Sequences of Fractional Factorial Plans

Sequences of Fractional Factorial Plans
Author: Sidney Addelman
Publisher:
Total Pages: 113
Release: 1969
Genre: Factor analysis
ISBN:

The report begins with the rationale underlying the performance of an experiment as a sequence of blocks and analyzing the data after each block has been observed. A description is given of several procedures for augmenting one-factor-at-a-time plans, some of which permit the estimation of interaction effects. The general procedure for obtaining orthogonal resolution IV plans as a sequence of two orthogonal main-effect plans is outlined. Consideration is given to adding small numbers of treatment combinations to resolution IV plans in order to obtain some information on a relatively few two-factor interaction effects. The remainder of the report deals with sequences of three or more fractional factorial plans involving from three to seventeen two-level factors. A summary of the properties of each sequence is presented. This summary contains the following information at each stage of every sequence: (1) The number of estimable main effects, (2) the number of estimable two-factor interaction effects, (3) the variance of the estimate of the mean, (4) the average variance of the estimable main effects, (5) the average variance of the estimable two-factor interaction effects, and (6) the average variance of the estimable main and two-factor interaction effects. (Author).

The Selection of Sequences of Two-level Fractional Factorial Plans

The Selection of Sequences of Two-level Fractional Factorial Plans
Author: Sidney Addelman
Publisher:
Total Pages: 28
Release: 1967
Genre: Mathematical statistics
ISBN:

The categorization of sequences of two-level fractional factorial plans involving from three to nine factors is presented. The categorization is based on the lengths of the interactions in the defining contrast for each regular fractional replicate in a sequence of plans. A typical sequence of plans is presented for each category with up to six factors along with a listing of the estimable parameters and their average variances at each stage of the sequence.

Orthogonal Fractional Factorial Designs

Orthogonal Fractional Factorial Designs
Author: Aloke Dey
Publisher:
Total Pages: 164
Release: 1985-09-30
Genre: Mathematics
ISBN:

A systematic and up-to-date account of fractional factorial designs giving uncorrelated estimates of relevant parameters. After basic concepts of design and analysis of factorial experiments are introduced, consideration is given to a detailed account of all available methods of obtaining orthogonal fractional factorial designs. Both symmetrical and asymmetrical pictorials are covered. Features an extensive table giving an index of fractional factorial designs. All recent work, including that unpublished, is included, and references provided.

Fractional Factorial Plans

Fractional Factorial Plans
Author: Aloke Dey
Publisher: John Wiley & Sons
Total Pages: 236
Release: 2009-09-25
Genre: Mathematics
ISBN: 0470317825

A one-stop reference to fractional factorials and relatedorthogonal arrays. Presenting one of the most dynamic areas of statistical research,this book offers a systematic, rigorous, and up-to-date treatmentof fractional factorial designs and related combinatorialmathematics. Leading statisticians Aloke Dey and Rahul Mukerjeeconsolidate vast amounts of material from the professionalliterature--expertly weaving fractional replication, orthogonalarrays, and optimality aspects. They develop the basic theory offractional factorials using the calculus of factorial arrangements,thereby providing a unified approach to the study of fractionalfactorial plans. An indispensable guide for statisticians inresearch and industry as well as for graduate students, FractionalFactorial Plans features: * Construction procedures of symmetric and asymmetric orthogonalarrays. * Many up-to-date research results on nonexistence. * A chapter on optimal fractional factorials not based onorthogonal arrays. * Trend-free plans, minimum aberration plans, and search andsupersaturated designs. * Numerous examples and extensive references.

Research in Sequential Factorial Designs

Research in Sequential Factorial Designs
Author: Sidney Addelman
Publisher:
Total Pages: 0
Release: 1967
Genre: Factorial experiment designs
ISBN:

This report is concerned with an investigation of sequences of fractional replicate plans for from three to seventeen two-level factors. Sequences of distinct and non distinct factorial replicate plans from single and multiple families of defining contrasts are compared. The sequences are then categorized according to the lengths of the interactions in the defining contrasts at various stages of the sequence. A set of generators is presented for the defining contrasts of the smallest fractional replicate plan in each sequence. (Author).