Design of Experiments    


Fiber Manufacturing

The first step in the modified chemical vapor deposition process for producing optical fiber is to deposit layers of glass on the interior walls of a tube. Changes in the speed of a moving torch affect uniformity in the thickness of the layers. Scott Vander Wiel , Daryl Pregibon and others have developed models for predicting how the glass deposition will vary along the length of the tube. They use reciprocal torch speed as the input to a transfer function modeled as the exponential of a cubic spline. To improve deposition uniformity, they have used the fitted model to design a new torch speed profile that has nearly on-target predictions. The model is necessarily a simplification of reality and initially it did not extrapolate well. Iterating through experimentation and refitting, however, produced a torch speed trajectory that produces substantially more uniform glass deposition. The methodology and software will enable engineers to design torch speed profiles for new fiber products and to update them for existing products.

Optimal Blocking Schemes for Fractional Factorial Designs

Systematic sources of variations in factorial experiments can be effectively reduced without biasing the estimates of the treatment effects by grouping the runs into blocks. For fractional factorial designs, because of the intrinsic difference between treatment factors and block variables, the minimum aberration approach has to be modified. Don X. Sun, C. F. Jeff Wu (U Michigan) and Youyi Chen (Chase Manhattan Bank) proposed a concept of admissible blocking schemes for selecting block designs based on multiple criteria. The resulting $2^n$ and $2^{n-p}$ designs are shown to have better overall properties for practical experiments than those in the literature, e.g., the National Bureau of Standards Tables (1957) and Box, Hunter and Hunter (1978).

The postscript file of the paper summarizing this work is also available.

Interaction Graphs for 3-Level Fractional Factorial Designs

Graph-aided methods for accommodating the estimation of interactions in factorial experiments have become popular among industrial users. Notable among them is the method of linear graphs due to G. Taguchi. Don X. Sun and C. F. Jeff Wu (U Michigan) develop some new graphs for 3-level fractional factorial designs. The proposed graphs have two new features: (i) Each edge of the graph can have one or two lines representing the two components of interaction in a 3-level design, (ii) There are two types of vertices and lines. A collection of graphs is given for 27- and 81-run designs.