dynamic) tuning of the bandwidth using semiconductor varactor diodes. Afterwards, to enhance the selectivity and out-of-band filtering response, second-order multi-mode designs are realized. For experimental verification, the hardware prototype is fabricated and characterized using the Keysight analyzer N9918A. The design filtering structures will pave an important role in tunable plasmonic circuits and systems.

Precision of full polynomial response surface designs on models with missing coefficients

The precision of using full polynomial response surface designs on models with missing coefficients (reduced models) is studied using efficiency measures. The loss in D- and G-efficiency of constructed first-order exact designs is minimized for the model with missing interaction coefficient. However, higher losses in D- and G-efficiency are recorded when constructed second-order exact designs are used on the model with missing interaction coefficient with few exceptions showing preferences for using the designs on the reduced model. Lower condition numbers are observed for the designs under the first-order reduced models thus indicating that the N-point exact designs are closer to being orthogonal for the reduced model than for the full model. Perfect orthoganality is achieved at design sizes 4 and 8. In fact, N-point exact designs of multiples of N=4 show perfect orthoganality when defined either for the full or reduced first-order models. In comparison to a design with perfect orthoganality, the second-order designs are far from being orthogonal.

Useful Numerical Statistics of Some Response Surface Methodology Designs

<p>Useful numerical evaluations associated with three categories of Response Surface Methodology designs are presented with respect to five commonly encountered alphabetic optimality criteria. The first-order Plackett-Burman designs and the Factorial designs are examined for the main effects models and the complete first-order models respectively. The second-order Central Composite Designs are examined for second-order models. The A-, D-, E-, G- and T-optimality criteria are employed as commonly encountered optimality criteria summarizing how good the experimental designs are. Relationships among the optimality criteria are pointed out with regards to the designs and the models. Generally the designs do not show uniform preferences in terms of the considered optimality criteria. However, one interesting finding is that central composite designs defined on cubes and hypercubes with unit axial distances are uniformly preferred in terms of E-optimality and G-optimality criteria.</p>

Alternative Second-Order N-Point Spherical Response Surface Methodology Design and Their Efficiencies

The equiradial designs are studied as alternative second-order N-point spherical Response Surface Methodology designs in two variables, for design radius ρ = 1.0. These designs are seen comparable with the standard second-order response surface methodology designs, namely the Central Composite Designs. The D-efficiencies of the equiradial designs are evaluated with respect to the spherical Central Composite Designs. Furthermore, D-efficiencies of the equiradial designs are evaluated with respect to the D-optimal exact designs defined on the design regions of the Circumscribed Central Composite Design, the Inscribed Central Composite Design and the Face-centered Central Composite Design. The D-efficiency values reveal that the alternative second-order N-point spherical equiradial designs are better than the Inscribed Central Composite Design though inferior to the Circumscribed Central Composite Design with efficiency values less than 50% in all cases studied. Also, D-efficiency values reveal that the alternative second-order N-point spherical equiradial designs are better than the N-point D-optimal exact designs defined on the design region supported by the design points of the Inscribed Central Composite Design. However, the N-point spherical equiradial designs are inferior to the N-point D-optimal exact designs defined on the design region supported by the design points of the Circumscribed Central Composite Design and those of the Face-centered Central Composite Design, with worse cases with respect to the design region of the Circumscribed Central Composite Design.

D-minimax Second-order Designs Over Hypercubes for Extrapolation and Restricted Interpolation Regions

The D-minimax criterion for estimating slopes of a response surface involving k factors is considered for situations where the experimental region χ and the region of interest ℜ are co-centered cubes but not necessarily identical. Taking χ = [ − 1, 1]k and ℜ = [ − R, R]k, optimal designs under the criterion for the full second-order model are derived for various values of R and their relative performances investigated. The asymptotically optimal design as R → ∞ is also derived and investigated. In addition, the optimal designs within the class of product designs are obtained. In the asymptotic case it is found that the optimal product design is given by a solution of a cubic equation that reduces to a quadratic equation for k = 3 and 6. Relative performances of various designs obtained are examined. In particular, the optimal asymptotic product design and the traditional D-optimal design are compared and it is found that the former performs very well.

Enhanced design efficiency through least upper bounds

Lower and upper spectral bounds are known for positive-definite matrices in under Loewner (Uber monotone Matrixfunktionen. Math Z. 1934;38:177–216) ordering. Lower and upper singular bounds for matrices of order in derive under an induced ordering. These orderings are combined here to the following effects. Given two first-order experimental designs in their upper singular bound enhances both and in that its Fisher Information matrix dominates those for both and thus ordering essentials in Gauss–Markov estimation. Moreover, if and are dispersion matrices for linear estimators under and respectively, then is the spectral lower bound for in . In essence this algorithm identifies elements in complementary to those of and combines these into . Case studies illustrate gains to be made thereby in first and second-order designs. Specifically, two examples demonstrate that designs optimal under separate criteria may be combined into a single design dominating both. In addition, selected examples demonstrate that classical second-order designs may be improved inter se.

Modified Robust Second-Order Slope-Rotatable Designs

Generally it is very difficult to construct robust slope-rotatable designs along axial directions. Present paper focuses on modified second-order slope-rotatable designs (SOSRDs) with correlated errors. Modified robust second-order slope-rotatability conditions are derived for a general variance–covariance structure of errors. These conditions get simplified for intraclass correlation structure. A few robust second-order slope-rotatable designs (over all directions, or with equal maximum directional variance slope, or D-optimal slope) are examined with respect to modified robust slope-rotatability. It is observed that robust second-order slope-rotatable designs over all directions, or with equal maximum directional variance slope, or D-optimal slope are notgenerally modified robust second-order slope-rotatable designs.

A Catalog of Orthogonally Blocked Three-Level Second-Order Designs With Run Sizes ≤ 100

Box–Behnken designs form a very popular class of three-level second-order designs when the number of factors is small, typically seven or less. For larger number of factors these designs are not as popular because then these designs require a large number of runs. This article provides a catalog of three-level second-order designs for 5–11 factors with run sizes ≤ 100. All the designs reported can be orthogonally blocked and are seen to have high D-efficiencies.

Nonlinear screening designs for defense testing: an overview and case study

Recent efforts to improve the statistical rigor of both developmental and operational testing include recommendations to consider second-order screening designs. In this paper, we provide a broad review of screening designs and second-order screening designs. We then consider a real-world wind tunnel experiment case study from the recent published literature and use subject matter expertise to consider the viability of second-order screening design, a recently developed design called the DSD+, to sufficiently screen important factors in complex, nonlinear systems of interest using just a single experimental design.

Investigating estimation error reduction strategies in complex engineering systems

When the manufacturing objective is process or product improvement, quality practitioners will frequently resort to one or more approaches within the broader class of response surface methodology. Several techniques, such as the dual response, robust parameter design, and desirability function approach, may be effective tools to solve the multi-response optimisation problem. All of these techniques are designed to identify the factor settings that lead to an optimal solution in terms of the mean or variance among characteristics. The skewness in the distribution of observations for one or more characteristics, however, is not considered. The techniques also traditionally rely on the fit of second-order response surface designs in estimating each response, which may be unreliable in some cases. In contrast, this paper offers an approach to solving complex multi-response optimisation problems that considers both the error associated with process skewness and the accuracy of a response surface.

G-Efficient Designs for Quadratic Mixture Models

This article introduces a novel method, named JC 1, for obtaining G-efficient mixture design to fit quadratic models. The advantage of JC 1 method over existing algorithms is that it gives G-efficient designs without need of generating all the extreme vertices, edge centroids and constraint plane centroids of the mixture experimental region. The performance of the new method is illustrated and its comparison is given with popularly used algorithms—Snee (1975) algorithm and Welch (1985) ACED algorithm for second-order (quadratic model) designs and it is observed that JC 1 method performs as well as the existing methods or sometimes better than those with additional advantage of large savings in computational efforts.

Small Box–Behnken designs with orthogonal blocks

Abstract A new method of constructing 3-level second-order designs using incomplete block designs with unequal block sizes is suggested to any number of factors. The method gives orthogonally blocked designs with small run sizes, high D -efficiencies and rotatability measures.

Small Three-Level Second-Order Designs With Orthogonal Blocks

Using suitable incomplete block designs with block size three, orthogonally blocked three-level second-order designs are proposed. These designs have reasonably high D-efficiencies and are often much smaller than the existing designs, in terms of block size and/or the total number of points.