R. E. Fry

Bio: R. E. Fry is an academic researcher. The author has contributed to research in topics: Plackett–Burman design & Fractional factorial design. The author has an hindex of 1, co-authored 1 publications receiving 11 citations.

Finding New Fractions of Factorial Experimental Designs

Abstract: A method of obtaining symmetrical balanced fractions of 3 n and 2 m 3 n factorial designs is proposed, based on an analysis of such designs into a complex of concentric hyperspheres in an n-dimensional factor space. Two examples are constructed, a half-replicate of a 34 design and a half-replicate of a 23 32 design. Analysis shows both designs to have useful properties and to be relatively easy to analyse. Comparison is made with a half-replicate of a 23 32 design recently published by W. S. Connor.

D-optimal fractions of three-level factorial designs

Abstract: D-optimal fractions of three-level factorial designs for p factors are constructed for factorial effects models (2 ≤ p ≤ 4) and quadratic response surface models (2 ≤ p ≤ 5). These designs are generated using an exchange algorithm for maximizing |X′X| and an algorithm which produces D-optimal balanced array designs. The design properties for the DETMAX designs and the balanced array designs are tabulated. An example is given to illustrate the use of such designs.

Techniques for Constructing Fractional Replicate Plans

Abstract: This paper is a review of techniques for obtaining the treatment combinations that comprise a fraction of a factorial arrangement. Several procedures for constructing fractional replicate plans, which in their original form appear to be different, are presented in a manner which illustrates their similarities. The techniques discussed include orthogonal and non-orthogonal plans for both symmetrical and asymmetrical factorial experiments. The plans developed range from those that permit estimation of main effects only, to those that permit estimation of main effects and all two-factor interaction effects.

Response surface designs for factors at two and three levels.

Abstract: : The choice of an experimental design suitable for fitting a graduating polynomial can be made according to a number of criteria, depending on the problem involved. Difficulties arise when, although the factors are continuous in nature, the number of levels is specified by some external considerations. For example, if some factors can be examined at only two levels, the graduating function cannot include quadratic terms in those variables, but all second order terms for variables to be examined at three or more levels can be permitted. For such cases, a restricted model and special experimental designs are needed. This paper considers the problem when there are some factors at two levels and some factors at three levels. (Author)

Response Surface Designs for Factors at Two and Three Levels and at Two and Four Levels

Abstract: The choice of an experimental design suitable for fitting a graduating polynomial can be made according to a number of criteria, depending on the problem involved. Difficulties arise when, although the factors are continuous in nature, the number of levels is specified by some external considerations. For example, if some factors can be examined at only two levels, the graduating function cannot include quadratic terms in those variables, but all second order terms for variables to be examined at three or more levels can be permitted. For such cases, a restricted model and special experimental designs are needed. This paper considers the problem when there are some factors at two levels and some factors at three levels, and when there are some factors at two levels and some factors at four levels.

Orthogonal Main-Effect Plans Permitting Estimation of All Two-Factor Interactions for the 2n3m Factorial Series of Designs

Abstract: If we assume no higher order interactions for the 2n3m factorial series of designs, then relaxing the restrictions concerning equal frequency for the factors and complete orthogonality for each estimate permits considerable savings in the number of runs required to estimate all the main effects and two-factor interactions. Three construction techniques are discussed which yield designs providing orthogonal estimates of all the main effects and allowing estimation of all the two-factor interactions. These techniques are: (i) collapsing of factors in symmetrical fractionated 3m–p designs, (ii) conjoining fractionated designs, and (iii) combinations of (i) and (ii). Collapsing factors in a design either maintains or increases the resolution of the original design, but does not decrease it. Plans are presented for certain values of (n, m) as examples of the construction techniques. Systematic methods of analysis are also discussed.