Synthesis maps for multivariate ordinal variables

Many quality characteristics of products or services are commonly evaluated on ordinal scales with a finite number of categories. A systematic analysis of categorical variables collected over time may be very useful for a profitable management strategy. In order to measure customer satisfaction or quality improvement in a process, two or more quality characteristics are often conjointly measured and summarized by suitable indexes. A common practice suggests evaluating a synthetic index by mapping each outcome of a multivariate ordinal variable into numbers. This procedure is not always legitimate from the measurement theory point of view. In this paper an alternative approach based on the algebraic theory of the ordered sets is proposed. This method avoids mapping multivariate components into numbers. Multivariate ordinal variable components are synthesized by ordering the multivariate sample space. The ordering criterion is defined on the basis of the specific characteristics of the process at hand. Practical effects in the use of this method are shown on a series of application examples.