Cost‐penalized estimation and prediction evaluation for split‐plot designs

Comparisons between different designs have traditionally focused on balancing the quality of estimation or prediction relative to the overall size of the design. For split‐plot designs with two levels of randomization, the total number of observations may not accurately summarize the true cost of the experiment, because different costs are likely associated with setting up the whole and subplot levels. In this paper, we present several flexible measures for design assessment based on D‐, G‐ and V‐optimality criteria that take into account potentially different cost structures for the split‐plot designs. The new measures are illustrated with two examples: a 2³ factorial experiment for first‐order models, where all possible designs are considered, and selective designs for a three‐factor second‐order model. Copyright © 2006 John Wiley & Sons, Ltd.     

Separation in D‐optimal experimental designs for the logistic regression model

The D‐optimality criterion is often used in computer‐generated experimental designs when the response of interest is binary, such as when the attribute of interest can be categorized as pass or fail. The majority of methods in the generation of D‐optimal designs focus on logistic regression as the base model for relating a set of experimental factors with the binary response. Despite the advances in computational algorithms for calculating D‐optimal designs for the logistic regression model, very few have acknowledged the problem of separation, a phenomenon where the responses are perfectly separable by a hyperplane in the design space. Separation causes one or more parameters of the logistic regression model to be inestimable via maximum likelihood estimation. The objective of this paper is to investigate the tendency of computer‐generated, nonsequential D‐optimal designs to yield separation in small‐sample experimental data. Sets of local D‐optimal and Bayesian D‐optimal designs with different run (sample) sizes are generated for several “ground truth” logistic regression models. A Monte Carlo simulation methodology is then used to estimate the probability of separation for each design. Results of the simulation study confirm that separation occurs frequently in small‐sample data and that separation is more likely to occur when the ground truth model has interaction and quadratic terms. Finally, the paper illustrates that different designs with identical run sizes created from the same model can have significantly different chances of encountering separation.     

Quality Management: Tools and Methods for Improvement

Results from the comparison of D, G, and A efficiencies and the scaled average prediction variance IV criterion are presented for the central composite, small composite, Notz, Hoke, Box–Draper, and computer-generated designs. These design optimality criteria are evaluated over the cuboidal design region for three, four, and five design variables.     

Comparison of Simplex Designs for Quadratic Mixture Models

Designs for quadratic regression are considered when the possible values of the controlable variable are mixtures x = (x ₁, x ₂, …, x _{q + 1}) of nonnegative components x _i with Σ ^{q + 1} ₁ x _i = 1. The designs that are optimum with respect to the D-, A-, and E-optimality criteria are compared in their performance relative to these and other criteria. Computational routines for obtaining these designs are developed, and the geometry of optimum structures is discussed. Except when q = 2, the A-optimum design is supported by the vertices and midpoints of edges of the simplex, as is the case for the previously known D-optimum design. Although the E-optimum design requires more observation points, it is more robust in its efficiency, under variation of criterion: but all three designs perform reasonably well in this sense.     

Using a genetic algorithm to generate D‐optimal designs for mixture‐process variable experiments

This article presents and develops a genetic algorithm (GA) to generate D‐efficient designs for mixture‐process variable experiments. It is assumed the levels of a process variable are controlled during the process. The GA approach searches design points from a set of possible points over a continuous region and works without having a finite user‐defined candidate set. We compare the performance of designs generated by the GA with designs generated by two exchange algorithms (DETMAX and k‐exchange) in terms of D‐efficiencies and fraction of design space (FDS) plots which are used to evaluate a design's prediction variance properties. To illustrate the methodology, examples involving three and four mixture components and one process variable are proposed for creating the optimal designs. The results show that GA designs have superior prediction variance properties in comparison with the DETMAX and k‐exchange algorithm designs when the design space is the simplex or is a highly‐constrained subspace of the simplex.     

Optimal design of a simple step‐stress accelerated life test under progressive type I censoring with nonuniform durations for exponential lifetimes

Thanks to continuously advancing technology and manufacturing processes, the products and devices are becoming highly reliable. However, performing the life tests of these products at normal operating conditions becomes extremely difficult, if not impossible, due to their long life spans. This can result in missed opportunities to introduce the products to the market in a timely manner and eventually loss of the market share. This problem is solved by accelerated life tests where the test units are subjected to higher stress levels than the normal usage level so that information on the lifetime parameters can be obtained more quickly. The lifetime at the design condition is then estimated through extrapolation using a regression model. In this work, the design optimization of a simple step‐stress accelerated life test under progressive type I censoring is studied with nonuniform step durations for assessing the reliability characteristics of a solar lighting device. Allowing the intermediate censoring to take place at the stress change time point, the nature of the optimal stress duration is demonstrated under various design criteria including D‐optimality, C‐optimality, A‐optimality, and E‐optimality. The existence of these optimal designs is investigated in detail for exponential lifetimes with a single stress variable, and the effect of the intermediate censoring proportion is assessed on the design efficiency.     

Robustness of response surface designs to missing data

In this paper, minimax loss response surface designs are constructed. These designs are more robust to one missing design point than the original designs. The proposed designs are compared with the designs in the literature, and they are better in terms of loss and number of runs. Moreover, the new suggestion for the value of α generates designs not only with less losses but also with higher D‐efficiency.     

Designing experiments for nonlinear models—an introduction

We illustrate the construction of Bayesian D‐optimal designs for nonlinear models and compare the relative efficiency of standard designs with these designs for several models and prior distributions on the parameters. Through a relative efficiency analysis, we show that standard designs can perform well in situations where the nonlinear model is intrinsically linear. However, if the model is nonlinear and its expectation function cannot be linearized by simple transformations, the nonlinear optimal design is considerably more efficient than the standard design. Published in 2009 by John Wiley & Sons, Ltd.     

Graphical Evaluation of the Prediction Capabilities of Partially Replicated Orthogonal Central Composite Designs

In this work, the performances of the partially replicated‐cube and ‐star (axial) portions of orthogonal central composite designs (CCD) in spherical regions are studied. The replication of the cube and star portions of the CCD without replicating the centre point for k = 3, 4, 5 and 6 number of factors is the main focus. The interest is to evaluate the performance of the CCD with respect to the stability, small prediction variance and prediction capability, when replication is at other points away from the centre of the design. The variance dispersion graphs and fraction of design space plots are the two graphical techniques used while D‐ and G‐efficiencies are the single‐value optimality criteria utilized in the assessment. The results show that replicating the star portions of the CCD considerably reduces the prediction variance, thereby improving the G‐efficiency in the spherical region and, therefore, recommended for prediction with precision and with smaller number of runs than replicating the cube. Copyright © 2014 John Wiley & Sons, Ltd.     

d-QPSO: A Quantum-Behaved Particle Swarm Technique for Finding D-Optimal Designs With Discrete and Continuous Factors and a Binary Response

Identifying optimal designs for generalized linear models with a binary response can be a challenging task, especially when there are both discrete and continuous independent factors in the model. Theoretical results rarely exist for such models, and for the handful that do, they usually come with restrictive assumptions. In this article, we propose the d-QPSO algorithm, a modified version of quantum-behaved particle swarm optimization, to find a variety of D-optimal approximate and exact designs for experiments with discrete and continuous factors and a binary response. We show that the d-QPSO algorithm can efficiently find locally D-optimal designs even for experiments with a large number of factors and robust pseudo-Bayesian designs when nominal values for the model parameters are not available. Additionally, we investigate robustness properties of the d-QPSO algorithm-generated designs to various model assumptions and provide real applications to design a bio-plastics odor removal experiment, an electronic static experiment, and a 10-factor car refueling experiment. Supplementary materials for the article are available online.     

Which Response Surface Design is Best: A Performance Comparison of Several Types of Quadratic Response Surface Designs in Symmetric Regions

The performance of a number of response surface designs for estimating a quadratic response surface model in symmetric experimerltal regions, k-spheres and hypercubes, is compared. The designs compared are composite designs, Box-Behnken designs, Uniform Shell designs, Hoke designs, Pesotchinsky designs, and Box-Draper designs. The performance criteria for the designs are their D-efficiency and their G-efficiency. All of the compared designs have high efficiencies. For large numbers of factors designs hnving higher efficiencies do exist; however, these designs have not yet been discovered.     

Three‐dimensional analyses of in‐plane and out‐of‐plane crack‐tip constraint characterization for fracture specimens

Three‐dimensional elastic–plastic finite element analyses have been conducted for 21 experimental specimens with different in‐plane and out‐of‐plane constraints in the literature. The distributions of five constraint parameters (namely T‐stress, Q, h, T_z and A_p) along crack fronts (specimen thickness) for the specimens were calculated. The capability and applicability of the parameters for characterizing in‐plane and out‐of‐plane crack‐tip constraints and establishing unified correlation with fracture toughness of a steel were investigated. The results show that the four constraint parameters (T‐stress, Q, h and T_z) based on crack‐tip stress fields are only sensitive to in‐plane or out‐of‐plane constraints. Therefore, the monotonic unified correlation curves with fracture toughness (toughness loci) cannot obtained by using them. The parameter A_p based on crack‐tip equivalent plastic strain is sensitive to both in‐plane and out‐of‐plane constraints, and may effectively characterize both of them. The monotonic unified correlation curves with fracture toughness can be obtained by using A_p. In structural integrity assessments, the correlation curves may be used in the failure assessment diagram (FAD) methodology for incorporating both in‐plane and out‐of‐plane constraint effects in structures for improving accuracy.     

Revealing the Cooperative Relationship between Spin,Energy, and Polarization Parameters toward Developing High‐Efficiency Exciplex Light‐Emitting Diodes

Experimental studies to reveal the cooperative relationship between spin, energy, and polarization through intermolecular charge‐transfer dipoles to harvest nonradiative triplets into radiative singlets in exciplex light‐emitting diodes are reported. Magneto‐photoluminescence studies reveal that the triplet‐to‐singlet conversion in exciplexes involves an artificially generated spin‐orbital coupling (SOC). The photoinduced electron parametric resonance measurements indicate that the intermolecular charge‐transfer occurs with forming electric dipoles (D^+?→A^??), providing the ionic polarization to generate SOC in exciplexes. By having different singlet‐triplet energy differences (ΔE_ST) in 9,9′‐diphenyl‐9H,9′H‐3,3′‐bicarbazole (BCzPh):3′,3′″,3′″″‐(1,3,5‐triazine‐2,4,6‐triyl)tris(([1,1′‐biphenyl]‐3‐carbonitrile)) (CN‐T2T) (ΔE_ST = 30 meV) and BCzPh:bis‐4,6‐(3,5‐di‐3‐pyridylphenyl)‐2‐methyl‐pyrimidine (B3PYMPM) (ΔE_ST = 130 meV) exciplexes, the SOC generated by the intermolecular charge‐transfer states shows large and small values (reflected by different internal magnetic parameters: 274 vs 17 mT) with high and low external quantum efficiency maximum, EQE_max (21.05% vs 4.89%), respectively. To further explore the cooperative relationship of spin, energy, and polarization parameters, different photoluminescence wavelengths are selected to concurrently change SOC, ΔE_ST, and polarization while monitoring delayed fluorescence. When the electron clouds become more deformed at a longer emitting wavelength due to reduced dipole (D^+?→A^??) size, enhanced SOC, increased orbital polarization, and decreased ΔE_ST can simultaneously occur to cooperatively operate the triplet‐to‐singlet conversion.     

Sequentially Generated Second Order Quasi D-Optimal Designs for Experiments With Mixture and Process Variables

Second order designs for experiments with mixture and process variables are proposed. They are constructed on the basis of continuous D-optimal designs by use of a three-stage procedure for sequentially generating optimal designs. The determinants of the information matrices of the designs obtained are very near to those of continuous D-optimal designs. Tables of discrete quasi D-optimal designs for q + r ≤ 7 are given, where q is the number of mixture components and r is the number of process variables. The experimenter can choose the number of trials N within the interval k ≤ N ≤ min(2k, k + 20), where k is the number of model coefficients. An application of the proposed designs in an investigation of truck tire properties is given.     

Chiral Octahydro‐Binaphthol Compound‐Based Thermally Activated Delayed Fluorescence Materials for Circularly Polarized Electroluminescence with Superior EQE of 32.6% and Extremely Low Efficiency Roll‐Off

Circularly polarized organic light‐emitting diodes (CP‐OLEDs) are particularly favorable for the direct generation of CP light, and they demonstrate a promising application in 3D display. However, up to now, such CP devices have suffered from low brightness, insufficient efficiency, and serious efficiency roll‐off. In this study, a pair of octahydro‐binaphthol ( OBN )‐based chiral emitting enantiomers, (R/S)‐OBN‐Cz , are developed by ingeniously merging a chiral source and a luminophore skeleton. These chirality–acceptor–donor (C–A–D)‐type and rod‐like compounds concurrently generate thermally activated delayed fluorescence with a small ΔE_ST of 0.037 eV, as well as a high photoluminescence quantum yield of 92% and intense circularly polarized photoluminescence with dissymmetry factors (|g_PL|) of ≈2.0 × 10^?3 in thin films. The CP‐OLEDs based on (R/S)‐OBN‐Cz enantiomers not only display obvious circularly polarized electroluminescence signals with a |g_EL| of ≈2.0 × 10^?3, but also exhibit superior efficiencies with maximum external quantum efficiency (EQE_max) up to 32.6% and extremely low efficiency roll‐off with an EQE of 30.6% at 5000 cd m^?2, which are the best performances among the reported CP devices to date.     

Split-Plot and Multi-Stratum Designs for Statistical Inference

It is increasingly recognized that many industrial and engineering experiments use split-plot or other multi-stratum structures. Much recent work has concentrated on finding optimum, or near-optimum, designs for estimating the fixed effects parameters in multi-stratum designs. However, often inference, such as hypothesis testing or interval estimation, will also be required and for inference to be unbiased in the presence of model uncertainty requires pure error estimates of the variance components. Most optimal designs provide few, if any, pure error degrees of freedom. Gilmour and Trinca (2012 Gilmour, S. G., and Trinca, L. A. (2012), “Optimum Design of Experiments for Statistical Inference” (with discussion), Applied Statistics, 61, 345–401.[Crossref], [Web of Science ®] , [Google Scholar]) introduced design optimality criteria for inference in the context of completely randomized and block designs. Here these criteria are used stratum-by-stratum to obtain multi-stratum designs. It is shown that these designs have better properties for performing inference than standard optimum designs. Compound criteria, which combine the inference criteria with traditional point estimation criteria, are also used and the designs obtained are shown to compromise between point estimation and inference. Designs are obtained for two real split-plot experiments and an illustrative split–split-plot structure. Supplementary materials for this article are available online.     

Three‐dimensional analyses of unified characterization parameter of in‐plane and out‐of‐plane creep constraint

Based on extensive three‐dimensional finite element analyses, the unified characterization parameter A_c of in‐plane and out‐of‐plane creep constraint based on crack‐tip equivalent creep strain for three specimen geometries (C(T), SEN(T) and M(T)) were quantified for 316H steel at 550 °C and steady‐state creep. The distributions of the parameter A_c along crack fronts (specimen thickness) were calculated, and its capability and applicability for characterizing a wide range of in‐plane and out‐of‐plane creep constraints in different specimen geometries have been comparatively analysed with the constraint parameters based on crack‐tip stress fields (namely R*, h and T_Z). The results show that the parameter A_c in the centre region of all specimens appears uniform distribution and lower value (higher constraint), and in the region near free surface it shows protuberant distribution and higher value (lower constraint). The parameter A_c can simultaneously and effectively characterize a wide range of in‐plane and out‐of‐plane creep constraints, while the parameters R*, h and T_Z based on crack‐tip stress fields cannot achieve this. The different capabilities of these parameters for characterizing in‐plane and out‐of‐plane creep constraints originate from their underlying theories. The parameter A_c may be useful for accurately characterizing the overall constraint level composed of in‐plane and out‐of‐plane constraints in actual high‐temperature components, and it may be used in creep life assessments for improving accuracy.     

Model-Based Sampling Design for Multivariate Geostatistics

The quality of inferences made from geostatistical data is affected significantly by the spatial locations, or design, of the sites that are sampled. A large body of published work exists on sampling design for univariate geostatistics, but not for multivariate geostatistics. This article considers multivariate spatial sampling design based on criteria targeted at classical co-kriging (prediction with known covariance parameters), estimation of covariance (including cross-covariance) parameters, and empirical co-kriging (prediction with estimated covariance parameters). Through a combination of analytical results and examples, we investigate the characteristics of optimal designs with respect to each criterion, addressing in particular the design’s degree of collocation. We also consider the robustness of the optimal design to the strength of spatial correlation and cross-correlation; the effects of smoothness and/or separability of the sampled process on the optimal design; the relationship between optimal designs for the multivariate problems considered here and univariate problems considered previously; and the efficiency of optimal collocated designs. One key finding is that optimal collocated designs are highly efficient in many cases. Supplementary materials are available online.     

Versatile Indolocarbazole‐Isomer Derivatives as Highly Emissive Emitters and Ideal Hosts for Thermally Activated Delayed Fluorescent OLEDs with Alleviated Efficiency Roll‐Off

Maintaining high efficiency at high brightness levels is an exigent challenge for real‐world applications of thermally activated delayed fluorescent organic light‐emitting diodes (TADF‐OLEDs). Here, versatile indolocarbazole‐isomer derivatives are developed as highly emissive emitters and ideal hosts for TADF‐OLEDs to alleviate efficiency roll‐off. It is observed that photophysical and electronic properties of these compounds can be well modulated by varying the indolocarbazole isomers. A photoluminescence quantum yield (η_PL) approaching unity and a maximum external quantum efficiency (EQE_max) of 25.1% are obtained for the emitter with indolo[3,2‐a]carbazolyl subunit. Remarkably, record‐high EQE/power efficiency of 26.2%/69.7 lm W^?1 at the brightness level of 5000 cd m^?2 with a voltage of only 3.74 V are also obtained using the same isomer as the host in a green TADF‐OLED. It is evident that TADF hosts with high η_PL values, fast reverse intersystem crossing processes, and balanced charge transport properties may open the path toward roll‐off‐free TADF‐OLEDs.     

Two-Level Multifactor Designs for Detecting the Presence of Interactions

A design optimality criterion, tr (L)-optimality, is applied to the problem of designing two-level multifactor experiments to detect the presence of interactions among the controlled variables. We give rules for constructing tr (L)-optimal foldover designs and tr (L)-optimal fractional factorial designs. Some results are given on the power of these designs for testing the hypothesis that there are no two-factor interactions. Augmentation of the tr (L)-optimal designs produces designs that achieve a compromise between the criteria of D-optimality (for parameter estimation in a first-order model) and tr (L)-optimality (for detecting lack of fit). We give an example to demonstrate an application to the sensitivity analysis of a computer model.