Selection and Screening Procedures to Determine Optimal Product Designs. (REVISED, April 1997)

To compare several promising product designs, manufacturers must
measure their performance under multiple environmental conditions.
In many applications, a product design is considered to be
seriously flawed if its performance is poor under any level of the
environmental factor. For example, if a particular automobile
battery design does not function well under some temperature
conditions, then a manufacturer may not want to put this design
into production. Thus, in this paper we consider the overall
measure of a given product's quality to be its worst performance
over the environmental levels. We develop statistical procedures to
identify (a near) the optimal product design among a given set of
product designs, i.e., the manufacturing design associated with the
greatest overall measure of performance. We accomplish this for
intuitive procedures based on the split-plot experimental design
(and the randomized complete block design as a special case);
split-plot designs have the essential structure of a product array
and the practical convenience of local randomization. Two classes
of statistical procedures are provided. In the first, the
delta-best formulation of selection problems, we determine the
number of replications of the basic split-plot design that are
needed to guarantee, with a given confidence level, the selection
of a product design whose minimum performance is within a specified
amount, delta, of the performance of the optimal product design. In
particular, if the difference between the quality of the best and
2nd best manufacturing designs is delta or more, then the procedure
guarantees that the best design will be selected with specified
probability. For applications where a split-plot experiment
involving several product designs has been completed without the
planning required of the delta-best formulation, we provide
procedures to construct a "confidence subset" of the manufacturing
designs; the selected subset contains the optimal product design
with a prespecified confidence level. The latter is called the
subset selection formulation of selection problems. Examples are
provided to illustrate the procedures.