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"February 1992" Bibliography: leaf 323-344. Develops a general strategy for factorial linear model analysis for experimental and observational studies, an iterative, four-stage, model comparison procedure. The approach is applicable to studies characterized as being structure-balanced, multitiered and based on Tjur structures unless the structure involves variation factors when it must be a regular Tjur structure. It covers a wide range of experiments including multiple-error, change-over, two-phase, superimposed and unbalanced experiments.

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Thesis (Ph. D.)--University of Adelaide, 1992. / "February 1992." Includes bibliographical references (leaf 323-344). Also available electronically.

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Satisfactory systems of confounding for symmetrical factorial experiments can be constructed oy the familiar methods, using the. theory of Galois fields. Although these methods can be extended to asymmetrical factorial experiments· (White and Hultquist, 1965; Raktoe, 1969) the actual construction of designs becomes much mor:e complicated for the general case and does not always lead to satisfactory plans. A different approach to this problem is to consider balanced factorial experiments (BFE), due to Shah (1958, 1960). Such BFE have a one-to-one relationship to EGD-PBIB designs given by Hinkelmann (1964). The problem of constructing BFE is then equivalent to constructing EGD-PBIB designs. A new method is proposed here to construct such designs. This method is based upon the so-called (1,1, ...,1)th-associate matrix and the operations symbolic direct product (SDP), generalized symbolic direct product (GSDP), symbolic direct multiplication (SDM), and generalized symbolic direct multiplication (GSDM). Let A₁ , A₂, ... , A_n be n factors in a factorial experiment, with A_i having t_i levels (i = 1, 2, ... , n). It is shown that an EGD-PBIB design with blocks of size t_i can be constructed, provided that t_iᵢ ≠ max ( t₁ , t₂, . . . , t_n ). This method is more general and more flexible than the method of Aggarwal (1974) in that any two treatment combinations can be γ-th associates where γ has at least two unity components, and it can be shown the number of possible candidates for such is 2^{n-i l} -1 for blocks of size t_i (i = 1, 2, .. , n -1), where t₁ < t₂ <...< t_n. This method is also more general than the Kronecker product method due to Vartak (1955}. Two types of PBIB designs· are used for reducing the numbers of associa,te classes in EGD-PBIB designs. When the t_i (i = 1, 2, ... , n) are equal, then some EGD-PBIB designs can be reduced to a hypercubic design. The EGD-PBIB designs with block size π [below jεA] t_j, where A is an arbitrary subset of the set {1, 2, ... , n} can be reduced to newly introduced F_A⁽ⁿ⁾-type PBIR designs. Since BFE results very often in designs with a large number of blocks, the notion of partial balanced factorial experiment (PBFE) has been introduced. It is investigated how such designs can be constructed and related to PBIB-designs similar to that between BFE and EGD-PBIB designs. Two new types of PBIB designs have been introduced in this context. / Ph. D.

The response surface problem is two-fold: to predict values of the response, and to optimize the response. Slope estimation criteria are well suited for the optimization problem. Response prediction capability has been assessed by plotting the average, maximum, and minimum prediction variances on the surface of spheres with radii ranging across the region of interest. Average and maximum prediction bias plots have recently been added to the spherical criteria. Combined with the prediction variance, a graphical MSE criterion results. This research extends these ideas to the slope estimation objective. A direct relationship between precise slope estimation and the ability to pinpoint the location of the optimum is developed, resulting in a general slope variance measure related to E-optimality in slope estimation. A more specific slope variance measure is defined and analyzed for use in evaluating standard response surface (RS) designs,where slopes parallel to the factor axes are estimated with equal precision. Standard second order RS designs are then studied in light of the prediction and optimization goal distinction. Designs which perform well for prediction of the response do not necessarily estimate the slope precisely. A spherical measure of bias in slope estimation is developed and used to measure slope bias due to model misspecification and due to the presence of outliers. A study of augmenting saturated orthogonal arrays of strength two to detect lack of fit is included as an application of a combined squared bias and variance measure of MSE in slope. A study of the designs recommended for precise slope estimation in their robustness to outliers and to missing observations is conducted using the slope bias and general slope variance measures, respectively. / Ph. D.

Sequential experimentation, especially for factorial treatment structures, becomes important when one or more of the following, conditions exist: observations become available quickly, observations are costly to obtain, experimental results need to be evaluated quickly, adjustments in experimental set-up may be desirable, a quick screening of the importance of various factors is important. The designs discussed in this study are suitable for these situations. Two approaches to sequential factorial experimentation are considered: one-run-at-a-time (ORAT) plans and one-block-at-a-time (OBAT) plans. For 2ⁿ experiments, saturated non-orthogonal 2ᵥⁿ fractions to be carried out as ORAT plans are reported. In such ORAT plans, only one factor level is changed between any two successive runs. Such plans are useful and economical for situations in which it is costly to change simultaneously more than one factor level at a given time. The estimable effects and the alias structure after each run have been provided. Formulas for the estimates of main-effects and two-factor interactions have been derived. Such formulas can be used for assessing the significance of their estimates. For 3^m and 2ⁿ3^m experiments, Webb's (1965) saturated non-orthogonal expansible-contractible <0, 1, 2> - 2ᵥⁿ designs have been generalized and new saturated non-orthogonal expansible-contractible 3ᵥ^m and 2ⁿ3ᵥ^m designs have been reported. Based on these 2ᵥⁿ, 3ᵥ^m and 2ⁿ3ᵥ^m designs, we have reported new OBAT 2ᵥⁿ, 3ᵥ^m and 2ⁿ3ᵥ^m plans which will eventually lead to the estimation of all main-effects and all two-factor interactions. The OBAT 2ⁿ, 3^m and 2ⁿ3^m plans have been constructed according to two strategies: Strategy I OBAT plans are carried out in blocks of very small sizes, i.e. 2 and 3, and factor effects are estimated one at a time whereas Strategy II OBAT plans involve larger block sizes where factors are assumed to fall into disjoint sets and each block investigates the effects of the factors of a particular set. Strategy I OBAT plans are appropriate when severe time trends in the response may be present. Formulas for estimates of main-effects and two-factor interactions at the various stages of strategy I OBAT 2ⁿ, 3^m and 2ⁿ3^m plans are reported. / Ph. D.

A parameter design introduced by Taguchi provides a new quality control method which can reduce cost-effectively the product variation due to various uncontrollable noise factors such as product deterioration, manufacturing imperfections, and environmental factors under which a product is actually used. This experimental design technique identifies the optimal setting of the control factors which is least sensitive to the noise factors. Taguchi’s method utilizes orthogonal arrays which allow the investigation of main effects only, under the assumption that interaction effects are negligible. In this paper new techniques are developed to investigate two-factor interactions for 2^t and 3^t factorial parameter designs. The major objective is to be able to identify influential two-factor interactions and take those into account in properly assessing the optimal setting of the control factors. For 2^t factorial parameter designs, we develop some new designs for the control factors by using a partially balanced array. These designs are characterized by a small number of runs and some balancedness property of the variance-covariance matrix of the estimates of main effects and two-factor interactions. Methods of analyzing the new designs are also developed. For 3^t factorial parameter designs, a detection procedure consisting of two stages is developed by using a sequential method in order to reduce the number of runs needed to detect influential two-factor interactions. In this paper, an extension of the parameter design to several quality characteristics is also developed by devising suitable statistics to be analyzed, depending on whether a proper loss function can be specified or not. / Ph. D.

Let V be an n-dimensional vector space over the field of q elements. By a geometric t-[q^n, k, λ] design we mean a collection D of k-dimensional subspaces of V, called blocks, such that every t-dimensional subspace T of V appears in exactly λ blocks in D. A large set, LS [N] [t, k, q^n], of geometric designs is a collection on N disjoint t-[q^n, k, λ] designs that partitions [V K], the collection of k-dimensional subspaces of V. In this work we construct non-isomorphic large sets using methods based on incidence structures known as the Kramer-Mesner matrices. These structures are induced by particular group actions on the collection of subspaces of the vector space V. Subsequently, we discuss and use computational techniques for solving certain linear problems of the form AX = B, where A is a large integral matrix and X is a {0,1} solution. These techniques involve (i) lattice basis-reduction, including variants of the LLL algorithm, and (ii) linear programming. Inspiration came from the 2013 work of Braun, Kohnert, Ostergard, and Wassermann, [17], who produced the first nontrivial large set of geometric designs with t ≥ 2. Bal Khadka and Michael Epstein provided the know-how for using the LLL and linear programming algorithms that we implemented to construct the large sets. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2016. / FAU Electronic Theses and Dissertations Collection