Synthesis maps for multivariate ordinal variables in manufacturing

Abstract

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.

Keywords:

• Multivariate ordinal variables
• Statistical process control
• Multidimensional ordinal structures
• Synthesis maps
• Ranking and ordering
• Lattice theory

Acknowledgements

The authors wish to acknowledge the support of the Ministero dell’Istruzione, dell’Università e della Ricerca Scientifica (MIUR – ITALY) under grant no. 2001138489, year 2001. ‘Metodi e modelli statistici per la valutazione della qualità e della Customer Satisfaction: aspetti oggettivi e soggettivi nell’ottimizzazione della qualità di beni e servisi’. Co-ordinator Professor A. Zanella.