#
**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.