Munir Akhtar

Response surface designs robust to missing observations

The effects of one or more missing values in a response surface design are examined and a number of robustness criteria considered. Central composite designs with a second order model are used to illustrate the selection of designs which are robust to one or two missing observations. These designs are compared with other designs such as rotatable designs and the outlier-robust designs of Box and Draper.

Construction of Neighbor Balanced Block Designs

Neighbor designs with complete blocks for all odd v (number of treatments) were generated by Rees (1967). Since then it is a well investigated field. Here, in this study some new algorithms have been developed to generate (a) complete block neighbor designs for v = 4s; s is a natural number, (b) neighbor balanced designs for k = v−1 when v is odd, (c) neighbor balanced designs for k = v−1 when v = 4s and (d) all order neighbor balanced complete block designs for v odd prime, in minimum number of blocks when right and left neighbor effects are equal. In all cases blocks are circular and well separated. A catalogue of complete block neighbor designs for v = 4s generated through algorithm given in part (a) is also presented.

Economical generalized neighbor designs for use in Serology

This paper considers the construction of generalized neighbor designs in circular blocks for several cases, which are useful in Serology. The initial blocks for the proposed designs are developed by using the method of cyclic shifts. Generalized neighbor designs are also constructed in linear blocks for v even. Catalogs of circular binary blocks generalized neighbor designs are compiled for all cases.

Circular Binary Block Second- and Higher-Order Neighbor Designs

Some new neighbor designs are presented here. Second-order neighbor designs for different configurations are generated in circular binary blocks. Third-order and fourth-order neighbor designs for some cases are also constructed. In all cases, circular blocks are well separated and these designs are obtained through initial block/s. At the end of the study, some models for analysis of these designs are also presented.

Augmented box-behnken designs for fitting third-order response surfaces

Box-Behnken designs are popular with experimenters who wish to estimate a second-order model, due to their having three levels, their simplicity and their high efficiency for the second-order model. However, there are situations in which the model is inadequate due to lack of fit caused by higher-order terms. These designs have little ability to estimate third-order terms. Using combinations of factorial points, axial points, and complementary design points, we augment these designs and develop catalogues of third-order designs for 3–12 factors. These augmented designs can be used to estimate the parameters of a third-order response surface model. Since the aim is to make the most of a situation in which the experiment was designed for an inadequate model, the designs are clearly suboptimal and not rotatable for the third-order model, but can still provide useful information.

Multilevel augmented pairs second-order response surface designs and their robustness to missing data

Missing observations can occur even in a well-planned experiment. The effect of missing observations can be much more serious when the design is saturated or near saturated. The levels of factor settings that make a design more robust to missing observations are of great importance in the sense that the loss for missing observations becomes minimum. In this study, new augmented pairs minimax loss designs are constructed, which are more robust to one missing design point than the augmented pairs designs presented by Morris (2000). New designs are compared with augmented pairs designs, central composite designs, and small composite designs under generalized scaled standard deviations. The model used is also studied for the regression coefficient estimates.

Construction of Neighbor-Balanced Designs in Linear Blocks

Neighbor-balanced designs are useful to remove the neighbor effects in experiments where the performance of a treatment is affected by the treatments applied to its adjacent neighbors. In this article, neighbor-balanced designs are constructed in linear blocks of (i) equal sizes and (ii) two different sizes k 1 and k 2.

Minimal Neighbor Designs in Linear Blocks

Neighbor designs are useful to neutralize the neighbor effects. In literature, most of the constructed neighbor designs are in circular blocks but linear blocks have more practical application in field experiments. In this article, some infinite series of minimal neighbor designs are constructed in proper linear blocks. There are many situations where minimal neighbor designs cannot be constructed in proper linear blocks. To overcome this problem neighbor designs in improper linear blocks and GN2-designs in proper linear blocks are constructed.

Universally Optimal Designs Balanced for Neighbor Effects

The performance of a treatment is affected by the treatments applied to its adjacent plots, especially in the experiments of agriculture, horticulture, forestry, serology and industry. Neighbor designs ensure that treatment comparisons are least affected by neighbor effects, therefore, this is a rich field of investigation. In this paper, criterion for construction of universally optimal neighbor balanced designs is discussed.

Efficient Response Surface Designs for the Second-Order Multivariate Polynomial Model Robust to Missing Observation

Standard central composite design (CCD) originally requires that its factorial portion contains a full factorial design or fractional factorial design of resolution V or higher so that all effects of vital interest could be estimated. A CCD can be an ideal choice for lower number of factors (k). For k > 5, the standard CCD becomes very large and when, with the purpose of reduction of design size, the initial fractional factorial of resolution III or IV is used, the lower order effects are confounded. Block and Mee (2001) proposed some economical designs for k > 5. The designs were named as repaired resolution central composite (RRCC) designs; these actually repaired the portion containing factorial fractions of resolution III or IV. After repairing, the words of length four or lower were de-aliased and the effects of vital importance became estimable. In this study, some new versions of RRCC designs are constructed. All classes of designs are studied for their robustness to missing data. Loss of missing different kinds of design points has been computed.