Nonparametric Permutation-Based Control Charts for Ordinal Data

Abstract

In the literature of statistical process control (SPC), design and implementation of traditional Shewart-based control charts requires the assumption that the process response distribution follows a parametric form (e.g., normal). However, since in practice, ordinal observations may not follow the pre-specified parametric distribution these charts may not be reliable. In this connection, this work aims at providing a contribution to the nonparametric SPC literature, proposing univariate and multivariate nonparametric permutation-based control charts for ordinal response variables which are not only interesting as methodological solution but they have a very practical value particularly within the context of monitoring some measure of user’s satisfaction, loyalty, etc. related to use of a given service. As confirmed by the simulation study and by the application to a real case study in the field of monitoring of customer satisfaction in services, we can state that the proposed NPC chart for ordered categorical response variables is certainly a good alternative with respect to the literature counterparts.