Orthogonally Blocked Mixture Experiments in Ellipsoidal Restricted Regions

In practical situations involving mixtures formed from several ingredients, interest is sometimes centered on the response in an ellipsoidal neighborhood around a standard formulation. We show that standard, orthogonally blocked, response surface designs, defined on a q ? 1 dimensional unit sphere, may be transformed into similarly orthogonally blocked q-ingredient mixture designs defined within an ellipsoid centered at the standard formulation. The method is illustrated using several examples of mixture experiments with three, four, and five ingredients, arranged in two, three, or four orthogonal blocks, obtained by projecting standard central composite designs and Box–Behnken designs into the ellipsoidal mixture region. Rotations of the resulting designs within the ellipsoidal regions are also considered.     

Designs Robust against Violation of Normality Assumption in the Standard F-test

In this article, designs are found for which the F-test of analysis of variance is insensitive to violation of normality assumption. Atiqullah (1962 Atiquallah, M. (1962). The estimation of residual variance in quadratically balanced least-squares problems and the robustness of the F-test. Biometrika 49: 83–91.[Crossref], [Web of Science ®] , [Google Scholar]) proved that the F-test for treatments adjusting for blocks in the intra-block analysis of a balanced incomplete block design is robust against non-normality in the observations. Here an attempt has been made to identify other designs robust in this sense. In particular, it is observed that for testing relevant hypothesis, a partially balanced incomplete block design in block design setup, under certain conditions, is robust. Robustness of a balanced treatment incomplete block design and a partially balanced treatment incomplete block design (Biswas, 2012 Biswas, A. (2012). Block designs robust against the presence of an aberration in a treatment-control setup. Commun Statist.Theor Methods 41: 920–933.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), in treatment-control design setup, is also studied. Moreover, a new measure of robustness is introduced for further study. The performance of the F-test in presence of non-normality in the observations for a quadratically balanced design is also examined.     

Randomized Response Techniques Using Maximum Likelihood Estimator

The randomized response (RR) technique with two decks of cards proposed by Odumade and Singh (2009) can always be made more efficient than the RR techniques proposed by Warner (1965), Mangat and Singh (1990), and Mangat (1994) by adjusting the proportion of cards in the decks. Arnab et al. (2012) generalized Odumade and Singh strategy (2009) for complex survey designs and wider class of estimators. In this paper improvement of Arnab et al. (2012) estimator has been made by using maximum likelihood method.     

Semiparametric estimator for a secondary analysis with correlated outcomes

ABSTRACT

Researchers are often required to reuse data that have been collected and analyzed for other purposes. Issues may arise if the outcome of this secondary study is related to the outcome of the first study and traditional methods may fail to deliver a consistent estimate. Here we propose a semiparametric approach that takes this correlation into account and produces asymptotically consistent and normally distributed estimates. We discuss its performance through simulations and apply the proposed method to a real dataset.     

Measures of uniformity in experimental designs: A selective overview

ABSTRACT

Discrepancies are measures which are defined as the deviation between the empirical and the theoretical uniform distribution. In this way, discrepancy is a measure of uniformity which provides a way of construction a special kind of space filling designs, namely uniform designs. Several discrepancies have been proposed in recent literature. A brief, selective review of these measures including some construction algorithms are given in this paper. Furthermore, a critical discussion along with some comparisons is provided, as well.     

A comparison of random balance and two-stage group screening designs: A case study

In this paper we focus on the problem of supersaturated (fewer runs than factors) screening experiments. We consider two major types of designs which have been proposed in this situ¬ation: random balance and two-stage group screening. We discuss the relative merits and demerits of each strategy. In addition, we compare the performance of these strategies by means of a case study in which 100 factors are screened in 20,42,62, and 84 runs.     

A simple method for constructing confounded designs for mixed factorial experiments

This paper presents the sinplesr procedure that uses wodular aryithmetic for constructing confounded designs for mixed factorial experiments. The present procedure and the classical one for confounding in symmetrical factorial experiments are both at the same mathema.tical level. The present procedure is written for

practitioners and is lllustrared with several examples.     

On the construction of orthogonal factorial designs of resolution 11

A new method of construction of orthogonal resolution IV designs for symmetrical and asymmetrical factorials has been presented. Many new series of orthogonal factorial designs of resolution IV can be obtained by the above general method.     

VARIATION REDUCTION AND ROBUST DESIGNS

In this paper we consider two strategies for variation reduction. One of them is the exploitation of interactions. We also discuss the role of experiments in discovering interactions and in particular the use of robust designs to obtain the interaction between control and noise factors. Then we attempt to reduce the variation in a measurement system using a robust design.