Nonparametric monitoring schemes in Phase II for ordinal profiles with application to customer satisfaction monitoring

Abstract

The quality characteristic of some production and service processes is represented by an ordinal profile. The ordinal profile describes the functional relationship between the categorical response with three or more ordered attributes and some explanatory variables. Statistical process monitoring (SPM) for ordinal profiles has been receiving increasing attention since it is of vital importance to monitor the product and service quality timely. However, exiting SPM methods are often inadequate due to the fact that they are sensitive to the parametric model/distribution assumptions which are often invalid in practice. Therefore, two robust and effective monitoring schemes based on the nonparametric regression are proposed in this paper, and they are the generalized likelihood ratio scheme and the exponential weighted moving average scheme. We analyze and compare the performance of the proposed monitoring schemes for detecting changes in the functional relationship by thorough numerical simulations and a real example. Extensive results show that the two monitoring schemes are efficient in monitoring the ordinal profiles and robust to the latent regression models. Moreover, the proposed monitoring schemes perform relatively better than an existing novel method in general.