The Quarterfold, a Sequential Augmentation Procedure for Resolution IV Fractions

Self Cite

The Taguchi approach for robust design has been a common practice in industrial experimentation for many years. However, these designs possess serious disadvantages such as the inability to estimate control × control interactions. In this article, we propose the application of the R3 algorithm as an augmentation tool for Taguchi experiments. The augmented Taguchi designs were compared with its competitors, mixed resolution designs, and D‐optimal augmentation, using performance indicators. The results showed that Taguchi designs augmented with the R3 algorithm are capable of estimating control × control interactions, possess similar values for performance indicators when compared with other techniques, and in most cases require less runs.

Section: Performance Indicatorsmentioning

confidence: 99%

“…The Type II error is defined as the number of significant terms not selected or missing in the model. The Type II error was obtained by comparing the true model with the linear regression equation and noting the absence of significant terms, Misra et al.…”

Section: Performance Indicatorsmentioning

confidence: 99%

Sequential experimentation approach for robust design

Ríos¹,

Guerrero²

2018

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“…The semifold, named by Barnett et al, uses half of the runs in a foldover experiment. Misra et al developed a procedure for sequential augmentation of resolution IV designs called the quarterfold. Rios et al developed the R3 algorithm for sequentially augmenting resolution III designs.…”

Section: Introductionmentioning

confidence: 99%

No‐confounding designs with 20 runs—Alternatives to resolution IV screening designs

Stone

Montgomery

Silvestrini

et al. 2017

When experimental resources are significantly constrained, resolution V fractional factorial designs are often prohibitively large for experiments with 6 or more factors. Resolution IV designs may also be cost prohibitive, as additional experimentation may be required to de‐alias active 2‐factor interactions (2FI). This paper introduces 20‐run no‐confounding screening designs for 6 to 12 factors as alternatives to resolution IV designs. No‐confounding designs have orthogonal main effects, and since no 2FI is completely confounded with another main effects or 2FI, the experimental results can be analyzed without follow‐on experimentation. The paper concludes with the results of a Monte Carlo simulation used to assess the model‐fitting accuracy of the recommended designs.

“…Higher numbered resolutions indicate more preferable designs. A full foldover of the initial fractional design consists of adding a second fraction of the same size as the initial, obtained by inverting the signs of one or more columns (two‐level designs) of the initial, or by rotating one or more columns (for three‐level and mixed‐level designs) . To clarify, the initial experiment is commonly referred to as the initial fraction or initial design, and the second fraction is known as the foldover fraction or additional fraction, and the two fractions assembled together become the combined design.…”

Section: Introductionmentioning

confidence: 99%

“…Misra et al proposed a new technique for augmenting Resolution IV fractions with a method known as a quarterfold that consists of adding small sets of runs in a sequential fashion until all the 2FIs of interest are decoupled. When the number of significant alias chains to be decoupled is small, the algorithm is very efficient, and in some cases, it requires less runs than a semifold.…”

Section: Introductionmentioning

confidence: 99%

Foldover Plans for Resolution IV Designs with 11 to 16 Factors

Galindo¹,

Ríos²,

Simpson³

et al. 2015

Self Cite

When there is a concern about the best way to apply the foldover technique to a Resolution IV fraction, it is often helpful to consult the literature available. Unfortunately, foldover plans for Resolution IV designs with 11 ≤ k factors are not provided. This article shows a methodology for the selection and classification of foldover plans for two‐level fractional factorial designs with 11 to 16 factors based on an exhaustive search and computer programming. The recommended foldovers are presented. This research extends the current foldover plans available for Resolution IV designs. Copyright © 2015 John Wiley & Sons, Ltd.