M.L. Aggarwal

A new method of construction of multi-level supersaturated designs

Abstract Fang et al. (J. Statist. Plann. Inference 86 (2000b) 239) have given a method of construction of multi-level supersaturated designs. Our paper presents a new method of construction of multi-level supersaturated designs, based on Galois field theory. The supersaturated designs constructed in the paper are E ( f NOD )-optimal.

A class of composite designs for response surface methodology

A class of efficient and economical response surface designs that can be constructed using known designs is introduced. The proposed class of designs is a modification of the Central Composite Designs, in which the axial points of the traditional central composite design are replaced by some edge points of the hypercube that circumscribes the sphere of zero center and radius a. An algorithm for the construction of these designs is developed and applied. The constructed designs are suitable for sequential experimentation and have higherD-values than those of known composite designs. The properties of the constructed designs are further discussed and evaluated in terms of rotatability, blocking, and D-optimality under the full second-order model.

Robust response surface design for quantitative and qualitative factors

Wu and Ding (1991) have given a systematic method for constructing the response surface designs for qualitative and quantitative factors when all the quantitative factors are controllable. In most of the experiments all the quantitative factors are not controllable some of them are uncontrollable or noise factors. In this paper we have given a method for constructing designs involving qualitative and quantitative factors using the technique given by Wu and Ding (1991) when the quantitative factors are divided into controllable and uncontrollable factors. We have also applied dual response surface optimization technique given by Lin and Tu (1995) to find the optimal setting for a set of design variables involving qualitative and quantitative factors.

Efficient three-level screening designs using weighing matrices

Screening is the first stage of many industrial experiments and is used to determine efficiently and effectively a small number of potential factors among a large number of factors which may affect a particular response. In a recent paper, Jones and Nachtsheim [A class of three-level designs for definitive screening in the presence of second-order effects. J. Qual. Technol. 2011;43:1–15] have given a class of three-level designs for screening in the presence of second-order effects using a variant of the coordinate exchange algorithm as it was given by Meyer and Nachtsheim [The coordinate-exchange algorithm for constructing exact optimal experimental designs. Technometrics 1995;37:60–69]. Xiao et al. [Constructing definitive screening designs using conference matrices. J. Qual. Technol. 2012;44:2–8] have used conference matrices to construct definitive screening designs with good properties. In this paper, we propose a method for the construction of efficient three-level screening designs based on weighing matrices and their complete foldover. This method can be considered as a generalization of the method proposed by Xiao et al. [Constructing definitive screening designs using conference matrices. J. Qual. Technol. 2012;44:2–8]. Many new orthogonal three-level screening designs are constructed and their properties are explored. These designs are highly D-efficient and provide uncorrelated estimates of main effects that are unbiased by any second-order effect. Our approach is relatively straightforward and no computer search is needed since our designs are constructed using known weighing matrices.

Optimal orthogonal designs in two blocks for Becker's mixture models in three and four components

Orthogonal block designs for Scheffes quadratic model in three and four components have been considered by John (Technical Report 8, Centre for Statistical Sciences, University of Texas, Austin, TX, pp. 1-17), Czitrom (Comm. Statist. Theory Methods 17 (1988) 105; Comm. Statist. Theory Methods 18 (1989) 4561; Comm. Statist. Simulation Comput. 21 (1992) 493), Draper et al. (Technometrics 35 (1993) 268), Chan and Sandhu (J. Appl. Statist. 26(1) (1999) 19), and Ghosh and Liu (J. Statist. Plann. Inference 78 (1999) 219). In this paper, we have constructed optimal orthogonal designs in two blocks for Beckers models in three and four components. We have also given conditions for orthogonality.

Records and Oscillating Random Walk

The distribution of the place of occurrence of the m-th record and of the maximum have been obtained in the case of an oRcillating random walk. Similar distributions have already been obtained for a simple random walk (both symmetric and unsymmetric) by F eller (1968) .

Optimum Designs for Parameter Estimation in Linear Mixture Models with Synergistic Effects

In this article, we derive optimum designs for parameter estimation in a mixture experiment when the response function is linear in the mixing components with some synergistic effects. The D- and A-optimality criteria have been used for the purpose. The Equivalence Theorem has been used to check for the optimality of the proposed designs.

Nearly Optimal Orthogonally Blocked Designs for Four Mixture Components Based on F-Squares

Prescott (1998) discussed nearly optimal orthogonally blocked designs based on latin squares for mixtures involving three and four components. Aggarwal et al. (2009a) studied orthogonal blocking of blends for Scheffés quadratic model using F-squares for the case when some components assume equal volume fractions and presented a general method for obtaining mates that are required to construct orthogonal blocks using F-squares. In this article, we obtain nearly D-, A-, and E-optimal orthogonally blocked designs in two blocks based on F-squares for four component mixtures for Scheffés quadratic, Beckers models, Darroch and Wallers quadratic, and K-mixture models.

Small robust response-surface designs for quantitative and qualitative factors

SYNOPTIC ABSTRACT Draper and John (1988) gave some specific response-surface designs for quantitative and qualitative factors. Wu and Ding (1998) gave a systematic method for constructing such designs. Aggarwal and Bansal (1998) gave robust response surface design for quantitative and qualitative factors using central composite designs. In this paper, we give a method for constructing robust response-surface designs for quantitative and qualitative factors using the small response-surface optimization approach given by Lin and Tu (1995) for finding the optimal setting for a set of design variables involving qualitative and quantitative factors.

Construction of Generalized Cyclic Combinatorially Balanced Designs for First Order Residual Treatment Effects

Designs combioatorially balanced for residual treatment effects of various orders, (especialJy first and second orders) with and without interactions were discussed in considerable details by williams (1949). Construction of combinatorially balanced designs for residual treatment effects was also considered by Patterson (1952); Hedayat and Afsarinejad (1975, 1978); Cheng and Wu (1980). An excellent account of such designs is given by Jones and Kenward (1989). In this paper, a method of construction of generalized cyclic designs combinatorially balanced for residual treatment effects of the first order without interactions, is presented. The method is based on an extension of theorems on symmetricaliy repeated difference sets developed by Bose (1939) and others. See Raghavarao (1971) for deiails, AMS (1980) Subject Classification: Primary 62k99; Secondary 05B10,05B30