A Note on Foldover of 2k − p Designs With Column Permutations

Foldover is a commonly used follow-up strategy in experimental designs. All existing foldover designs were constructed by reversing the sign of columns of the initial design. We propose a new methodology by allowing the permutation of columns in foldover. Focusing on resolution IV designs, we show that almost all designs are better than existing results with respect to the minimum aberration criterion. While augmenting a design by a foldover with column permutations may result in a nonregular combined design, the proposed designs all have a resolution of 4.5 or higher, for which no two-factor interaction is fully aliased with any other two-factor interactions.     

Semifolding 2 k–P Designs

This article addresses the varied possibilities for following a two-level fractional factorial with another fractional factorial half the size of the original experiment. Although follow-up fractions of the same size as an original experiment are common practice, in many situations a smaller followup experiment will sufIice. Peter John coined the term “semifolding” to describe using half of a foldover design. Existing literature does include brief mention and examples of semifolding but no thorough development of this follow-up strategy. After a quick examination of the estimation details for semlfoldmg the 2^{4 – 1} _IV design, we focus on following 16-run fractions with a semifold design of eight runs. Two such examples are considered—one in which the initial fraction ia resolution IV, the other resolution III. A general result is proven for semifolding 2 ^{k – p} _IV designs. Conducting full foldover designs in two blocks is also recommended.     

The 2 k — p Fractional Factorial Designs

“Cats is dogs and dogs is dogs and rabbits is dogs, and squirrels in cages is parrots ….”     

Blocking of 3(2 n–k ) Designs

3(2 ^n–2) designs may be divided into two blocks, one of size 2 ^n–1 and the other of size 2 ^n–2 by blocking on one of the defining contrasts and into three blocks of size 2 ^n–2 by blocking on all three defining contrasts. Blocking on an effect which is not a defining contrast gives two blocks of 3(2 ^n–3) runs each. In this paper these methods are applied to 3(2 ^n–k ) designs with twelve or twenty-four points. The designs considered are the 3(2^4–2) and 3(2^5–2) designs with all main effects and all two factor interactions estimable (assuming that higher order interactions are negligible), and saturated main effect plans with twelve points and up to eleven factors.     

The 2 k — p Fractional Factorial Designs Part II.

“… … …. but that there turtle is an insect.”     

A Note on the ‘Round Robin’ Design

The ‘Round Robin’ design was suggested as suitable for screening a group of treatments. But in this design the variances of treatment are very dependent on the relative position of treatments. This detracts from its value as a screening design.     

Mechanism of Inelastic Phonon Scattering on the Quadrupolar o–H2 Impurity in p–H2 Matrix

A quantum–mechanical problem on inelastic phonon scattering by a quadrupolar pair defect is discussed. As an example of the physical system, where this mechanism is of great concern, the solution of o–H ₂ molecules in p–H ₂ matrix is considered. The effective relaxation time _p of a phonon collision with a pair defect as a function of the phonon frequency is calculated. Due to intrinsic degrees of freedom, pair defects give rise to the resonance phonon scattering above a certain temperature T ₀ , which for o–H ₂ —p–H ₂ mixtures is approximately 6 ÷ 7 K.     

An Algorithm for the Construction of “D-Optimal” Experimental Designs

This paper presenm the algorithm “DETMAX” whose purpose is to construct experimental designs that are “D-optimal.” These are designs for which the determinant of X'X is maximum, where X is the “matrix of independent variables” in the usual linear model y = Xβ + ε. Although the algorithm does not guarantee D-optimality, it has performed well in many cases where D-optimal designs are known. Five examples are given, illustrating the use of DETMAX to construct designs “from scratch” and to augment existing data. A FORTRAN listing is available on request.     

Statistical description of the effect of Zr addition on the behavior of microcracks in Cu–6Ni–2Mn–2Sn–2Al Alloy

As possible substitutes for high-strength Cu–Be alloys, Cu–6Ni–2Mn–2Sn–2Al alloys have been developed. To clarify the physical background of the effect of trace Zr on the fatigue strength of such alloys, the initiation and propagation behavior of a major crack that led to the fracture of the tested specimens was monitored. When the stress amplitude was less than σ _a = 350 MPa, the fatigue life of the alloys with Zr was about 2–2.5 times larger than that of the alloy without Zr. When σ _a > 350 MPa, the effect of Zr addition on the fatigue life dramatically decreases as the stress amplitude increases. The increased fatigue life due to Zr addition resulted from an enhancement of the crack initiation life and microcrack growth life. The enhanced crack initiation life was mainly attributed to the strengthening of grain boundaries due to the precipitation of SnZr compounds. A statistical analysis of the behavior of multiple cracks was made to quantitatively evaluate the scatter in fatigue behavior. The statistical analysis supported the conclusions obtained from the behavior of a major crack.     

A Note on G. S. Watson's Paper ‘A Study of the Group Screening Method”

In a paper in this Journal, Watson (1961) has discussed the use of group screening methods for detecting effective factors. The methods are analogous to those suggested by Dorfman (1943) for the medical problem of detecting a rare defect among members of a large population by using pooled blood samples. One step in Watson's derivation of the probability that an effective factor is declared significant is invalid. The purpose of this note is to derive the correct expression for this probability and show how the correction affects the subsequent theory. None of Watson's qualitative statements about the efficiency of group screening methods nor his numerical example are seriously affected.     

A model for the prediction of liquid–liquid interfacial energies

A model for the calculation of liquid–liquid interfacial energies is presented. It is based on the assumption that the interface can be treated as a separate thermodynamic phase. Its derivation has been performed in an analogous way as the derivation of the Butler equation for the surface tension of liquid alloys. It requires as input parameters the excess free energy and the compositions of the bulk phases as functions of temperature. In addition, it also requires the partial molar volumes of the components. Comparison with existing experimental data for Al–Pb, Al–In, and Cu–Co in a non-equilibrium state shows very good agreements. For Al–Bi, the experimental data are either over or underestimated by a factor of ≈1.7, depending on which of the two thermodynamic assessments is used. For the Al-based systems, the calculated Al-mole fraction in the interface layer is close to the arithmetic average of the Al-mole fractions of the bulk phases.     

Study on the plasma erosion resistance of ZrO2p(3Y)/BN–SiO2 composite ceramics

ZrO_2p(3Y)/BN–SiO₂ composite ceramics were prepared by hot pressed sintering. The Kr plasma was incident normally to the sample surface to measure the plasma erosion resistance, and XRD, TEM, SEM were used to characterize the phase composition and morphology of composite ceramics before and after Kr plasma erosion. The composites were composed of h-BN, amorphous SiO₂, m-ZrO₂ and t-ZrO₂, which keep stability in the process of Kr plasma sputtering. Two kinds of zirconia phases (t-ZrO₂, m-ZrO₂) and lamellar h-BN evenly distributed in ZrO_2p(3Y)/BN–SiO₂ composite ceramics, and the lath microstructures were observed in m-ZrO₂ particles. The plasma erosion resistances of ceramic composites increase significantly with the increase of ZrO₂ content. Pits with diameter sizes of several micrometers were observed on the surface of composites after plasma sputtering, which indicate that one or several grains are sputtered out during the plasma sputtering process. The edges of the grains become smoother for the preferential sputtering to the sharp edge of the grains during plasma sputtering.     

Effect of TiO2 on the sintering temperature and dielectric properties of Li2O–MgO–ZnO–B2O3–SiO2 ceramic composites for LTCC applications

Journal of Materials Science: Materials in Electronics - The effects of injecting TiO2 to a Li2O–MgO–ZnO–B2O3–SiO2 (LMZBS) microwave dielectric composite on sinterability,...     

Effect of atmosphere on the electrical properties of TiO2–SnO2 varistor systems

This work illustrates the advancement of research on TiO₂-based electroceramics. In this work will be presented that the addition of different dopants, as well as thermal treatments at oxidizing and inert atmosphere, influences of the densification, the mean grain size and the electrical properties of the TiO₂-based varistor ceramics. Dopants like Ta₂O₅, Nb₂O₅, and Cr₂O₃ have an especial role in the barrier formation at the grain boundary in the TiO₂ varistors, increasing the nonlinear coefficient and decreasing the breakdown electric field. The influence of Cr_Ti is to increase the O and O₂ adsorption at the grain boundary interface and to promote a decrease in the conductivity by donating electrons to O₂ adsorbed at the grain boundary. In this paper, TiO₂ and (Sn,Ti)O₂-based studies of polycrystalline ceramics, which show a non-linear I–V electrical response typical of low voltage varistor systems are also presented. All these systems are potentially promising for varistor applications.     

Effects of MgO on properties of Li2O–Al2O3–SiO2 glass–ceramics for LTCC applications

Li₂O–Al₂O₃–SiO₂ (LAS) glass–ceramics for low temperature co-fired ceramics (LTCC) application were prepared by melting method, and the effects of MgO on the sinterability, microstructure, dielectric property, thermal expansion coefficient (CTE) and mechanical character of this glass–ceramics have been studied. The X-ray diffraction images represent that the main phase is β-spodumene solid solutions. And some ZrO₂ and CaMgSi₂O₆ phases in LAS glass–ceramics are detected. The LAS glass–ceramics without additive (MgO) sintered at 800° had the dielectric properties: dielectric constant (ε_r) of 5.3, dielectric loss (tanδ) of 2.97 × 10^?3 at 1 MHz, CTE value of 1.06 × 10^?6 K^?1, bulk density of 2.17 g/cm³, and flexural strength of 73 MPa. 5.5 wt% MgO-added LAS glass–ceramic achieves densification at 800° exhibited excellent properties: low dielectric constant and loss (ε_r = 7.1, tanδ = 2.02 × 10^?3 at 1 MHz), low CTE (2.89 × 10^?6 K^?1), bulk density = 2.65 g/cm³ as well as high flexural strength (145 MPa). The results indicate that the addition of MgO is helpful to improve the dielectric and mechanical properties. The formation of CaMgSi₂O₆ crystal phase with higher CTE leads to the increase of CTE value of LAS glass–ceramics due to the increasing MgO content, and the increase of CTE is favourable for matching with silicon (3.1 × 10^?6 K^?1). The prepared LAS glass–ceramics have the potential for LTCC application.     

Effect of the type of Pt precursor on Pt–Ni nanostructures for electro-oxidation of ammonia

The properties of Pt–Ni nanostructures were successfully controlled by employing different Pt precursors in the preparation of Pt–Ni nanocomposites, which were synthesized by a co-reducing Pt and Ni precursors. Pt–Ni nanostructures were obtained by leaching Ni species from the Pt–Ni nanocomposite. The use of H₂PtCl₆ as a precursor yielded aggregated small Pt particles, while [Pt(NH₃)₄]Cl₂ yielded large hollow Pt nanostructures. A possible mechanism leading to the morphological difference between the two structures was suggested. Owing to a higher electrochemically active surface area and a favorable surface structure, hollow Pt nanostructures from the [Pt(NH₃)₄]Cl₂ precursor showed significantly better performance in ammonia oxidation than the aggregated Pt particles resulting from the H₂PtCl₆ precursor.