Cumulative correspondence analysis of ordered categorical data from industrial experiments

When conducting matrix experiments in several industrial situations, engineers deal with an ordered categorical response. Several techniques have been proposed for the analysis of ordered categorical data with a focus on quality improvement in industrial settings. In such context, Correspondence analysis, a popular descriptive/exploratory technique designed to analyze simple two-way and multi-way tables, could be useful to analyze the strength of association between variables. Unfortunately, Correspondence analysis does not keep into account the information arising from the ordinal nature of variables. In order to overcome that problem, a variant of Correspondence Analysis, based on the decomposition of Taguchis statistic, has been proposed. In this paper we highlight the properties of the decomposition of Taguchis index, showing how such technique could be applied in the context of industrial experiment. The procedure is illustrated with a case study and our findings support that the proposed analysis is capable of solving industrial problems with an ordered categorical response in a multifactor state system.