January 2001

Volume 8 • Number 1

Contents

**Variable Selection in Product Design **

*A key element in off-line quality control is to identify
the best set of variables to use in designing a product
that will meet customers’ expectations. Given the multidimensional
nature of quality, this set of variables is not easy to
identify. Indeed, the variables of interest as determined
by the customers are often numerous and not precise. In
this article, a procedure of selecting those variables that
make a product a winner in the market for its quality, and
for further consideration in the product or process design,
is proposed. Specifically, the authors show how the information
collected using the quality function deployment technique
may be incorporated into a Bayesian variable selection model.
The choice of the Bayesian setting is guided by the requirement
of flexibility and practical importance of variables in
the final model specification, especially ensuring the inclusion
of the customers’ requirements in the product design..
*

*Key words: Bayesian inference, factor analysis, Gibbs
sampling, production and operations management, quality
control, quality function deployment *

*by*** Felicien Kanyamibwa, Prudential Insurance Company
of America, David P. Christy, Pennsylvania State University,
Duncan K. H. Fong, Pennsylvania State University**

*INTRODUCTION*

A key element in off-line quality control is to identify
the best set of variables to use in designing a product that
will meet customers’ expectations. Frequently, customers
describe a product by some underlying characteristics. Certain
characteristics, such as quality, are not directly observable,
but may be described by observable variables as well as the
relationships among those variables. Since cost considerations
may limit the number of possible product characteristics that
can be incorporated into a design, it is essential in product
design to identify a small set of variables that describe
the characteristics among a larger set of observable variables.
The problem of variable selection in product design may then
be stated as follows: Given customers’ expectations regarding
quality, find a small set of predictors that can be used to
design a product that meets those expectations.

With the multidimensional nature of quality, this subset
of variables is not easy to identify because the variables
of interest, as determined by customers, are numerous and
not precise. In order to perform a sound design, some techniques
are needed to sort out and redefine these variables. Two approaches
may be followed in addressing this problem.

- Focus on measuring the differences among products and
from an ideal product as determined by customers. This approach
implies finding a smaller set of variables to describe the
products using data-dimension reduction techniques.
- Focus on relationships among different groups of variables.
The purpose is to explain and predict the values for one
group of variables given the values of another group of
variables.

Among the many data-dimension reduction techniques that have
been used to address product quality and related problems
are multidimensional scaling (MDS), factor analysis (FA),
and correspondence analysis(CA). Moore and Winer (1987) used
MDS to relate the distance between a given brand and the ideal
brand of a segment in a given period to the market share,
the relative price, and the advertising share of the brand.
Long (1983) used FA to identify a small number of latent or
winning factors of brands. Shin, Fong, and Kim (1998) used
CA to address the size problem of the house of quality in
quality function deployment. A good literature review of these
and other techniques can be found in Elrod (1988).

These methods, however, have limitations when applied in
product design. One limitation is the relative subjectivity
associated with conclusions drawn from the models. Indeed,
subjective judgment and intuition are dominant in the decision
about the number and naming of the latent factors or groups
derived from observable variables. These latent factors or
groups are unobservable and most often not precise. Yet, a
reasonable degree of precision is necessary in product design.
Nevertheless, one of these methods may be used as a starting
point for a more elaborate analysis. Later, factor analysis
is used as part of the solution to the variable selection
problem in product design.

A difficulty in dealing with quality is related to its measurement.
One common approach is to measure quality as an index calculated
from customer surveys. This approach tends to ignore the multidimensional
nature of quality. Lilien, Kotler, and Moorthy (1992) pointed
out several issues that complicate the measurement of quality.
These include the following:

- Customers do not process large numbers of attributes in
practice, but they express their expectations in terms of
factors that may be described by a multitude of observable
variables.
- Customers do not search or evaluate all the brands of
which they are aware.
- The process of buying goes from information search, to
attribute perceptions, to consideration set formation, to
purchase, and finally to postpurchase feedback.
- Different, given, perceived attributes are not necessarily
weighted the same for different customers.

Hence, the process of modeling quality may start with a translation
of customers’ perceptions into measurable elements, and
then if it is infeasible to include all of the elements into
the product design, selecting only those that heavily influence
final product quality.

Techniques such as quality functional deployment (QFD) have
been used to address issues of translating perceptions of
quality into product quality characteristics. QFD combines
aspects of value analysis and engineering with market research
technique in a strategic quality management framework that
has been called the house of quality (Hauser and Clausing
1988; Giffi, Roth, and Seal 1990). Interested readers may
also refer to Farrel Jr. (1994) and Raynor (1994). Researchers
and practitioners together have underscored the need for analytical
improvements of the QFD technique. This work constitutes a
contribution in that direction.

The purpose of this work is to develop a procedure for selecting,
for further consideration in the design of products or processes,
those variables that make the product a winner in the market
for its quality. Given that the most important factor in product
design should be quality, the values for product characteristics
are determined by the level of quality that must be achieved.
Therefore, a one-factor analytic model is considered. In the
procedure, factor analysis is first used to uncover the principal
quality factor from a market data set. Then, the quality factor
is used as the dependent variable in a variable selection
model. To develop the procedure of exogenous variable selection,
the hierarchical model of stochastic search proposed by George
and McCulloch (1993) is adopted.

The objective is to develop a Bayesian model to help identify
the best subset of predictors. After the model is established,
the promising subsets of predictors are identified as those
associated with higher (posterior) probabilities, which will
be determined through the Gibbs sampling technique. Unlike
classical inference that aims to determine the best model
from the given data set alone, the authors’ Bayesian
model will incorporate all available prior information (say,
from a related study) into the analysis.

The choice of the setting in the Bayesian variable selection
procedure is guided by the requirement of flexibility and
practical importance of variables in the final model specification,
especially the customers’ requirements inputs in the
product design. The practical importance of variables is captured
by incorporating the QFD information into an initial model,
which will be updated as additional data are collected.

The remainder of this paper is organized as follows: In the
next section, the QFD technique is defined, and how it captures
the dimensions of quality is explored. Observable quality
correlates, through which product quality can be estimated,
are also introduced. Following that, model assumptions are
made, and its components are described. Following that, how
the prior information–especially the QFD output–is
incorporated into the model is discussed. Then, a real example
is used to illustrate the method; it is also analyzed. Finally,
some concluding remarks are presented.