Determination of the Joint Confidence Region of Optimal Operating Conditions in Robust Design by Bootstrap Technique

Robust design has been widely recognized as a leading method in reducing variability and improving quality. Most of the engineering statistics literature mainly focuses on finding "point estimates" of the optimum operating conditions for robust design. Various procedures for calculating point estimates of the optimum operating conditions are considered. Although this point estimation procedure is important for continuous quality improvement, the immediate question is "how accurate are these optimum operating conditions?" The answer for this is to consider interval estimation for a single variable or joint confidence regions for multiple variables. In this paper, with the help of the bootstrap technique, we develop procedures for obtaining joint "confidence regions" for the optimum operating conditions. Two different procedures using Bonferroni and multivariate normal approximation are introduced. The proposed methods are illustrated and substantiated using a numerical example.Comment: Two tables, Three figure

Unbalanced and Minimal Point Equivalent Estimation Second-Order Split-Plot Designs

Restricting the randomization of hard-to-change factors in industrial experiments is often performed by employing a split-plot design structure. From an economic perspective, these designs minimize the experimental cost by reducing the number of resets of the hard-to- change factors. In this paper, unbalanced designs are considered for cases where the subplots are relatively expensive and the experimental apparatus accommodates an unequal number of runs per whole-plot. We provide construction methods for unbalanced second-order split- plot designs that possess the equivalence estimation optimality property, providing best linear unbiased estimates of the parameters; independent of the variance components. Unbalanced versions of the central composite and Box-Behnken designs are developed. For cases where the subplot cost approaches the whole-plot cost, minimal point designs are proposed and illustrated with a split-plot Notz design

Classes of Split-Plot Response Surface Designs for Equivalent Estimation

When planning an experimental investigation, we are frequently faced with factors that are difficult or time consuming to manipulate, thereby making complete randomization impractical. A split-plot structure differentiates between the experimental units associated with these hard-to-change factors and others that are relatively easy-to-change and provides an efficient strategy that integrates the restrictions imposed by the experimental apparatus. Several industrial and scientific examples are presented to illustrate design considerations encountered in the restricted randomization context. In this paper, we propose classes of split-plot response designs that provide an intuitive and natural extension from the completely randomized context. For these designs, the ordinary least squares estimates of the model are equivalent to the generalized least squares estimates. This property provides best linear unbiased estimators and simplifies model estimation. The design conditions that allow for equivalent estimation are presented enabling design construction strategies to transform completely randomized Box-Behnken, equiradial, and small composite designs into a split-plot structure

Magnetic Ordering and Superconductivity in the RE2_2Ir3_3Ge5_5 (RE = Y, La-Tm, Lu) System

We find that the compounds for RE = Y, La-Dy, crystallize in the tetragonal Ibam (U$_2$Co$_3$Si$_5$ type) structure whereas the compounds for RE = Er-Lu, crystallize in a new orthorhombic structure with a space group Pmmn. Samples of Ho$_2$Ir$_3$Ge$_5$ were always found to be multiphase. The compounds for RE = Y to Dy which adopt the Ibam type structure show a metallic resistivity whereas the compounds with RE = Er, Tm and Lu show an anomalous behavior in the resistivity with a semiconducting increase in $\rho$ as we go down in temperature from 300K. Interestingly we had earlier found a positive temperature coefficient of resistivity for the Yb sample in the same temperature range. We will compare this behavior with similar observations in the compounds RE$_3$Ru$_4$Ge$_{13}$ and REBiPt. La$_2$Ir$_3$Ge$_5$ and Y$_2$Ir$_3$Ge$_5$ show bulk superconductivity below 1.8K and 2.5K respectively. Our results confirm that Ce$_2$Ir$_3$Ge$_5$ shows a Kondo lattice behavior and undergoes antiferromagnetic ordering below 8.5K. Most of the other compounds containing magnetic rare-earth elements undergo a single antiferromagnetic transition at low temperatures (T$\leq$12K) while Gd$_2$Ir$_3$Ge$_5$, Dy$_2$Ir$_3$Ge$_5$ and Nd$_2$Ir$_3$Ge$_5$ show multiple transitions. The T$_N$'s for most of the compounds roughly scale with the de Gennes factor. which suggests that the chief mechanism of interaction leading to the magnetic ordering of the magnetic moments may be the RKKY interaction.Comment: 25 pages, 16 figure

Unusual Ground State Properties of the Kondo-Lattice Compound Yb2Ir3Ge5

We report sample preparation, structure, electrical resistivity, magnetic susceptibility and heat capacity studies of a new compound Yb$_2$Ir$_3$Ge$_5$. We find that this compound crystallizes in an orthorhombic structure with a space group PMMN unlike the compound Ce$_2$Ir$_3$Ge$_5$ which crystallizes in the tetragonal IBAM (U$_2$Co$_3$Si$_5$ type) structure. Our resistivity measurements indicate that the compound Yb$_2$Ir$_3$Ge$_5$ behaves like a typical Kondo lattice system with no ordering down to 0.4 K. However, a Curie-Weiss fit of the inverse magnetic susceptibility above 100 K gives an effective moment of only 3.66 $\mu$$_B$ which is considerably less than the theoretical value of 4.54 $\mu$$_B$ for magnetic Yb$^3+$ ions. The value of $\theta_{P}$ = -15.19 K is also considerably higher indicating the presence of strong hybridization. An upturn in the low temperature heat capacity gives an indication that the system may order magnetically just below the lowest temperature of our heat capacity measurements (0.4 K). The structure contains two sites for Yb ions and the present investigation suggests that Yb may be trivalent in one site while it may be significantly lower (close to divalent) in the other.Comment: 9 pages, 4 figures. submitted to Phys. Rev.

Efficiency in nanostructured thermionic and thermoelectric devices

Advances in solid-state device design now allow the spectrum of transmitted electrons in thermionic and thermoelectric devices to be engineered in ways that were not previously possible. Here we show that the shape of the electron energy spectrum in these devices has a significant impact on their performance. We distinguish between traditional thermionic devices where electron momentum is filtered in the direction of transport only and a second type, in which the electron filtering occurs according to total electron momentum. Such 'total momentum filtered' kr thermionic devices could potentially be implemented in, for example, quantum dot superlattices. It is shown that whilst total momentum filtered thermionic devices may achieve efficiency equal to the Carnot value, traditional thermionic devices are limited to efficiency below this. Our second main result is that the electronic efficiency of a device is not only improved by reducing the width of the transmission filter as has previously been shown, but also strongly depends on whether the transmission probability rises sharply from zero to full transmission. The benefit of increasing efficiency through a sharply rising transmission probability is that it can be achieved without sacrificing device power, in contrast to the use of a narrow transmission filter which can greatly reduce power. We show that devices which have a sharply-rising transmission probability significantly outperform those which do not and it is shown such transmission probabilities may be achieved with practical single and multibarrier devices. Finally, we comment on the implications of the effect the shape of the electron energy spectrum on the efficiency of thermoelectric devices.Comment: 11 pages, 15 figure

The Prediction Properties of Inverse and Reverse Regression for the Simple Linear Calibration Problem

The calibration of measurement systems is a fundamental but under-studied problem within industrial statistics. The origins of this problem go back to basic chemical analysis based on NIST standards. In today's world these issues extend to mechanical, electrical, and materials engineering. Often, these new scenarios do not provide "gold standards" such as the standard weights provided by NIST. This paper considers the classic "forward regression followed by inverse regression" approach. In this approach the initial experiment treats the "standards" as the regressor and the observed values as the response to calibrate the instrument. The analyst then must invert the resulting regression model in order to use the instrument to make actual measurements in practice. This paper compares this classical approach to "reverse regression," which treats the standards as the response and the observed measurements as the regressor in the calibration experiment. Such an approach is intuitively appealing because it avoids the need for the inverse regression. However, it also violates some of the basic regression assumptions

Supplementation of porcin in vitro maturation medium with FGF2, LIF, and IGF1 enhances cytoplasmic maturation in prepubertal gilts oocytes and improves embryo quality

In porcine production (IVP) systems, the use of oocytes derived from prepubertal gilts, whilst being commercially attractive, remains challenging due to their poor developmental competence following maturation (IVM). Follicular fluid contains important growth factors and plays a key role during oocyte maturation; therefore, it is a common supplementation for porcine IVM medium. However, follicular fluid contains many poorly characterized components, is batch variable, and its use raises biosecurity concerns. In an effort to design a defined IVM system, growth factors such as cytokines have been previously tested. These include leukaemia inhibitory factor (LIF), fibroblast growth factor 2 (FGF2), and insulin-like growth factor 1 (IGF1), the combination of which is termed 'FLI'. Here, using abattoir-derived oocytes in a well established porcine IVP system, we compared follicular fluid and FLI supplementation during both IVM and embryo culture to test the hypothesis that FLI can substitute for follicular fluid without compromising oocyte nuclear and cytoplasmic maturation. We demonstrate that in oocytes derived from prepubertal gilts, FLI supplementation enhances oocyte meiotic maturation and has a positive effect on the quality and developmental competence of embryos. Moreover, for the first time, we studied the effects of follicular fluid and FLI combined showing no synergistic effects