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Random execution of run sequences is employed in response surface designs to avoid bias in the response. Since the randomization of run sequences may induce frequent changes in the factor levels, which makes it difficult or expensive for the experimenter, especially when hard-to-change factors are involved in the experiment. Mostly, second order response surface designs (SORDs) are being used to explore the functional relationship between the response and the input variables. But when the lack of fit of the model becomes significant, it is desirable to explore the relationship with a polynomial model of order three. This requires third order rotatable designs (TORDs), which can be sequentially implemented by adding few more runs to the SORDs. In this paper, the construction of sequential TORDs with minimum level changes in the run sequences has been discussed. [ABSTRACT FROM AUTHOR]

The field of whole genomic studies and investigations is currently focused on change-point detection. Over time, various segmentation techniques have been proposed to identify these change points. To effectively locate segments within a genome, it is helpful to pinpoint the intervals or boundaries between them, which are known as change points. By treating these change points as outliers, they can be identified. The anomalies or outliers in a dataset are the observations which are significantly different from the rest of the observations. They can be attributed to some measurement errors or properties of the data themselves. Studying the fluctuations over different segments also revealed the heterogeneity between consecutive segments. In this paper, anomaly identification approach or influential point detection has been discussed and studied in cow genome data of chromosome 25. Furthermore, the observed anomalies have been confirmed to determine whether or not they are true change points. The two-step technique resulted in the identification of change sites based on observed abnormalities and is efficient in terms of calculation time and cost. This study aims to detect any anomalies in genomic data and determine the exact points at which the data segment significantly differed from the rest of the segments. We have developed relevant R codes for data processing and applied methodologies. [ABSTRACT FROM AUTHOR]

Incomplete block designs bring out useful information from agricultural experimentation with high precision when there is a crunch in resources in terms of homogeneous blocks that can accommodate all the treatments. Balanced incomplete block designs or 2-designs are the most popular class of incomplete block designs. t-designs represent a generalized class of balanced incomplete block designs in which the number of blocks in which any t treatments (t≥2) occur together is a constant. In order to obtain tbalance, we may require large number of blocks and replications. Partially balanced t-designs are introduced for experimental situations where it is not possible to get balanced t-designs. Two series of such designs are obtained using cyclic development of initial block(s). Association of the proposed designs with t-packing designs are also demonstrated. [ABSTRACT FROM AUTHOR]

In agricultural, animal, fisheries and industrial experimentation under block design setup, systematic trend may affect the response under consideration. Although remote, these effects may still have high influence on response and hence should be incorporated in the model for proper model specification. Completely trend resistant block designs, also known as trend free block designs, are an important class of designs where the analysis can be done in usual manner as in case of normal block designs since trend effects and treatment effects are orthogonal. Literature is available on different aspects of trend resistant incomplete block designs mainly focusing on balanced incomplete block designs. This article deals with the construction of completely trend resistant Partially Balanced Incomplete Block (TR-PBIB) designs. Two methods of constructing such designs have been discussed. The information matrices for the class of designs developed have been derived and SAS code for the generation of the developed designs has also been provided. [ABSTRACT FROM AUTHOR]

This paper describes the response surface model for mixed-level factors of the form 2n×3 where experimental units/plots experience the overlap effects from immediate left and right neighboring units. Conditions have been derived for the orthogonal estimation of the parameters of the model. A method of constructing mixed-level response surface designs of the form 2n×3 has been proposed. The designs developed satisfy the derived conditions of rotatability. Further, the method has been extended to the case of mixed-level rotatable designs of the form 2n×3n. An algorithm for the estimation of overlap effects has also been discussed, along with an illustration. [ABSTRACT FROM AUTHOR]

The use of an appropriate design is a very important aspect of agroforestry experimentation. Since different species of trees may interact spatially, plots in agroforestry could be connected through network of trees which would create non-directional adjacency effects on a plot. Hence, there is a need to take the "direct effect of trees" and "tree network effects" on the crop into account when designing an agroforestry experiment. Tree network effect refers to the influence a tree exerts on the surrounding plots as a result of adjacency of the plots. In this paper, a class of network designs incorporating effects of trees from adjacent plots has been obtained. The characterization properties of the designs have also been studied. The designs are found to be variance balanced for the estimation of direct as well as network effects of trees. They are also highly efficient designs, and hence, are recommended for agroforestry experimentation with multiple tree species and a single crop. [ABSTRACT FROM AUTHOR]