Development and Use of Foldover Methods

Session Chair: Robert Mee, University of Tennesee - Knoxville


Use of the Fold-Over Technique to Resolve an Ambiguity on the MESSENGER Resistor Problem

Manny Uy
Johns Hopkins University

Abstract: An eight-run 2(4-1) fractional factorial experiment was performed in order to investigate which factors were causing the increase in resistance of precision resistors on the power supply of MESSENGER spacecraft, just a few weeks before launch at Cape Canaveral. After a quick analysis of the initial results, the analysis appeared to support a two-factor interaction between the two resistor batches and relative humidity. In order to resolve this, a fold-over experiment requiring another eight runs was quickly added. The result did resolved the ambiguity, i.e. the two batches of resistors behaved differently with moisture (or relative humidity), with the "old" batch increasing in resistance with moisture exposure while the "new" batch appear to be stable with moisture. Because it would have been very expensive to replace the "old" resistor batch from the various circuit boards inside the spacecraft, it was decided to leave them on board as long as the spacecraft was blanketed with dry nitrogen gas before launch. After launch, moisture is not a problem in space. The MESSENGER spacecraft has now achieved orbit around the planet Mercury.


Another Look at Semifoldover for Two-Level Orthogonal Designs

David J. Edwards
Virginia Commonwealth University

Abstract: Foldover is a classic technique for selecting follow-up experimental runs. As foldover designs require twice as many runs as the initial design, they can be inefficient if the number of effects to be dealiased is smaller than the size of the original experiment. Semifoldover refers to adding half of a foldover fraction and is a technique that has been investigated for regular two-level designs as an alternative to foldover. In this talk, the concept of minimal dependent sets (MDSs) and the criterion MDS-resolution and MDS-aberration (Lin, Miller, and Sitter 2008) will be utilized to compare semifoldovers of two-level orthogonal designs (both regular and nonregular) with regards to their ability to discriminate among competing models. MDS-optimal semifoldovers will be presented for selected two-level designs of various run sizes. General properties of semifoldover designs will also be presented. Finally, MDS-optimal foldover plans will be discussed and compared with recommendations based on the popular minimum aberration criterion.


Optimal Blocked Semifoldover Designs

William Li and Po Yang
University of Minnesota and DePaul University

Abstract: Foldover designs have been in the literatures for many years, the new added runs are used to de-alias confounded effects. Semifoldover designs are partial foldover designs obtained by adding half of the new runs. It is known that, in many cases, a semifoldover design can de-alias as many main factors or two-factor interactions as the corresponding foldover design. Since, usually, the new runs are performed in a different time, we are interested in considering these designs when a block factor is included. In this article, we consider blocked semifoldover designs. We study when the block factor does not affect the results which are obtained in the case a block factor is not involved and when the block factor affects the results. The optimal blocked semifoldover designs are also tabulated. Moreover, given an original design, there are many semifoldover design, we classify the equivalent semifoldover designs and, also, provide a way to obtain the equivalent semifoldover designs.


Sequential Synthesis of Nanomaterials via Level Expansion

Yougdeok Hwang
University of Wiconsin - Madison

Nanotechnology is changing the way people live and work. In particular, one-dimensional nanostructures, such as nanowires, nanotubes and nanobelts, are the building blocks of the next generation devices and systems in electronics, optics, energy and biomedicine. Synthesis of nanomaterials is playing an increasingly important role in nanotechnology. Motivated by a real problem for sequential synthesis of nanomaterials, we propose a new design method, called level-expansion. Level-expansion is a modification of the popular fold-over method. Suppose an experiment using a two-level fractional factorial design with resolution III is conducted. The fold-over method gives a follow-up design at two levels by reversing the signs of initial design, whereas the level-expansion method provides a follow-up design by expanding some factors to four levels. The main advantage of level-expansion over fold-over is that the former can entertain some nonlinear effects. Statistical properties of the proposed method are examined. The effectiveness of this method is illustrated by simulation examples and a case study for sequential synthesis of Zinc-oxide nanowires. This is joint work with Tae Wan Kim, Fei Wang and Xudong Wang of Department of Materials Science and Engineering, UW-Madison and Xu Xu, Peter Z. G. Qian of Department of Statistics, UW Madison.