The notion of canonical efficiency factors is re-examined in the context of arbitrary block designs, and a simple statistical interpretation of these is provided. Some related issues are also discussed. Key words: Block designs, Efficiency factor, Orthogonal design, C-design.

  In a mixture experiment the mean response is assumed to depend only on the relative proportion of ingredients or components present in the mixture. Scheffé (1958, 1963) first systematically considered this problem and introduced different models and designs suitable in such situations. Optimum designs for the estimation of parameters of different mixture models are available in the literature. The problem of estimating the optimum proportion of mixture components is of great practical importance. Pal and Mandal (2006) first attempted to find a solution to this problem using the trace criterion. They adopted a pseudo-Bayesian approach with invariance property of the second order moments of the optimum mixing proportions. In this paper the same criterion has been employed to find a solution to the problem, but with a pseudo-Bayesian approach, with assumed values of only the second order moments of the optimum mixing proportions. Key word : Mixture experiments, Second order models, Non-linear function, Asymptotic efficiency, Trace criterion, Optimum designs.

  The co-ordinate column-wise exchange algorithms of Nguyen (1996) and Lejeune (2003) have been modified to generate efficient supersaturated designs (SSDs) for two-level factorial experiments. Designs have been generated for two different settings viz. (a) the design is balanced in the sense that for an n run design, the +1 and ?1 levels appear n/2 times each for all the factors; (b) the design is balanced and there is a subset of factors that are mutually orthogonal. The upper bound on the number of active factors that are estimable through the design has also been obtained by computing the rank of design matrix X using the necessary condition of Srivastava (1975). Catalogues of efficient SSDs have been prepared for number of runs 10 ? n ? 20, n = 2t in (a) and n = 4t in (b), t a positive integer, and number of factors n + 2 ? m ? 2n. A comparison of the designs generated has been made with the designs available in the literature. Key words: Co-ordinate column-wise exchange algorithm, E(s2)-efficiency criteria.

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  Ring theory is used to construct a complete set of sum of squares orthogonal F-squares (SSOFSs or SSOF-squares) for n = 6. Sum of squares orthogonality of this set is exhibited with a numerical example. Previous methods involved field theoretic methods together with trial and error with computer codes. Sum of squares orthogonal Latin squares have been constructed for any value of n, SSOLS (n, n ? 1), not just prime powers as in Projective Geometry. Attempts to construct a SSOLS (6, 5) set using ring theory are discussed. Key words: Computer code, Row frequency F-square, Column frequency F-square, Semi-F- square, F-rectangle, Factorial, Main effect, Interaction effect, Field theory.

  This paper considers statistical issues in experimentation for the development of so-called ?modern? (allopathic) medicine, particularly for degenerative diseases. The allopathic approach became popular because of its great successes in controlling epidemics, and also the spectacular advances in surgery. However, in the field of degenerative diseases and prevention of diseases, much further work is needed. It is well known that allopathic drugs have, in general, large numbers of side effects. In this paper, we discuss this field and its statistical aspects. Key words: Allopathic drugs, Degenerative diseases, Preservatives.

  Some early uses of experimental designs and more recent applications are reviewed. Role of experimental designs in controlled sampling is appraised. Some new work on constructing balanced bootstrap replicates from stratified random samples is also reported. Key words: Linear programming, Controlled sample selection, Balanced sampling plans.

  The existence on affine ?-resolvability with some properties has been discussed for block designs in literature since 1942 for ? = 1 and in particular since 1963 for ? ? 2. Non-existence of affine a-resolvable group divisible designs of regular type is known (Kageyama 2008). Also, Kageyama (2007) disproved the validity of such concept for triangular designs when ? = 1, 2. In this paper, for 3 ? ? ? 10, the non-existence will be shown. Key words: Triangular design; ?-resolvable; Affine ?-resolvable.

  The methodology of longitudinal data analysis (LDA) has been discussed with particular reference to applications in studies on nutrition and animal breeding. It is based on the concept of intra-individual variation first advocated by Sukhatme in nutrition studies. First the process view of nutrition is discussed with an auto-regressive Markov process for analysing data on protein or energy intake. The general theory of linear models with correlated errors is then used, in the context of half-sib mating design used in animal breeding, to develop the structure of covariance matrix. Its elements are in terms of four components of variation and one serial correlation coefficient. The observational components of variance are related to the causal components of variation based on genetic considerations. Intra-individual heritability (h 2) in a narrow sense, in contrast to the usual heritability (h2) used in quantitative genetics literature, is introduced that depends on the process variance and the average serial correlation coefficient. As a consequence, a useful test for the existence or otherwise of additive × local environmental interaction effects has become available. A significant process variance with a significant autocorrelation function or its associated variogram indicates a significant h 2 . The heritability of k repeated measurements is derived and used to develop a new formula for the heritability of the progeny test used in animal breeding. This formula indicates that the LDA leads to increased accuracy in predicting the breeding value of the male on the basis of offspring?s performance. The estimation of the parameters of the linear model with correlated errors, particularly the covariances, by restricted maximum likelihood method is also described.

  Wynn (1976) introduced a difference type estimator for estimating the population proportion using simple random sampling. Later Singh et al. (1986) modified the Wynn (1976) estimator and also suggested another difference type estimator for the ratio of two population proportions using auxiliary information. In this paper we propose a linear weighted estimator for the ratio of two population proportions. The proposed estimator is more efficient than usual ratio estimator, Wynn- type (1976) estimator and Singh et al. (1986) estimator. A numerical study is also conducted to evaluate the performance of different estimators. Key words : Ratio of proportions, Bias, Mean square error, Efficiency.

  Identification of correct model is essential for optimization of processes and systems in engineering and the sciences. Supersaturated designs provide an important tool for evaluating a large number of factors in the initial phase of an experiment. Several procedures have been proposed in literature over the last decade or so for identification and estimation of correct model using supersaturated designs. A review of these methods is provided in this paper. A generalization of the contrast variance method to situations where coefficients of active effects are neither all equal nor linearly related is also provided. Since no method seems to be consistently superior over other methods, it is concluded that results obtained using competing methods should be carefully evaluated before a final model is selected. Key words: Active factors, Adjusted p-values, All-subsets regression, Bayesian approach, Bootstrap method, Contrast variance method, Intrinsic Bayes factor, Monte Carlo, Partial least squares, Penalized least squares, Plackett-Burman design, Search designs, Stepwise regression, Stochastic search variable selection.