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January 2001
Volume 8 • Number 1


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


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.

  1. 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.
  2. 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.