Level-expansion: A statistical sequential design methodology with application to nanomaterial synthesis

Xu Xu, Youngdeok Hwang, Taewan Kim, Fei Wang, Xudong Wang, Peter Chien

Research output: Contribution to journalArticlepeer-review


Nanotechnology is an era-defining breakthrough across science and engineering. For example, one-dimensional nanostructures such as nanowires, nanotubes, and nanobelts are widely regarded as critical building blocks for creating the next generation of devices in electronics, optics, energy, and biomedicine. Motivated by a practical problem of sequential synthesis of nanowires, we propose a new statistical design augmentation method, called level-expansion. For a fractional factorial design at two levels, this method creates a follow-up design by expanding some of the factors in the initial design to four elaborately chosen levels and reversing the signs of the remaining factors. The augmented design produced as such strikes a fine balance between dealiasing and entertaining nonlinear effects. Some statistical properties of the proposed method are derived. The effectiveness of the proposed method is successfully illustrated with a case study for growing a type of zinc-oxide nanowire. The use of level-expansion in the case study unveils some previously unknown nonlinear relationships between the concentration of polyethyleneimine and the length of nanowires. This finding is important for nanoscientists to invent new zinc-oxide nanowires with better macroscopic transport properties. Besides nanotechnology, the proposed method applies broadly to problems in many other scientific fields with similar traits where a follow-up design is needed for the dual purposes of investigating nonlinear effects and dealising.

Original languageEnglish
Pages (from-to)97-107
Number of pages11
JournalJournal of Quality Technology
Issue number1
StatePublished - 2 Jan 2020


  • design augmentation
  • design of experiments
  • fractional factorial design
  • nanotechnology


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