The 2 k — p Fractional Factorial Designs Part II.
About: This article is published in Technometrics.The article was published on 1961-11-01. It has received 202 citations till now. The article focuses on the topics: Fractional factorial design.
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TL;DR: This work proposes a new class of designs that have three levels, provide estimates of main effects that are unbiased by any second- order effect, require only one more than twice as many runs as there are factors, and avoid confounding of any pair of second-order effects.
Abstract: Screening designs help assess the relative impact of a large number of factors. Experimenters often prefer quantitative factors to have three levels rather than two, but common screening designs use only two factors. This article proposes a new class of..
335 citations
Cites background from "The 2 k — p Fractional Factorial De..."
...An undesirable property of resolution III fractional-factorial screening designs (Box and Hunter, 1961) is that they completely confound the main effects of the factors with one or more two-factor interactions....
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320 citations
TL;DR: A resource management perspective on making a complete or reduced factorial design decision is advocated, in which the investigator seeks a strategic balance between service to scientific objectives and economy.
Abstract: An investigator who plans to conduct an experiment with multiple independent variables must decide whether to use a complete or reduced factorial design. This article advocates a resource management perspective on making this decision, in which the investigator seeks a strategic balance between service to scientific objectives and economy. Considerations in making design decisions include whether research questions are framed as main effects or simple effects; whether and which effects are aliased (confounded) in a particular design; the number of experimental conditions that must be implemented in a particular design and the number of experimental subjects the design requires to maintain the desired level of statistical power; and the costs associated with implementing experimental conditions and obtaining experimental subjects. In this article 4 design options are compared: complete factorial, individual experiments, single factor, and fractional factorial. Complete and fractional factorial designs and single-factor designs are generally more economical than conducting individual experiments on each factor. Although relatively unfamiliar to behavioral scientists, fractional factorial designs merit serious consideration because of their economy and versatility.
319 citations
Cites background from "The 2 k — p Fractional Factorial De..."
...This concept has been called the maximum resolution criterion by Box and Hunter (1961a, 1961b)....
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TL;DR: Two quadratic models were developed for yield of activated carbon and adsorption of malachite green oxalate using Design-Expert software and showed an excellent agreement with the amounts predicted by the models.
265 citations
Cites background from "The 2 k — p Fractional Factorial De..."
...For four variables, the recommended number of tests at the center is six (Box and Hunter, 1961)....
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TL;DR: In this paper, the algebraic structure of fractional factorial (FF) designs with minimum aberration is explored and an algorithm for constructing complete sets of FF designs is proposed.
Abstract: Summary Fractional factorial (FF) designs with minimum aberration are often regarded as the best designs and are commonly used in practice. There are, however, situations in which other designs can meet practical needs better. A catalogue of designs would make it easy to search for 'best' designs according to various criteria. By exploring the algebraic structure of the FF designs, we propose an algorithm for constructing complete sets of FF designs. A collection of FF designs with 16, 27, 32 and 64 runs is given.
256 citations