Synthesis maps for multivariate ordinal variables in manufacturing

• Published in: International journal of production research Vol. 44; no. 20; pp. 4241 - 4255
• Main Authors: Brondino, G., Franceschini, F., Galetto, M., Vicario, G.
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis Group 15.10.2006; Washington, DC Taylor & Francis; Taylor & Francis LLC
• Subjects: Applied sciences; Exact sciences and technology; Inventory control, production control. Distribution; Lattice theory; Mapping; Multidimensional ordinal structures; Multivariate analysis; Multivariate ordinal variables; Operational research and scientific management; Operational research. Management science; Quality control; Ranking and ordering; Statistical process control; Studies; Synthesis maps; Statistical process control; Lattice theory; Hierarchical classification; Ordered set; Process improvement; Clientele; Satisfaction; Synthesis maps; Multidimensional ordinal structures; Lattice; Multivariate ordinal variables; Ranking and ordering; Algebraic method; Ordering; Set theory
• ISSN: 0020-7543; 1366-588X
• DOI: 10.1080/00207540500507443

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.